A mammomcmous NETWORK son DATA pmces‘sn-Nq , IN SCHOOLS: A MATHEMATICAL MODEL Thesis for the Degree of Ed; D. 7 MICHIGAN sure UNIVERSiTY Rex Leroy Wood 7 19:56 THESiS This is to certify that the thesis entitled A Telecommunication Network for Data Processing in Schools: A Mathematical Model presented by Rex Leroy Wood has been accepted towards fulfillment of the requirements for DOC tor ' Sdegrce in Education 444*— / '7 L” A, Date _Ma‘ 0-169 LIBRARY Michigan State University ABSTRACT A.TELECOMMUNICATIONS NETWORK FOR DNTA PROCESSING IN SCHOOLS: ‘A MATHEMATICAI.MODEL by Rex Leroy'wood Statement of the Prdblem This study is concerned with the definition of a.prOblem, quanti- fying the various properties that describe the components of the prdblem, suggesting a solution to the problems and testing that solution. The prdblem simply defined is to configurate a computer system in which local school district offices, comprising the constituent school districts of the intermediate school district, Oakland Schools, Michigan, can send data over telephone wires to a single powerful computer, have that data processed and returned over the telephone wire to an output printer de- vice. My: Quantifying the properties of the components involves recording- in appropriate form, data about individual districts such as the number of students, the number of employees, the quantity of purchasing activ- ity, and the calendar of various events taking into consideration the time of day, week, month and year. The solution suggested is in the form of electronic devices interconnected to constitute a telecommuni- cations network. This network contains the elements of a computer, re- mote terminal devices located in local school district offices and the interconnecting communication lines. These quantified properties con- stitute a.mathematical model. The test of the solution of the prdblem Rex Leroy WOOd is the simulation of the mathematica1.model. The study is further concerned with the interpretation of the results of the simulation. Conclusions and Recommendations The successful simulation of the mathematical model of data pro- cessing applications in schools using telecommunications facilities demonstrates that simulation is a technique that school administrators can use in their management roles. The computer output from the simu- lation run provides specific assistance to the staff of Oakland Schools and local district personnel in the definition and resolution of re- lated prdblems. The model provides a base for configurating a system sensitive to changing demands of local school districts. Optimization of the system is possible through remodeling and repeated simulation runs. The flow diagrams and computer program.in the appendixes provide adequate documentation for replication of the project. Further attention.by both school and technical personnel is needed to exploit the mathematical analysis tools to the benefit of educational administration. A TEIECOMMUNICATIONS NETWORK FOR DATA PROCESSING IN SCHOOLS: A MATHEMATICAL MODEL by Rex Leroy Wood A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF EDUCATION COHEGE OF ENCATION .1966 @ Copyrighted by REX IROY WOOD £361 . ill‘iqilli flit... I WW8 The writer wishes to express his appreciation to the many people who have made this dissertation possible: To Dr. Stanley 3. Hacker, chairman of his doctoral connittee, who gave of his time and wise counsel in guiding the writer through the re- search project. The guidance was professional, appropriate and a source of personal satisfaction. To Dr. Fred Vescolani, Ted w. Ward and Kenneth J. Arnold, members of his doctoral cannittee, for helpful suggestions and encouragement during the progress of the study. To Dr. William J. Emerson, Superintendent of Oakland Schools, and Dr. Kenneth w. Brown, Deputy Superintendent of Oakland Schools, for per- sonal encouragement and administrative support in the several phases of the project. To Charles Hoover, systems engineer for International Business Machines Corporation, for several man weeks of direct technical and in- valuable assistance in the building of the mathenatical model. To the many superintendents, school business officials, principals and other school personnel in the constituent school districts of Oakland Schools for cooperation in the data collection phase of the project. To the staff members of Oakland Schools for technical and profess- ional counsel. And finally, to my wife, Donna Jean, whose patience and encourage- ment has contributed imensely to the completion of the study. 111 ACKNOWLEDGMENTS . . . . . LIST OF TABLES. . . . . . LIST OF ILLUSTRATIONS . . Chapter I. II. III. V. INTRODUCTION. . TABEB OF CONTENTS Statement of the Prdblem. Need for the Study. . . . . . The Significance of the Study Delimitation of the Study Summary . . . . . . . . . REVIEN OF THE LITERATURE. O 0 BUILDING THE MODEL. . . o . . Introduction. . . . . . . Block Types and Purposes. Block Instruction Format. Summary. . . . . . . . . O O O 0 DESCRIPTION OF THE MATHEMATICAI.MODEL Introduction. . . . . . . General Properties. . . . Specific Description. . . PROGRAM BRANCHES OF'THE MODEL Introduction. . . . . Network Communication File Inquiry. . . Purchasing. . . . Accounts Payable. Payroll. . iv 0 O O O 0 O O O O O O O 0 0 O O O O O 0 O O Page iii vi vii on WWNMH l-’ 1h 17 21 23 23 2h 33 33 36 '7 t 39 he #9 Chapter Page Student Master File Maintenance. GradeReporting................. 5h StudentScheduling............... 56 smaryOOOOOMOOOOOOO0.00.0000 58 8‘ VI. INTERPRETATION OF THE SIMULATION RUN . . The Simulated Calendar . Facility Utilization. .. . . . . . . . . . . . . 65 Queuing Results. . . . . . . . . . . . . . . . . 71 Program Applications . . . . . . . . . . . . . . 7% Summary. . . . . . . . . . . . . . . . . . . . . 79 8’ VII. _CONCLUSIONS. . . . . . . . . . . . . . . . . . . Introduction . . Conclusions. . . . . . . . . . . . . . . . . . . 81 Problem.Areas. . . . . . . . . . . . . . . . . . 83 Recommendations. . . . . . . . . . . . . . . . . 8h Summary. . . . . . . . . . . . . . . . . . . . . 85 APPENDDCES AFIOWCHARTS 86 B.COMPUTERPROGRAM.................. 11% c. FACIIITYUTIIIZATIONGRAPHS............. 158 BIBHOGMY . O O O O O O O O O O O O O O O O O O O O O O O O O l- 191 v. Table 1. LIST OF TABLES SystemVariables..................... VolumesbyDistrict................... TerminalFacilities.................... Distribution of Number of Purchase Orders by District Size. 0 O O O O O O O O O O O O O O O O O O O O O O O O 0 Distribution of Probability of Vendor and Catalog Item Being Stored in Central File and Associated Dunbar of Messages Required for Processing. . . . . . . . . . . . . Frequency Distribution of Line Items Per Purchase order. 0 O O O O O O O I 0 O Q 0 O O O O O O O O O O O O 0 Distribution of Number of Accounts Payable Vouchers byDistrictSize.................. .. Distribution of Terminal Waits for Approximately 100,000 Transactions. 0 O O O I O O O O O O O O O 0‘ O O O O O O 0 vi sang 1:1 73 \l LIST OF ILLUSTRATIONS Figure l. Gal-3nd SChOOIS map. 0 I O O O O O O O O O O O O O O O 2. Illustration of Accounts Payable Interaction with Working Day One Falling on Monday. . . . . . . . . . . 3. Illustration of Accounts Payable and Payroll Interaction with Working Day one Falling on Wednesday. 1:. Calendar as Created by the Simulator . . . . . . . . . 5. Facility Utilization - Composite of District Terminals. O O O O 0 O O O O 0 O O O O O O O O O O O O 6. Facility Utilization - Central Fast Printer. . . . . . 7. Facility Utilization - Central Computer. . . . . . . . 8. Distribution of Statistics of Payroll Batch Processing - Fourteen Batches Per Week . . . . . . . . 9. Distribution of Statistics of Accounts Payable Batch Processing - Thirty Batches Per Month. . . . . . . . . 10. Distribution of Statistics of Daily Purchase Order BatCh meessim. O O O O 0 O O O O O O O O O O O O O 0 vii Page hi: 1&5 61 67 70, 75 76 CHAPTER I INTRODUCTION Statement of the Prdblem This study is concerned with the definition of a.problem, quanti- fying the various properties that describe the components of the prOblem, suggesting a solution to the problem, and testing that solution. The prdblem simply defined is to configurate a computer system in which local school district offices, comprising the constituent school dis- tricts of Oakland Schoolsl, can send data over telephone wires to a single powerful computer, have that data processed and returned over the telephone wire to an output printer device. Quantifying the prop- erties of the components involves recording in appropriate form, data about individual districts such as the number of students, the number of employees, the quantity of purchasing activity, and the calendar of various events taking into consideration the time of day, week, month and year. The solution suggested is in the form of electronic devices interconnected to constitute a telecommunications network. This network contains the elements of a computer, remote terminal devices located in local school district offices and the interconnecting communication lines. The test of the solution of the problem is the simulation of the mathe- matical model. The study is further concerned with the interpretation of the results of the simulation. iAn intermediate school district in metropolitan Michigan. Need for the Study The Oakland Schools intermediate school district has provided a regional computer service for its constituent districts since 1961. The demands on the regional center for computer service has grown con- siderably in the ensuing five years. Longer range planning than present staffing permits has'become increasingly evident. These demands are in- creasing as enrollments grow, as new programs are adopted and as agenc- ies providing revenue demand more accountibility of funds. The present facilities are being challenged to meet these growing demands. Two types of problems are of concern. One, punched card data is brought in for immediate processing; an appointment is necessary to avoid delays and wasted waiting time of local district personnel. It is becomming increasingly difficult to schedule these appointments. If sent in by a carrier, at least two days turn around time delays the time when the output is available to the local district. The other type of problem has to do with peak loads. Peak loads are primarily caused by high volume of input and output since the present system has only one input station and one printer output station. The basis need then, is to provide for transportation of data on a more economical and expedit- ious basis and to provide the system with multiple input and output stations. The queuing or waiting in line would be reduced for personnel. JObs might be in queues but personnel would not be waiting for work to be completed away from their work station. The Significance of the Study Data processing techniques for the solution of prdblems of edu- cation are being explored at local, regional, state and national levels. Many projects stimulated by the availability of federal grants have been and are being proposed for funding. These projects vary from local dis- trict projects to projects encompassing several contiguous states. The local district project, except in the largest of cities must, for lack of student or financial base, be limited. At the other extreme, the multi-state projects, although necessary and important, are too far re- moved from the day to day concerns of local district personnel. This study attempts to demonstrate that on a regional basis, local school districts can pool their resources to a point of having a base sufficient to justify the establishment of an organization, adequately staffed, expertly trained and properly equdpped to provide data process- ing services, sophisticated and extensive, but also serving the day to day mundane clerical functions of the employees of school districts. Delimitation of the Study As initially conceived this study would have encompassed all of the school districts of the state of Michigan recognizing the next eche- lon of administration. Although the state of the art of computer simur lation is rapidly advancing, the program available at the time of model building was not adequate to accommodate the many variables and volumes necessary for the study on a state level. The limited background of the writer also precluded attempting to build a model of this magnitude. It was also relevant that the mathematical model have a basis of experience upon which to build. Therefore the study is limited to the constituent school districts of Oakland County. The study, or model components in terms of activities simulated, is further limited to those computer services presently automated in the constituency, plus the extension into some additional business office applications and into an information retrieval application. The information retrieval or file inquiry compon- ents of the model assumed that the other applications would build elec- tronic files as data were processed throughout the year. For example, financial statements for management purposes or for reporting purposes would be available through the file inquiry application. It would be an output function, that is data woxld flow from the central computer to the remote terminal. It would not be necessary to send data in as the data would hate been accumulated from the purchasing, accounts payable and payroll applications. Personnel records would also be on electronic files and could be updated through a message switching routine or re- trieved through a file inquiry routine. Data for the study has come from three basic sources. The first source,involving volumes, was the official reports of the local school districts to the state department of education. The data used from these sources were census figures, membership fi ares, and numbers of employees. A second source represented data collected by the members of the Tele- processing Feasibility Study Committeel. The data collected by this group defined the purchasing actisity and the accounts payable volumes. The purchasing activity data involved numbers of purchase orders, the distribution of the number of line items per purchase order and variance 1The Teleprocessing Feasibility Study Committee was composed of the Director, Merlin Reeds of oakland Schools; George Dexter, Birmingham; Byron Oliver, Farmington; Mel Staebler, Pontiac; Ferris Peabody, Royal Oak; James Smythe, Sonthfield; Nicholas Mengnini, Waterford; and John Williams,‘Walled Lake. These seven members were appointed as middle management executives to conduct in depth studies within their respect- ive istricts and to present their recommendations for board of educa- :ion action. The study was conducted during the period of September through December, 1965. in purchasing by time of year. The third source of data was primarily the considered Judgment of the writer. This Judgment was frequently subjected to a critical analysis by members of the Teleprocessing Feasibility Study Committee. The writer's Judgment was further condi- tioned by five year's eXperience in working closely with local school district teachers, counselors, principals, business administrators and superintendents in the development of applications to data processing. These data were primarily concerned with timing cycles. The basis for data is presented in the description of the programs branches in Chapter V. Summary The mathematical model of a teleprocessing network to serve an educational environment presented herein describes one situation, that is, one intermediate school district encompassing its constituent local school districts, and one set of particular procedures appropriate to the readiness of the personnel in that situation. The computer output from the simulation run of the model, when analyzed, serves as a.management tool. First, the initial run reveals the weakness in the configuration. The weak points are identified and the magnitude of the weakness is re- vealed. Management can.make the decision to live with the weaknesses, setting up appropriate rules to minimize the potential prdblams, or an alternate decision to reconfigurate tolminimize the weaknesses can be made and the new'model can‘be resimulated. Since computer runs are re- latively inexpensive compared to a bad or poor configuration decision, the second or alternate decision seems desirable. The computer run of the model described in this study is an act- ual first run of a suggested configuration of equipment to process certain specified applications or procedures. The findings or interpretations are'based on this first run and not on repeated runs as would be desir- able. The restraints of time and cost for computer runs precluded addi- tional runs for purposes of this study. The mathematical model, as a management tool, is operational and may be rerun with changes in variables at the discretion of management as the planning progresses for the development of the actual telepro- cessing center. Further, the model may be modified to accommodate any conceptually similar environment in any geographic area; indeed, the environment need not have any specific geographic boundaries. Further, the concept may be extended. The model currently is macroscopic in that the smallest time element is one-half second and the time period one year. In terms of timing, one-half second elements are large blocks of time to third generation computers. A new'model focusing attention on peak periods of the month or year could give additional insight into the prdbable be- havior of the system. Conceptually the model could.be expanded to en- compass the linkage of several computer centers each with its remote terminal devices, and the whole, perhaps linked to an even more power- ful and sophisticated computer center. These last two ideas are not presented with the thought of con- clusions and recommendations but to assist the reader in understanding the level of utilization of the model. In this study, simulation is employed to find and describe mean- ingful relationships among the many factors and variables that constitute the description of the mathematical model. Reruns woudd.test and retest the sensitivity of controllable factors. This study is limited to the interpretation of the output of the simulation of one year of operation. Certain changes will.be suggested by this interpretation. The techni- que is not suggested as a precise tool that will enable the executive to make an unqualified decision, but rather as a tool that will focus attention on the more crucial problem areas. Quantifying the input to the mathematical model as an exercise alone helps to bring the problems into focus. Analyzing the output data further enlightens the executive or man- agement team.to a'better understanding of the probable operating environ- ment; its efficiencies and its limitations. CEAPI'ERII REVIEWOFTEEIITERATURE In 1963, Luton R. Reedl conducted a nationwide survey of the data processing systems in the public schools. Reed's survey identified 288 school2 systems in the United States which had some type of data pro- cessing system in operation. One system3 reported having data trans- mission equipment, but that same system did not report having a computer. This would seem to indicate a card-to-card communications device. Reed recognized the potential of data transmission in relation to the regional concept, ”One aspect of data processing which makes it feasible for smaller school districts is the ability to transmit data electrically from outlying. points to a central processing center.“ Grossman and Howe5 in their text, Data Processing for Educators, indicate that one of the specific purposes of the California Research lLuton R. Reed, Data Processi stems, A Guide for Educational Administrators. Contra New York Segool Sttu Council, 1961!. _ 2Ibid., 20. 3Ib1d., 37. thid., 18. 5Alvin Grossman and Robert L. Howe, Data Processingtfor Educators. Chicago: Educational Methods, Inc. , 1965. and Development Center in Educational Data Processing is: ”The conduct and support of simulation studies. --It is evident that certain types of complex decision processes can be performed by computer systems more efficiently than by humans. The potential of these techniques in education appears to be great. Efficient use of data would allow edu- cators to make decisions and allow them to experiment with techniques and solutions before trying them in schools.” The preceding statement is the second of seven purposes of the Research and Development Center. The seventh purpose is the establish- ‘ ment of regional data processing centers. The regional center is per- ceived as the appropriate organization for handling all data processing for small districts, some processing fbr medium sized districts and certain specialized computing for the largest school district. The regional center would be a service organization.providing those data processing services that the local districts could not provide for theme selves. As late as January, 1966, Business Publications Internationa1,in- troduced a new section entitled ”Automation Educator“ in its monthly magazine, Business Automation. A review of these sections fails to re- veal any evidence that computer technology is being used in educational decision making. Neither the ”Printout” sections listing new'books and films nor the ”Available Literature" sections which lists primarily ven- dor materials disclose any reference to publications covering the topic of using a mathematical analysis approach to problem solving for the educator. In the non-education section, Senter Stuart writes on the topic: ”Optimization - It Can Pay orr'.1 Although his presentation is business 1Senter Stuart, ”Optimization - It Can Pay Off," Business Automation, XIII, No. 3 (March, 1966), 16-149. 10 and industry oriented, certain conclusions are appropriate to the en- vironment of the network described by this mathematical model. Relevant points made are: 1. Large and frequently repetitive tasks should be optimized even at considerable cost. 2. The cost factor of producing a report may'be less consequential if the deadline for the report is critical. That is, optimize in spite of cost in some instances. 3. The output from the computer system should be ap- propriate to its use. Often times, management receives too much output. Stuart focuses appropriate attention upon acprOblem faced by every data processing establishment. His concern is for optimizing the operations. Management is also necessarily concerned about the optimization of the configuration of the equipment in the third and fourth generation com- puter systems of which he speaks. JOhn'w. Sullivanl, in an address to the Florida.Association of Educational Data Systems in February, 1965 entitled ”Education and Auto- mation" challenges educators to be better informed about present day technology; His challenge, "And may I suggest that any subject that I name that you do not know its proper utilization, that as a professional you could be classified by your administrator as being deficient!" He then lists the following as subjects about which educators should know lJOhan. Sullivan, ”Education and Automation,'.A Paper read before the Florida Association of Educational Data Systems, Boca Raton, Florida, February, 1965 . 11 their utilization, advantages, capabilities and limitations: 1. Operations Research or Management Science Techniques, i.e., Queuing Theory, Linea-r Programing, PERT; to name Just three. , 2. Statistical sampling, including Bayesian Concept. 3. Scientific forecasting, including Hueristics. h. Management Decision-Making by Exception. 5 . Real Time Processing Similarities/Dissimilarities to Batch Processing. 6. Critical Path Methods of Cost, Scheduling, etc. 7. Single Information Flow Design Criteria. 8. Simulation and Game Theory. 9. Concept of Slack. 10. Retrieval, Linguistic and Algorith Procedures for Whole Document Processing, Automatic Abstracting, Index- ing, etc. Prior to recent months, periodicals devoted to education or even to educational data processing are notably silent in the use of com- puters in management decision roles. Change however is taking place. The subtopics: Pupil Management, Personnel Management, Physical Re- source Management, and School District Planning are all included in the article ”The Role of Computers in School System“ in the January, 1966 issue of Monitor.1 Trocchi indicates that PERT (Program Evaluation and Review Technique) can be used to control school construction. Since School construction is primarily contracted, few educators have become very knowledgeable of its usefulness even though the architectual and contracting films have been using this technique to serve school dis. tricts . lRobert Trocchi, ”The Role of Computers in School Systems”, Monitor, IV, No. 6 (January, 1966), 6-9. Schlaiferl points out the advantage of the high speed computer in 1959 prior to the advent of the relatively low cost third generation comput- ers in seeking solutions to business problems. Most of the techniques listed by Sullivan were known and used in operations research prior to 1959 but most frequently by large organizations with specialists on their staffs. Today many of these techniques are available as tools in the form of programs written for computers. Much of the literature in the field is the trade publications of the vendors of equipment, forms, and various kinds of services. These are promotional in nature and are slanted to topics indicating what is coming. Even advertising in many of the widely circulated magazines seeks to advise the executive of the new tools available to him to bring him current, concise, relevant information that he may make wise and timely decisions. Lindsay2 emphasizes that "Mathematical analysis is a tool to be used by management - not a substitute for it." He points up the need for the use of specialists in working with management to identify problems, de- fining relationships and interpreting results. Significantly he indi- cates that tools of mathematical analysis can be used in several ways: 1. To find the optimum combination of a very large number of interrelated factors. 2. To find the best solution, or at least a good solution, to problems involving uncertainty of future events. lRobert Schlaifer, Probability and Statistigs for Business Decisions. New'York: McGraerill Book Company, Inc., 1959., 325. 2Fran‘klinA. Lindsay, New Techniques fOr’Management Decision Making, New York: MbGraweHill Book Company, Inc., 1963., 2~3. 3. To find meaningful relationships among many interacting factors and to separate the important factors from the unimportant. 1+. To develop ways of collecting and processing significant data at minimum cost. 5. To relate quantitatively the operational objectives of the individual segments of a business or government organ- ization, or even of individual workers, to the over-all objectives of that organization. 6. To test the sensitivity of any given solution to changes in controlling factors. Lindsay concludes, "It is my own belief that probability theory, simulation, and mathematical programing will have a major impact on management over the next few years.” at \' 11} CHAPTER III BUILDING THE MOIEL Introduction The proposed mathematical model was to be simulated according to a manufacturer's program. The specific program chosen was the General Purpose Systems Simulator II ,a program available from International Business Machines Corporation.1 Before proceeding to build the model, it is necessary to adOpt the conventions, terminology and symbolism pre- scribed by the program. One of the conventions is that a flow diagram must be drawn. (Appendix A) The flow diagram is a group of block type symbols connected by lines indicating the direction of movement of the traffic in the model. Units of traffic are introduced into the model at selected points of origin. The blocks through which the units of traffic move represent the kind of ”activity to be performed at each point. The re- spective positions of the blocks indicate the sequence of activities to be performed until the unit of traffic is completely serviced and exits from the model. A clock time is associated with each unit of traffic, at its time of origin and at each block through which it moves. 1 , General Purpose Systems Simulator II, International Business Machines, Technical Publications Department, white Plains, New York, 1963. 15 Units of traffic to be serviced are called transactions. These transactions have certain properties that have a bearing on how they move through the system. One such property is called transit time. It is the total elapsed time that a transaction remains in the model. This transit time is frequently modified in the model in order to measure portions of the transit time that are more meaningful than total elapsed time. Parameters are values or properties that can be assigned to trans- actions. This enables the model builder to assign appropriate values to transactions as they move through the system. Parameters assigned to transactions may be set by the model builder or may be set dynamically by the simulator program. A The simulator program attaches a time priority to each transaction. The model builder or the simulator may assign or modify this priority as it moves through the system. A The transit time of a transaction is the sum of the action times at the blocks through which the transaction moves. The action time may be a constant, a variable or compound in nature. The action time is computed from two values, a mean time and a modifier. The expression 10:5 is translated by the program as an average of 10 time units plus or minus 5 time units. Each value of 5, 6, 7, ....15 have equiprobability of being the action time at a block having that action time specification. A convention of the simulator program provides for the introduction of algebraic expressions into the model. These algebraic expressions have the code name Variable and are made up of one or more Systems Vari- ables connected by the arithmetic signs of +, a, t, / where «2» is plus, - is 16 - is minus, * is multiply and / is divide. The System Variables are coded and defined as follows: TABLEl SYSITM VARIABIES Mnemonic Definition Pn . . . . . Parametern M1 . . . . . Transit time D1..... Delaytime Nn . . . . . Entry count, block 11 Wn . . . . . Current count, block 11 Pa . . . . . Facility status, facility 11 Sn . . . . . Storage‘occupancy, storage n Rn . . . . . Storage remainder, storage :1 Qn . . . . . Queue length, queue n Cl . . . . . Clock time Vn . . . . . Variable, number n Xn . . . . . Stored value, cell n Tm . . . . Table mean of table 11 Kn . . . . . Constantn RNl . . . . Random number FNn . . . . Function value, function n A storage can hold up to its rated capacity of transactions, the simulator keeps records on its status. A facility can service only one transaction at a time, e.g., a bank teller is an example of a facility. A queue is a waiting line. The simulator keeps records on its length and the time that each transaction spends in the queue. 2 <> 17 Block Types and Purpose .ADVARCE, computes an action time and determines the next block. ASSEMBLE, reunites two parts of a previously split transaction. ASSIGN, assigns a value to a parameter of the transaction. COMPARE, tests an environmental condition based on the value of two system.variables. ENTER, places a transaction in a storage. GATE (Facility), tests a facility for busy or not busy. GATE (logic), tests a switch for set or reset condition. GATE (Storage), tests for full or empty status. GATE (Match), transaction at a match or assembly block. //\\ \\// 18 GENERATE, puts transactions into the system. HOLD, uses a facility not being used by a prior transaction. INTERRUPI‘, uses a facility, even interrupting a previous transaction using the facility with a HOLD or SEIZE block. IEAVE, a transaction leaves a storage. IOGIC, sets or resets a switch. IDOP, returns to a previous block until the trans» ‘action has been in LOOP BIDCK value of X times. MARK, resets clock time of a transaction to zero. MATCH, tests the presence of a companion trans- action at another MATCH block. ORIGINATE, another way of putting a transaction into the system. l9 QUEUE, transactions remain in this block until 'accepted inthe next, data is recorded on how many are in the queue and'how long each remains. RELEASE, facility is made available to the next transaction seeking service . SAVEX, puts avalue in a cell for future refera ence . IIZE, facility becomes dedicated to a trans- action until REIBASED or INI'ERMJPI'ED. SPLIT, divides a transaction into two parts to be routed along different paths, parts may be reassembled . TABUIATE, puts data being accumulated in table format for outputting purposes. mm, transactions exit this block type. 20 Block Instruction Format Location MEAN Mbdifier Selection.Mode (i3, {Associated with each block are numbers or terms that control the action of a unit of traffic while in the block, and its departure route. The location is a number giving identity to the block unique in the entire system. The mean represents the average amount of time that a transaction will remain in the block. The mean.may be a variable or a number. The modifier controls the spread or the variance in the action time. The range in action time is the mean.p1us or minus the modifier. The selection.mode may be blank implying only one path leaving; it may be the term.BOTH meaning that it will follow the first path if avail- able, otherwise the second path will be taken. The selection mode could be All” meaning that several paths will be tested in sequence with the transaction taking the first available path. The selection mode could be a number. The number is a probability factor of taking the second path, otherwise the first path is followed. Functions are sets of paired numbers that can be introduced into the simulation.mode1. This makes it possible to insert extensive data in a rather simple format. Functions may be continuous or discrete. A continuous function provides for interpolation if an exact value is not recorded for the independent variable in the function. {A discrete func- tion does the equivalent of a direct table look up and can read only exact values recorded. An example of this is a function which records 21 the number ofstudents in afdistrict to the district identification number. Given the preceding conventions the flow diagram.comprised of a number of blocks graphically represents the action that is to take place in the simulation of the model. To present the model to a computer for the sumulation run it is necessary to code each variable, function, table, block, etc., in a format acceptable to the computer program. This is accomplished by adhering to a set of coding rules and punching these data into standard eighty column cards. Appendix h is a complete print out of’the mathematical model as presented to the computer for the simulation run. Each line with an * in the first print position is considered a comment and serves only to remind the programmer of the purpose of the adjacent instructions. All other lines of print are preceded by‘a number and have unique purposes in the model. Any greater detailed description would be technical and not relevant to most readers. Appendixes A.and B and the General Purposes Systems Simulator II Manual.provide adequate documentation for the replication of this study. Changes in volumes, variables and parameters could be readily made for more depth analysis. SEE Johnson1 writing in the Journal of Educational Psychology concludes: ”Though at its outset a computer model is likely to oversimplify and indeed misrepresent, the model would provide a clearly defined base ;M. Clemens JOhnson, ”Adaptive Computer Model", Journal of Educational ngcholoq, LV, No. l, 66. 22 for future improvements and greater opportunities for precise commun- ication. A concept and its operation which have been quantified would be better understood than verbal explanations alone.” The need to quantify as many of the factors of the environments as the model expects to simulate is a concept which must be at the fore- front of the model builders thinking in order to minimize the dangers suggested by Johnson. Although the process of making improvements as a result of findings of each successive run can be performed repeatedly, a complex simulator model may require extensive manpower to evaluate output and to modify the computer input. The computer runs may be ex-- pensive if facilities are not readily available or if re-runs are made without adequate consideration of the expected returns in relation to the expense. Improved simulator programs and better price performance from computers in the future will reduce or eliminate this concern. With these problems in mind, the model builder should also design the model to facilitate the process of'changing specifications for re«= runs. With this capability it would be advantageous to I'rim the model" many times changing certain controlling parameters each time. Compariw sons would reveal the relative influence of these parameters and would assist in more quickly arriving at an optimun model. Experience in model building and an awareness by management per» sonnel on the values of the technique in operational research will result in making more precise and meaningful data available to the model. This is Johnson's thesis that "the model would provide a clearly defined base for future improvements . " Lipid. 23 CHAPTER IV DESCRIPTION OF THE MATHEMATICAI.MODEL Introduction The purpose of‘building a.mode1 in any endeavor is to provide the planners and builders of the eventual operational product with a'better understanding of its potential capabilities, limitations and general characteristics. By building a product to scale (test model) in spatial dimensions and subjecting it to test conditions, engineers are able to predict with some degree of certainty the prdbable performance of the production model. The physical characteristics of the model are con- trolled (input) and recorded in precise mathematical terms. Results of tests of operational characteristics (output) are likewise measured, tabulated and correlated with input data. Engineering competency and statistical analysis of data guides the model designer in.making changes in his model for subsequent testing purposes. Retest and redesign con- tinues until performance is acceptable. The model herein described is analogous to a physical model with the exception that as a.mathematical model the physical characteristics are assumed. The model is "run” not in a wind tunnel, an aeronautics type laboratory; not on a test track, an automotive industry type labor- story, but simulated in a computer. The performance is recorded, tabue lated and printed out at the conclusion of the computer simulation. 214 General Properties The properties of this specific model can be enumerated as follows: 1. A system of a number of electronic devices are interconnected by telephone line linkage, the total being considered an entity. The total system as an entity has as a property the interrelationship of its parts. The total physical electronic devices as connected, including connecting wires, constitute the physical model as represented mathematically. Each electronic device is also an entity. It has as prop- erties its function in the system, its relative power (speed) in performing this function and a relationship to the system and its several parts. Each device is known as a facility. The purpose of the facility is to service appropriately the task assigned to it as the system operates in its totality. The facilities in this model are of two types. One facility is a computer or central processing unit. Essentially all activity in the system is routed through the central pro- cessing unit at least once during its life in the system. The other facility type is referred to as a remote terminal or terminal and is an input and output device. Its funda- mental property is speed; the rate that it can send or receive data expressed as fifteen character messages. In the case of receiving, it also has the property of being able to print at a comparable speed. The model has three levels of terminals defined. Each terminal is defined according to the expected loading on it, or by decision of 3. 25 the local district participant in the Teleprocessing Feasi- bility Study. The school district is an entity that has as its properties a geographic location, a given number of students, a given number of secondary students, a given number of employees and either a given amount of business activity as determined by survey or an estimated amount based on a correlation with the number of employees. (Table 2) With each school district there is an associated facility, the facility being the terminal previously defined. It is noted here again that the property of a teminal is power in terms of speed. The properties of a district can be generalized as those characteristics which contribute to a loading on its associated facility. The geographic area (Figure- 1) served by the system is an entity that encanpasses all'of the several school districts that are associated with a terminal device. For purposes of consistency, this geographic area is said to be associ- ated with the central processing facility. This geographic area will be referred to as the intermed- iate district. Thamhaudistriets are weferredto as constituent districts. A A property of the intermediate district that is of import- ance then is the sun of the characteristics of the con- stituent districts that contribute to the loading on the total system. The word "sum" should not .be considered in its simplest form here, but rather as a combination of an addi- tive err... and an interaction effect. TABLE 2 VOLUMES" BY DISTRICT Student s* Purchasing Payables District Code 1 K-12 7:12 mafies'l- *1- H- Avondale 01 3&78 1167 208 Berkley 02 891m 1098 558 Birmingham 03. 16110 7132 1231 Bloomfield Hills oh 6821 30h7 561 Brandon 05 13498 635 88 9 200 Clarenceville O6 3815 1302 280 Clarkston 07 5319 201.6 331 Clawson O8 #519 1701; 287 Dublin 09 1 1 Farmington 10 13130 51.01; 955 30 537 Ferndale ll 82h8 3691 5110 12 1 1 Hazel Park 13 8124 3328 522 Holly 1h 2838 1173 181 Huron Valley 1;; 51.27 207 3 27 9 Lake Orion 16 1881: 1731; 273 Lamphere 17 5131 1563 367 Iyon Township 18 2361 9114 158 Madison 19 14931 1713 296 Novi 20 9:2 272 67 Oak Park 21 7153 . 3122 678 Oxford 22 2170 903 137 Pontiac 23 23278 88614 151.7 33 1000 Rochester at 61:59 2807 539 Royal Oak 25 20069 851.6 1333 ‘ 26 750 Southfield 26 12865 55.06 1131+ at 501+ Troy 27 M95 1891» 27h walled Lake 28 8033 3569 566 10 208 Waterford 29 161.13 650h 1105 west Bloomfield 30 261.2 1111. 161 * Source - Form A and D Reports to Michigan Department of Education, 1965. ** Source - Teleprocessing Feasibility Study Comittee Survey. Oaklandacheeh- “Hater-edit undetermined Administration Seamus: tulle for localdistrietedeeaaddata 28 5 . Applications or tasks to be performed consitute another set of entities that provide for the traffic through the model. General properties of these entities are those of initiating action in the model, of directing the pathway of each initiated action, and sharing the function of load determination with loading factors assigned by the constituent districts . gogcific Description 1. The total system assumed in this specific model contemplates a central computer with peripheral equipment adequate for file storage for the functions and loading presented in the model. For example, the kindergarten through twelfth grade enrollments totaled 212,000 in Oakland County, September, 1965.1 Allowing one thousand characters of file storage for each student would require magnetic file storage of 212 million characters. Student accounting is the application expected to require the greatest amount of file storage, but if other applications boosted this requirement to a billion, this would not be prohibitive in the complex and powerful system assumed in the model. Further asslmed “ in peripheral equipment would be different levels of accessibility to files, depending on the function and the times of day, week, month or yearythat these files would be used. Files would be temporarily moved to fast access areas durim times of high utilization. ‘ Most input I would originate at the remote terminals and most output developed would be returned to the same terminal. However, a 600 line per minute printer lCompiled from the official reports of local districts to the Department of Education, State of Michigan. 29 is assumed at the intermediate district for in house functions and for outputting grade reporting and student schedules if the input origin- ates at one of the slower terminals and the remote fast terminal in an adjacent district is busy. The total physical system then would have: a central computer, its on site electronic files, application and system control programs resident in the computer memory or filed for automatic retrieval, an on site fast printer, and thirty remote terminals. (Table 3) Three term- inals would have power to print 300 lines per minute, four terminals could print at the rate of 150 lines per minute and the balance could print 15 lines per minute. 2. The parts of the physical system with the computer facility described are enumerated above. Each remote terminal would be associ- ated with a school district. The power of the terminal assigned was de- termined on the basis of expected loading, equipment on the market, relative cost and the readiness of the district to exploit the power of the system. In the early phase of the model building, which was July to December of 1965, six-150 line per minute terminals were contemplated. Phase one of a two phase study involving seven of the largest districts upgraded this power by a total of 600 lines per minute for the system. Each terminal would be equipped with a card reading device that would provide for sending input, in batch mode. Output could be punched card, printed, or both. System design would be expected to minimize the amount of input in relation to output. For example, to perform an accounts payable routine, vendor files and standard catalog files would be expected to provide names, addresses, descriptions, etc. , with exceptions allowable. This- would negate having to send massive volumes of data one way. 3O TABLB_3 TERMINALIEACILITIES Teminal ‘ Assigned to No. of No. of ta1 Speeds: Terminal Attached Attached ~12 Line Per No. Terminal 7-12 load District Code Minute Students Avondale 01 15 23 Berkley O2 15 26 Biminshm 03 300 3 6615 13777 Bloomfield Hills 0‘1 15 03' Brandon 05 15 29 Clarenceville 06 15 10 Clarkston 07 15 29 Clawson 08 15 03 Dublin 09 15 28 Farmington 10 150 3 15711 6978 Ferndale 11 15 26 12 15 10 Hazel Park 13 15 25 Holly 1h 15 29 Huron Valley 15 15 28 Lake Orion 16 15 23 Iamphere 17 15 25 Iyon Township 18 15 28 Madison 19 15 25 Novi 20 15 10 Oak Park 21 15 26 Oxford 22 15 29 Pontiac 23 300 3 6008 lh872 Rochester 2h 15 23 Royal Oak 25 150 3 660k 16150 Southfield 26 300 ’ 3 10811 16317 Troy 27 15 03 J Walled Lake 28 150 h 7670 11239 waterrord 29 150 h h757 11261 West Bloomfield 3O 15 28 31 3. The specific school districts are the 29 constituent school districts of Oakland Schools Intermediate District. (Figure 1) They are numbered 1 to 30 consistent with a coding system in use in the five year history of the present regional data center. Terminal or district twelve is really non-existent as that district was annexed to an adjoining district in 1961. District and terminal nine has no secondary students and does not enter into the grade reporting or student scheduling routines. Table 1 lists the number of employees, purchasing volume, accounts payable volume, number of students in kindergarten through twelfth grade, and number of students in seventh through twelfth grade. These figures provide the basic variable input volumes into the system by district size. It will be noted that terminal twelve will call for no loading based on size, however communications and file inquiries will be initi- ated from that terminal. h. The geographic area associated with the central processing facility is the intermediate school district of Oakland Schools, approx- imately 900 square miles Just northwest of Detroit. Its southeastern area through the central area is suburban, its northern and western areas are rural and small cities or villages. The constituent districts vary in size from under two square miles to over eighty square miles. Enroll- ments vary from.under 1,000 students to over 23,000. Annual operating budgets range from.under a half million to over twelve million dollars. 5. Specific applications built into the model are enumerated below. Some applications not specifically budlt into the model are assumed to be allowable within a related application or to be accomplished within the 32 file inquiry application. For example, inventory control could be an inherent part of purchasing and accounts payable with periodic reports emanating from the file inquiry routine. Detailed descriptions of the listed applications appear in the next chapter. a. Network Communications b. File Inquiry c. Purchasing d . Accounts Payable e. Payroll f. Student Master File Maintenance g. Student Scheduling h. Grade Reporting 1 . Timekeeping Timekeeping is a control function in the simulator program. It does not use any appreciable time in the model. A similar function in an operational model would require very little time. 33 CHAPTER V PROGRAM BRANCHES OF THE MODEL Introduction As each application was developed in the model, it was the concern of the builder to initiate each unit of traffic at its appropriate time. The unit of traffic should move as the initiator, the local district operator, would prefer it to move within the limits of capability of the system and its affected parts. Priorities appropriate to the appli- cation and delay of a unit of traffic at any point in the system should be controlled. An amount of time sufficient to provide the service needed is exacted from each affected facility. It should be noted that units of traffic have widely varying characteristics. One type enters the system about every 3.2 minutes and remains only seconds unless de- layed by lack of facilities to service it. Another type enters only once per year but is intermittently delayed between functions and will remain in the system several weeks. Several types exist between these extremes as will.be described in detail under eaCh application. A unit of traffic when introduced into the system is electronically stamped with an arrival time. When it leaves is known as its departure time. The elapsed time is transit time and in several instances the transit times were tabulated by the simulation.program for analysis. Another characteristic of a unit of traffic is the amount of use that it will make of the facilities. One type will make frequent use 3% but only a.minute or two at a time, while the other extreme is a unit of traffic that enters only once annually but uses several hours of terminal time, perhaps intermittently, and several minutes of computer time. Again the typical unit of traffic is between these two extremes. Another important characteristic of a unit of traffic is the prior- ity that is assigned to it. Priorities are established in two ways. With one, the mode1.builder decides and assigns, or programs to have the simulator assign according to some condition. The second type of prior- ity is determined by the amount of time a unit of traffic is delayed past its scheduled departure time from its present location in the system. If the model builder or the simulator program assigns a priority, that priority takes precedence over units of traffic Just delayed by facili- ties being busy. In addition to these techniques, certain types of trans- actions are permitted to interrupt facilities even if engaged in servicing a.high priority unit of traffic. However an interrupted facility may not be interrupted. This feature permits the flow of file inquiry type traffic between the parts of a larger batch type transaction. In one instance, the loading that a unit of traffic puts on the system is calendar dependent. Purchasing is assumed to be four times normal in June and July and two times normal in May and August. In another case, student file maintenance is in a weekly cycle but only during the school year. Units of traffic that are expected to stay in the system from one to several.hours are structured to arrive in the system.within.the first four and one-half hours of the day. This minimizes the amount of un- finished batches remaining in the system from one day to the next. It is expected that the users of the remote terminals would behave in this 35 way. If they did not, its effect would be to relieve the system from pressure as the alternative of more freedom would tend to even out the loading on the system. The basis for assumptions that are made in the model building are many and varied, usually more than one would apply in each assumption. The bases for assumptions are as follows: 1. The writer's background knowledge of the behavior of the departments in the constituent school districts, parti- cularly as it applies to applications now processed at the regional computer center. Limited surveys conducted by participants in the Tele- processing Feasibility Study. Consensus of participants of the Teleprocessing Feasi- bility Study. The writer's background knowledge of machine capabili- ties in handling particular types of applications. Technical information supplied by the vendor (Inter- national Business Machines) systems engineer. Personal interviews with Teleprocessing Feasibility Study participants and other school administrators. Actual on-the-Job experience by the writer in working at several levels with school district personnel in analyz- ing, designing, programming, and implementing data process- ing procedures in educational applications. Bayesian theory of probability cited by Schaifler:1 ”The theory of probability does not replace Judg- 1Robert Schaifler, Probability and Statistics for Business Decisions, New'YorkzlchraweHill Book Company, Inc. 1959, 333. 36 ment and experience. Its utility lies rather in the fact that it allows us to make more effective use of our Judgment and experience by assigning prdbabilities to those events on which our experi- ence and Judgment bear most directly rather than to events which will actually determine costs but with which we have had relatively little direct experience." Since the model is hypothetical, the only precisely reliable data that can.be entered is that which has been tabulated in terms of counts: students, employees, etc. However, when the above bases for assumptions failed to being the problem into sharp foCus, the most pessimistic assump- tions were made. Finally, this model, as with any model in its early stages, will at best yield only a,macroscopic description of the characteristics of the final working production.mode1. Optimization of a mathematical model would require several runs to determine the sensitivity of each of the many interacting variables. ‘Ultimate optimization of a production.mode1 is beyond the scope of this study. Network Communications The purpose of this program application is twofold. First, as a daily routine and second as an intermittent routine. It is anticipated that each morning, ten minutes of the day of each facility should be set aside for the following: 1. Center to terminal instructions. 2. Terminal to center problems. 3. Announcements of’general interest to the local districts. h. Other. In the model, an eight hour day is assumed starting at 8:30 each morning. This routine would be performed at this time by the central 3'? processor every day unless the central processor was in a state of “interrupt" which is a highly improbable event. It would also be per-g ' formed by every terminal not busy at that time, and in turn for those teminal facilities that were busy. Some terminals could be busy at 8:30 a.m. for other applications, but the probability is low. The second purpose of network communications is another activity that the industry refers to as message switching. That is, any district could initiate the sending of a message to one, all or any mix of dis- tricts. This. event is scheduled to occur eight times daily on a vari- able schedule of every hour, plus or minus half an hour. Each of the eight units of traffic would put a five second loading on the computer and from one to three minutes of loading on each of from one to thirty terminals. Each terminal would average eight minutes of this type of comunication daily. The central processor would re- quire only forty seconds daily to serve this application. Message content could be for any of the reasons listed under the 8:30 a.m. branch or any other reason. This branch is not to be confused with file inquiry. In this application, messages originate outside the machinery network and do not get into files. File Inquiry File inquiry is another general purpose application and has two branches, each serving a different classification of problem. The first type would typically be a district asking to see or receive a single record of not more than a few hundred characters from its cen- tral electronic file. The second type would be the request by a district for having a several page report generated and sent to its teminal. 38 Files to be accessed under this general purpose application could be any of the district files generated by the other special purpose applications . The request to see a single record inquiry was programmed to enter the system every 3.2 minutes with a spread of 3.2 minutes. This means that a unit of traffic of this type would enter the system on the aver- age of every 3.2 minutes, they could come in adjacent time units or be 6.h minutes apart. This would result in an average of five file inquir- ies per day by each terminal. Each inquiry would use two minutes of terminal time and five secondsof central Jprocessor time. An average of ten minutes per day per terminal and twelve and one-half minutes of central processor time would be the overall loading. A file inquiry requesting a several page report was estimated to be one per day per district. This was accordingly programed to put a unit of traffic into the system every sixteen minutes on the average or from zero to thirty-two minutes apart. loading per terminal per day would average ten minutes, varying five to fifteen minutes. The daily load on the computer would be thirty uses of an average of thirty seconds each, or fifteen minutes. The Teleprocessing Feasibility Study Comittee concurred in these assumptions by system but was critical of the lack of variance by dis- trict. It should be noted here that the districts with more powerful terminals could actually get equal reports in much less time or larger reports in the model as built. Out'put is a function of terminal power and this application ties up the terminal for a time element independ- ent of the amount of output. 39 Purchasing This branch of the model provides for a daily batch of purchase orders originating from each district terminal. The clock time of origin is distributed over a four and one-half hour time period. Fifty percent of these units of traffic are randomly originated between 9:00 a.m. and 10:00 a.m. Tuenty-five percent are randomly originated between 10:00 a.m. and 11:30 a.m. The balance are originated between 11:30 a.m. and 1:30 p.m. This distribution is in keeping with the asslmption that districts will wish to complete a batch process of this type during the same day. Data for this procedure was collected by participants in the Teleprocessing Feasibility Study. Therefore, a table of relationships between number of employees and number of purchase orders originating daily was developed. For those districts providing data, the actual count of purchase orders entered the system. For those not represented, a table look up function was used to estimate the number. Since the data came from five of the ten largest districts, the smaller districts were put in the table at near the low of the sample of five. Districts with up to one hundred employees were estimated to have one to nine purchase orders daily directly proportional to the number of employees. If employees numbered one hundred to five hundred fifty, daily purchase orders were set at nine also. All larger districts had greater purchasing activity as translated by the table look up function. (Table is) The above discussion covers the distribution of arrival of batches and the number of purchase orders expected per batch. ho TABLE h DISTRIBUTION OF NUMBER OF PURCHASE ORDERS BY DISTRICT SIZE (NUMBER OF EMPLOYEES) Number of Volume of Purchase Employees Orders 0-100 . . . . . . . . . . . 1-9 101-550 . . . . . . . . . . 9 551—1000 . . . . . . . . . 10-30 lOOlell60 . . . . . . . . . . 2h-29 116191300 . . . . . . . . . . . 2h-25 1301-1800 . . . . . . . . . . . 26-33 Another concern is the amount of data necessary to process one purchase order. This concern divides itself into two parts. Can the purchase order be expedited by inputting a catalog number and a vendor number only, or will descriptive information.be needed? This distri- bution was established by consensus of the participants of the Tele- processing Feasibility Study as follows: TABLE 5 DISTRIBUTION OF PROBABILITY OF VENDOR AND CATALOG ITEM BEING STOIED IN CENTRAL FIIE AND ASSOCIATED NUMBER OF MESSAGES REQUIRED FOR PROCESSING 1 Catalog File Hm: "—5. Yes No Vendor Yes ¥_76.5 (2) 9.9 (61 File no 8.5 (6) 5.1 (101* These table values are derived from the following assumptions: a. 85% of all items will be in the file. b. 7i of all items will not be in file. c. 8% will be for services not in file. hl d. 90$ of items will be from vendors on file. e. 50$ of non-file items will.be from vendors on file. f. 80$ of services will be from vendors on file. It will require one message to access either catalog or vendor file, five messages each if information is not on the file. IMinimum input would be if both the item and the vendor were on file, one message each or two messages. If neither were on file, five messages each or ten.messages would be required. Combinations would require six messages each. Since 85$ of the items are assumed to be in the catalog and 90% will be from vendors on file, it is expected that 76.5$ of the time (85$ of 90$) only two messages would be required per line item on the pur- chase order. The next consideration is for the number of line items per purchase order. .A survey completed by the Teleprocessing Feasibility Study group resulted in the following table. TABIE6 FREQUENCY DISTRIBUTION OF IINE ITEMS PER PURCHASE ORDER number of Line Items Frequency Per Purchase Order 1.000.000.0000... 2................12‘% 5 . . . . . . . . . . . . . . . . 20$ 10 . . . . . . . . . . . . . . . . 10$ 20000000000000.0005i 50 . . . . . . . . . . . . . . . . 5$ The months studies were September and Octdber, not heavy purchas- ing months. To incorporate a loading factor for summer purchasing, line A2 items were multiplied by two during the months of’May and August; by four during June and July. The respective means of numbers of line items per purchase order for these three periods are 6.7, l3.h and 26.8. ”Five variables have been discussed related to the purchasing branch. a. Distribution of entry into the system. b. Batch size by district. c. PrObability of items and vendors in file. d. Distribution of the number of line items per purchase order. e. Seasonal adjustment of loading. Processing is by daily‘batch with inputting and outputting progress- ing by purchase order. The computer is interrupted for five seconds for each purchase order and the terminal utilization varies widely as deter- mined by the five variables discussed above. The number of daily inter- ruptions of the computer is estimated to be about four hundred. Total daily utilization for the computer for this procedure would then.be about seventeen.minutes. Accounts Payable The accounts payable routine reflects present behavior of local school district personnel in their dealing with vendors. A standard agreement that is common provides for a discount if bills are paid on or before the tenth of each month. This is usually extended if districts have a fixed monthly cycle that does not fall within these ten days. Also typical in the pattern is the fact that most boards of education meet during the first two weeks of the month in a business session, one purpose being to review and approve bills presented at that time. A few districts do pay on a regular basis throughout the month with approval ‘43 of the board. Auditing is performed after the payment of bills. The reason for this mode of operation has been dictated by the peaking of the work load caused by processing during one brief period during the month. In an automated system this would not be necessary and it is assumed that all districts, large and small, would prefer the pattern that would consolidate accounts payable activities toward the first of the month. The freedom in the production model would permit process- ing at' any time and divergence from the pattern would in fact relieve pressure on the system. The assumption of restriction here is an attempt to display pressure on the system by movement from some present patterns to the - present model pattern. An assunption is made that boards of education will meet before the fifteenth of the month and that the fifteenth will fall on or after the tenth working day of the month. If these batches were to be processed according to an even distribution over the first Six'working days of the month, the would allow for some time after the automated run for any additional preparation needed prior to board meetings. Boards of education rarely meet on Fridays and the first working day of a month could fall on amt day of the week. . Another factor, holidays, although ’ not (built into! the model, directs us as model builders to provide for a "mdge" factor in time allowed to process this application. Independence Day in July, Labor Day in September, and New Year's Day would almost always present a disruption in normal schedules. Memorial Day and Good Friday could affect operational schedules. The assmed mathematical model starts a fiscal year on a Monday, July 1. Day one of succeeding months will not be one hundred percent hh consistent with fact due to technical problems of representing the act- ual calendar in the mathematical model. The actual calendar based on a Monday, July 1 start yields a distribution of working days per month as follows: One twenty-day month, four twenty-one day months, four twenty-two day months and three twenty-three day months. This distribution, dis- regarding holidays, was established as a function to determine or pick the first working day of each month. Attempts should be made in future models to relate the model to an exact calendar situation with holidays included. At this time, however, it is not seen as a radical weakness of the system. The payroll application, to be explained next, is seen to have a weekly cycle and should be noted here as interacting at least once monthly with the accounts payable application. If the first day of the month falls on Wednesday, the day designated for payrolls, interaction would occur twice during that month. Figure 2. Illustration of Accounts Payable and Payroll Interaction with Working Day One Falling on Monday. Mon. } fiTues . Weds . Thurs . Fri . V/Xéf/ZV/ l 8 9 10 11 12 § 13\ 1h 15 i 16 17 $18 \ 19 20 21 22 1&5 Figure 3 . Illustration of Accounts Payable and Payroll Interaction with Working Day One Falling on Wednesday. Mon . Tues . Weds . Thurs . Fri . / shes/4.; as 6. //s s 7 a *\\11.\. 12 13 9 10 These illustrations reflect interaction of only two sizeable appli- cations on the center and on the system as a total. In the first illus- tration, accounts payable for any one district has only a 16 2/3$ prob- ability of falling on Wednesday, payroll has a 50$ probability. The probability of both events occurring on the same day is 8 1/3$. In the second illustration accounts payable has a 33 l/3$ probability of fall- ing on one of the two Wednesdays, a 50$ probability exists that payroll would coincide with the same day. The probability of interaction by terminal 1: day one falls on Wednesday is 16 2/3$. Pursuing this line of thinking it can be demonstrated that throughout the year the prob- ability is 10$ that in an average month the payroll and accounts payable will fall on the same day. These are model probabilities, in a pro- duction enviromnent personnel behavior would reduce these probabilities because of prior knowledge and experience. Further these probabilities concern interaction within the same day. Each action would have inde- pendent arrival times in the system, arriving according to the same prob- ability within a four and one-half hour period from the beginning of the day. Their interaction within the day could range from zero to one com- pletely overlapping the other, should one or the other fail to progress 16 because of error. An example of no interaction: An accounts payable batch arrives at 9:30 a.m., sends data for ten minutes, processes data for three minutes, returns data for eighty minutes, the transaction is completed in ninety-three minutes including waits and interrupts. If the bi-weekly payroll arrives after 11:03 a.m. no interaction occurs. An example of interaction: A payroll batch arrives at 9:155 a.m. and sends data for ten minutes and at 9:55 a.m. it is waiting for the central processor. At 9:55 a.m. the central processor computes the payroll requiring five minutes. At 9:57 a.m. the accounts payable requiring fifteen minutes is sent in. At 10:00 a.m., payroll computing is complete, but outputting cannot proceed until 10:12 a.m. when the accounts payable batch is queued in a central file. Now the terminal is seized for outputting payroll and will hold for perhaps an hour. The central processor will compute and hold the accounts payable transaction but cannot return output until the payroll transaction is completed. If we adopt the symbolism: H > I Acounts payable input Payroll input Accounts payable throughput, no error :56" I II 3" Accounts payable throughput, with error TP - Payroll throughput, no error TPB . Payroll throughput, with error 0A :- Accounts payable output oP - Payroll output 1+7 Then the following would be possible sequences with waits or queuing preceding any step. IA - TA - QA - IP - TP - OP - this represents no interaction, each transaction would be mutually exclusive in time. IA - TAE - IP - TP - TA - OP - 9A - this would be maximum inter- action: first in, last out; last in, first out. IA - IP - TA - TP - QA - 0P - this would be a normal interaction; first in, first out; last in, last out. Interaction is a vital concern of this study and the simulator Aprogram reflects all interactions in determining transit times of the thousands of units of traffic in the system; by tabulating the queues that build up indicating pressure points in the system. The discussion of the interaction of accounts payable with one other type of trans- action, i.e., payrolls, illustrates how the system.remains sensitive to the calendar, the clock and the traffic in the system. Further discus- sion of interaction logic in the description of the model would be redun- dant. The origin of units of traffic in the accounts payable application has been reviewed with reference to the calendar and with the time of day. The next variable of concern is the volume. Data for input into this branch was collected by participants in the Teleprocessing Feasi- bility Study Group. .All smaller local districts in the intermediate school district were assumed to have accounts payable input equal to the smallest of the large districts from which the sample was drawn. This application also assumed that the output from.purchasing would include pertinent information placed in central files that would be referred to at accounts payable time. The quantity of data needed from the remote terminal at accounts payable processing time would be minimal. h8 The volume of input was entered into the system with a table look up technique using data as indicated in Table 7. TABLE 7 DISTRIBUTION OF NUMBERS OF ACCOUNTS PAYABLE VOUCHERS BY DISTRICT SIZE no. of Employees Volume of A/P (Vouchers) 0-100 . . . . . . . . . . . . 1-200 101-550 . . . . . . . . . . . . 201-208 551-1000 . . . . . . . . . . . . 209-537 1001-1160 . . . . . . . . . . . . 536-50h 1161-1300 . . . . . . . . . . . . 505-750 1301-1800 . . . . . . . . . . . . 751-1000 The routine sends two-fifteen character messages in for each voucher needed in the batch, the computer assembles this data with data on file and returns twenty-fifteen character messages per voucher in the output phase of the routine. This is considered adequate to print required registers, control figures and voucher checks. A sample: A.batch of five hundred vouchers would require one thousand messages fOr input. Approximately seventeen minutes of input time would be needed for the slower terminals, two minutes of computer time would be required and nearly three hours of output time would be needed on'a terminal of this level. Total elapsed time if no queuing occurred would be about three hours and twenty minutes. The input phase, the throughput phase and the output phase are discrete operations in this branch of the model. This differs from.the purchasing routine in that purchasing seizes the terminal once, and holds throughout but seizes the computer once briefly for each purchase order. 1&9 One additional feature assumes that upon the completion of the throughput or processing phase, an audit trail would be sent to the term- inal for control purposes. It further assumes that 10$ of the batches are in error and the unit of traffic is returned to the process phase after an elapsed time of up to ten minutes is allowed for correction of this error. It would be at such a time that a payroll batch as dis- cussed earlier might get into line ahead of accounts payable yielding a first in, last out situation. P223211 In the payroll branch we have the most experience to Justify the data that enters into the model. The first payroll on our present reg- ional data processing center was initiated in September of 1962. Between that date and January of 1966, eighteen additional local districts auto- mated their payrolls and are currently being processed by the regional data processing center. There is one exception, Waterford School Dis- trict has installed its own computer. Of the present eighteen school districts approximately one-half process their payrolls on one Wednesday and the other half of the school districts process on the following Wednesday. The mix of the size of the districts processing on Wednes- days has come by chance, and by chance has evened out quite well. The mathematical model also leaves this to chance. On the first payroll day in the model, fourteen districts are selected at random to be processed. On the following Wednesday the opposite fourteen districts are marked for processing. This procedure is then repeated on a bi-weekly basis insuring that each district is processed twenty-six times during the year. It is recognized that this is not a real life situation but it 50 provides at this early stage of model building a chance to look at different types of interaction. Payroll days could have been set for each one of the twenty-eight districts. The temptation might have been to set equal loadings per week in which case the interaction would not‘ have been real. The other temptation would have been to load one week unreasonably heavy and the other week light. Again this would not hare been realistic. Allowing the matter to fall to chance once every two weeks insured a look at several kinds of mixes. Every school district in Oakland County is on a bi-weekly payroll period. The typical calendar of events in the payroll application is that time sheets or other evi- dence of attendance is forwarded from.building level to district level offices on Mbnday following the Friday payroll ending period. ,MOndays and Tuesdays are devoted to organizing these source documents, updating the payroll punched card file and arriving at a control figure for this payroll batch. The batch then can usually be ready for computer input sometime between.Tuesday afternoon and Wednesday. On the other end of the period, Friday'morning is distribution time, checks need to be in the district mail to reach school employees at the respective buildings. Thursday then serves one of two purposes; first if there is any prdblem with the payroll it allows time to recover; second, Thursday is also available for*preparation of the checks for circulation to the employees on the fellowing day. .As in the previous two applications, payroll is handled in.the model in a batch mode. That is, the payroll clerk in the local district prepares the payroll in.punched card format and has it ready to transmit. Once it is started it continues transmitting until the complete file is stored at the center in a queue. These departure times are spread over 51 a four and one-half hour period starting at nine o'clock on Wednesday morning. Approximately seven would leave district offices between 9:00 and 10:00 aam. On the average three and one-half batches would leave between 10:00 and 11:30 amms, and the remaining three and one-half would leave between 11:30 atm. and 1:30 in the afternoon. The arrival time at the center would be a function of the departure time, the number of employees and the terminal speed at the district office where the batch originated. In the discussion of input flow there is departure time, transmitting time, and arrival time. Payroll batches have each been assigned priority six which is equal to accounts payable priority dis- cussed in the earlier application. One payroll batch is a unit of traffic. Upon its arrival at the center it is stamped with a time and has a.priority associated with this time. Its priority of six places it ahead of all transactions with assigned priority less than six. The com- puter notes the time and processes the batch in turn. Processing here means using all of the necessary information pertaining to each individ- ual and the payroll as a total. Upon the completion of this processing, an audit trail is returned to the terminal for inspection by the payroll clerk. Up to ten minutes is allowed for this operator function of re- viewing the audit trail. The model assumes that 10$ will be bad runs. If the payroll is considered bad and rejected, up to one hour is allowed for the local district to recover and re-enter the system. Following the signal that a good payroll.has been computed, the unit of traffic than awaits availability of the local district terminal to receive the output from the batch. Computer time is estimated at one hundred twenty employees per minute on the central processing. Returning output is straight forward but very time consuming as the assumption is made that 52 ten times as much data will flow back to the district as is required to flow into the central processor. Voluntary deduction registers, check registers, and voucher checks are standard output for this routine. The mathematical model as built and run assumes that all payroll output would flow back to the terminal of origin. In an operational model it is to be assmed that oftentimes small terminal users would choose to direct this high volume output to a faster terminal by prior arrangement. As in the other applications it is assumed that as payroll batches progress through the quarter, fiscal and calendar year appropriate in- formation will be retained‘ on each employee. Also that an appropriate distribution of expenditures of salary accounts are automatically ac- complished in the computer on days of the payroll batch processing. What about government reports? Currently required are a quarterly report to the retirement fund board, and an annual routine reporting withholding statements to employees with copies going to the internal revenue. These two routines are not programed specifically into the payroll branch or into an individual application. The ability to pro- vide these reports would be an integral part of the system and could be generated centrally for purposes of speed or could be sent to local districts through the file inquiry routine. The payroll applications require only about two percent of the computer time to handle the approximately 15,000 employees in the in- dividual school districts. loading on the individual terminals would vary considerably according to the size of the teminal and the size of the district. The large district with a small terminal would require several hours and the situation then likely would be deemed unsatis- 53 factory. This prdblem.was anticipated and will be discussed further in the interpretation of the results. Student Master File This is the first of three major branches in student record ac- counting included in the mathematical model. Child accounting records are initiated in.Michigan at the time of the school census. This census is conducted between.May 10 and May 31 each year. At that time the pert- inent personal information is recorded for each child from 0-19 years of age. In the beginning this file would be loaded on to central electronic files. This branch of the model is concerned with the updating of the student record for those students actually in school. The volume for this branch is determined by the membership of the school. This file maintenance routine is considered to be a weekly batch process. It is expected that each district would update approximately 2.5% of its stu- dents records weekly throughout the forty week school year. This would be routine maintenance and not the type of updating that would come about through the grade reporting or student scheduling routines to be discussed in more detail in the next section. This activity is sched- uled to be completely at random and occurring on the average once per week per district. The loading on the computer for this activity would be approximately forty-five minutes per week. The loading terminal would vary considerably. Large districts with small terminals such as Oak Park might require up to thirty'minutes on a batch basis. Timing estimates were based upon ninety characters of information being transmitted for each student file updated. It should be noted here that input only is considered in this routine. No output is anticipated. 5h File inquiries for summary reports would be expected to flow from the earlier described routine. Also the grade reporting and student sched- uling routine have extensive reports flowing as output using these files as a source. The kindergarten through twelvth grade enrollments as of October, 1965 are the volumes that are used in the model. (Table 2) Grade Reporting In this routine ample evidence is available concerning the manner in which secondary schools behave in conducting their grade reporting procedures. The school year is typically blocked into six periods of six or seven weeks. Report cards are sent to parents sometime late in the week following the end of a marking period. In the model, Wednesm day morning of the fifteenth, twenty-second, twentymninth, thirtymfifth, fOrty-second, and forty-ninth week following the start of the fiscal year were designated as the start of the grade reporting period. Batches were anticipated to arrive according to the following schedule of days: Wednesday - fOur, Thursday - eight, Friday a eight, Monday - four, and Tuesday - four. The arrival.times within the day were anticipated ac- cording to an earlier described distribution which would anticipate the arrival early in the day in order to complete the batches within the same day. SWmmarizing the last paragraph it will be noted that the grade reporting routine is spread over six periods of the school year. Within each period the individual.batches are spread over five days with four or eight batches being processed on each of the days. Within the day the batches are distributed over a four and oneohalf hour period start- ing at 8:30 atmt each morning. 55 From the information Just presented it is apparent that four grade reporting routines will interact with the payroll days. These four districts might or might not be on payroll on that given week. The expected interaction.would be two per grade reporting period. Out- putting of grade reporting is extensive and this interaction is likely to result in queuing and delayed reports at least in some cases. The distributions discussed to this point are concerned with the start of the batch from the local terminal. The transmission time is again a function of the terminal speed for any number of students for which records must be transmitted. Upon the completion of the sending of the input the batch waits in queue at the center for access to the computer for processing. Ninety characters of input for each student flows to the center. Considerable file organization is anticipated at this time to facilitate the continuous processing of other transactions in the system. The grade reporting batch is divided into twenty parts for processing by the computer. Primary concern at this time is with organizing the file in an appropriate order for outputting the report cards and class lists, the reports connected with the grade reporting period. Upon the completion of this compute phase, the output would be placed in a queue and wait to be outputted to the district. In all previous activity output was returned to the terminal or origin. In this routine it is anticipated that four hundred characters of infbrmation for each student would be needed to print report cards and other data. Even for the smaller districts this would require hours on the slower type terminal. The decision was made to send the output from districts with small terminals to one of two places. The first choice would be to output on a fast terminal in a neighboring district. 56 At the time that the batch is ready to be outputted the fast terminal nearest the terminal of origin is tested fer being busy. If busy, the central.printer is tested for being busy. If'the central.printer is busy the batch then waits for either of these two devices and is outputted to the device that becomes available first. The loading on the computer for this routine is approximately twelve hours to process about 85,000 secondary students. The loading on the terminal is complex and will be described in more detail in the interpretation of results. This is the first routine using the central printer and it is used then only for overflow. Student Scheduling In this routine the pattern of behavior of secondary school person- .nel is well known. Fer a period of the past feur years local school principals and central computer personnel have worked together in arrive ing at a standard calendar of events in the student scheduling routine. .As in other branches of the mathematical.model.the concern is with the entry of the various events into the model, the time necessary to process, and the time to return output to the point of origin or to the designated output terminal. In Oakland County, student scheduling has been for many districts a one-cycle operation with that cycle having its beginning in early spring and extending possibly until late August. A few of the school districts have scheduled by semester in which case there are two events during the year. For this model the following assumptions are made: all districts will schedule for September 1, at the school year start with scheduling taking place for the full year. Each school will be scheduled twice, 57 once during the spring for major planning purposes and again in mid- Atgust allowing for the updating of requests by students resulting from spring failures or summer school changes. The spring activity is sched- uled to start March 1 with input arriving from districts at the rate of one district per working day and spread over thirty working days follow- ing March 1. At the time of the arrival of input, the program will produce a potential conflict matrix and a complete summary report result- ing from the input. In other words, working papers will be returned to the local school district upon receipt of the input. Through-put or the actual placing of students in classes is sched- uled to start April 1. The first attempts to schedule are distributed over the period April 1 to approximately» May 15. Prediction for success of the scheduling is set at 33 l/3$ meaning that on the average each school will have to be scheduled three times. In the event of a failure the school isarescheduled for processing from two hours to six days later. This allows the principal or other school personnel to make adjustments to the master schedule or make contact with students in order to increase the probability of success on the next run. Upon the successful com» pletion of the through-put phase of student scheduling the batch is routed to the output portion of the grade reporting routine. As in the case of grade reporting, output would go back to the terminal of origin in the case of districts having large terminals but otherwise would go the district having a fast terminal nearest the point of origin, or to the central fast printer. This phase of student scheduling should be completed no later than June 15. The next phase of student scheduling takes place the second and third weeks of August. It differs from phase one in two respects. The 58 input is expected or considered to be at the center so that no input phase is required. The throughput phase is scheduled one hour apart for each district and is predicted to be 100% successful as it is pri- marily an updating of the spring scheduling routine. Upon the completw ion of the scheduling on the computer the batch is routed to the output phase of grade reporting as indicated earlier. §EEEEEZ The balance of the routines in the model might be termed house» keeping routines. They serve to set appropriate signals in the model to set appropriate switches for examining the behavior of the various transactions in the model. For example, before any transaction may use a terminal device it must test to determine whether or not the terminal is busy. If the terminal is busy, that particular transaction is placed in a queue. The contents of this queue by terminal are measured and tabulated in the output from the simulation run.« Likewise it is nec» essary to keep indicators set appropriately to determine the month of the year, the day of the month, the week and the day of the week. These housekeeping routines insure that the activity will flow'through the system in the simulation run as nearly as possible describing the real life situation. One additional discrete routine takes a sampling of the status of the terminal facilities every hour on the half hour. This means that . fOrty_times per week the environment is sampled to determine how busy the devices are. This information is tabulated and tables printed out at the end of the simulation run.. The half hour point was picked in» stead of the hour*point to avoid the constant start of the day in which 59 all terminals would be busy in the network communication. If the hour point instead of the half hour point had been selected, once each day all thirty terminals would have been marked as busy. Therefore, the half, hour point was chosen to get a random sampling of the business of the terminals. Many different types of, transactions have been described in the above sections. With much effort and with the aid of a calculating machine, actual loadings upon the computer and upon the several terma inals could be totaled week by week to come up with an anticipated expected percentage of utilization. Such a procedure would be very time consuming and laborious and its accuracy would be subject to ques- tion. Further, no interaction among the transactions could be seen. Only time and experience will determine for certain how such an environ- ment would behave . The simulation of this environment, however, should give clues as to the potential behavior. Procedures would be adjusted in order to make the model run more smoothly. In the simulation run detemination would be made of those areas in which. adjustment in be- havior may become necessary, assuming configuration of a system with specifications set forth in the model. 60 CHAPTER VI INTERPRETATION OF THE SIMULATION RUN The Simulated Calendar The natural calendar could start a July let to June 30th fiscal year on any working day of the week and that first working day could be July lst, 2nd or 3rd. The assumption, purely for convenience was made that the model year would start on a Monday. Successive first days of the month would be entirely at random within the normal probability of the number of working days within a month falling between twenty and twenty-three days. Figure it illustrates the simulated calendar. The random generation of number of working days per month adequately dis= tributed the first days of the month among the days of the week to pro» vide a good mix of different situations throughout the simulation year. Significant cyclic operations are indicated on the calendar. To retain clarity daily and weekly applications. other than payroll, are not illus- trated. In the description of the student scheduling branch, June 15th was established as the latest day that spring student scheduling would be completed based upon a number of probability factors. The model simu» lated completion of the student scheduling as of June 3rd. The calendar requires little interpretation. It provides a con- venient reference for purposes of visualizing the environment as the various activities are being analyzed. “SE‘CZCA *550C3G3C13> HJEUII1§:EUFB'TIEUCD Week 10 13 Figure A. C A L E N D A R As Created By The Simulator Student File Maintenance 61 % Accounts Payable Payroll Student Scheduling 31930351l31<3CDZZ ZJEUIIICDFBCDCD SJPUUUE=IEJCDEUCD week 15 16 17 18 19 23 25 26 id Figure A. (con't.) T W' 111 Grade Reporting 62 FC:233>C4 H153¢>CZ313UJFJTU :2632113>E= Week Student Scheduling Figure A. (con't.) 27 28 30 31 32 33 3h 35 Begins ’ 36 37 OOOOOOOOOOOOOOOO 38 eeeeeeeeeeeeeeee 39 IIIIIIIIII ho Student Scheduling 63 F‘stU’II>> «a»: PUZZCZCq Week Ll h2 LB Ah LS L6 h? LB #9 50 51 52 53 Figure A. (con't.) ll 1' eeeeeeeeee eeeeeeeeee eeeeeeeee eeeeeeeeee eeeeeeeeee eeeeeeeeee eeeeeeeee eeeeeeeee eeeeeeeeee eeeeeeeeee VV I221: 4 File Maintenance Ends eeeeeeeeee Student 4 Scheduling Completed 6h 65 One branch of the simulator program sampled the status of the terminals hourly on the half-hour mark. Forty readings per week were tabled. The means of these tables by week ranged from a low of 2.h to a high of h.9. The 90th percentile ranged from h to 10. On the average throughout the year only three to four terminals would be busy at any one instant, the other twenty-six would be available for non-programmed use . Facility Utilization The concern for optimization in a teleprocessing environment would dictate that each facility have a high utilization while at the same time servicing the transactions entering the system with a minimum of delay. In the early phases of model building, average utilization on an annual basis was considered desirable, however, further analysis of the problem indicated that these results would not indicate on going behavior. Ideally, daily statistics would allow us to pinpoint probable pressures in the environment. A compromise of weekly statistics was dictated by economics. After the computer program was debugged, the simulation of the one year's operation required seventy-two minutes of time on an IBM 1521; computer at a cost of approximately ten dollars per minute. Many hours of an 131 19319 computer time was used in debugging the mathemat- ical model prior to the production run. These considerations dictated accepting the single run at this time. Even as this is being written there is a request to change the facility configuration and add two more program branches to the model and rerun. The weekly utilization tables, it published with this manuscript, would have required fifty-Six tables. These have been omitted and represented graphically in Appendix C . The graphical representation does not include all of the infomation avail- able in the tabled output from the computer but does focus attention on the activity at each facility. The graph represents utilizations at each facility for the entire year with information drawn from each of the fifty-six tables for each graph. Utilization by type of terminal is of interest and will be dis- cussed later. Figure 5 demonstrates another summari zation of facility utilization. This graph demonstrates the range, variance, and mean of remote tenninal facility utilization. The leftmost point in any week records the percentage of utilization of the least busy terminal, the rightmost point records the highest percentage for the week. The difference represents the range and is indicative of the variance. The X is the average utilization recorded for the thirty terminals. The low percentage points vary little from week to week but the terminals registering these low points are the terminals of the smaller districts. The high percentage points vary a great amount. The thirty-fourth week registered the lowest high percentage utilization of fifteen percent. One of the most obvious relationships disclosed is the impact that grade reporting and student scheduling have on the enviromnent. If a continuous line were drawn connecting each high percentage point week by week, the peaks would represent one or both of these activities. Each terminal registering these peaks are districts with high speed printers. This utilization is boosted by sane outputting for smaller terminals. Outputting for smaller districts is shared by the central printer. (Figure 6.) This illustration also demonstrates the impact of grade reporting and student scheduling outputting on the environment. It has been 67 X 50 WEEK +++++5++++ ++++5++++ ++++5++++ ++++S++++ ++++5++++ * AVERAGE 40 EK. 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Ol Fugue 6 101 FAST PRINTER FACILITY UTILIZATION. E m {TI X 0 p NmN wHHOOOOo OO quomeumeoomqompumeoomqom um NNNNNNNHHHHHHH w 0 PERCENTAGE HY WEEK. PERCENT 10 2O 30 40 50 +++++5++++ ++++S++++ ++++5++++ ++++5++++ ++++5++++ +* +* . +* +* +* +****’*****‘ Up 0" Jr \‘a \‘o ‘9 Jo ‘0‘ fl‘ 4‘ ’7‘ 5‘ J- A $1- V'a q‘ :.:: +* +* +e * +***e** eeeeee +** (3:: ’2‘2‘43333 §" fi‘ +* +* +* +* +Ja \b ~‘v J; ‘9 «'5 ”l «'a .‘a « 'rvrq ’I‘fl‘::‘:i‘fl"t‘ +x= e 2:: e 2.: e =:= * =:< =1: e 2: ‘9 'I\ +* * +* 3;: g: 40 +e +e +* +* :z: +****e* ************ +e=e at: exam: *2: ~l, +* +* +*** +*e****ee****= +*****=**:ke +**“*** +** ****** +*** +*e* +**#***ee**ee*** +* ***$**** +* +* +* +* +* +* +++++5++++ ++++5++++ ++++5++++ ++++S++++ ++++5++++ PERCENT 10 20 3o 40 4 Jo do .‘a '4 J: Jo a“ a" a" ’t‘ fl. :l‘: v. \ i e* '\ ”It“ 4) '3 '3‘- q: R )L * * 'n" .x. e m o ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 68 69 suggested that a.modcl change directing all small district grade report- ing and student scheduling to the central fast printer be made. This would have the effect of leveling out the peaks as demonstrated in Figure 5, but would boost the utilization of the central printer. In the actual operational environment options would be available. .A dis- cussion of the queuing problems will support the redirecting of the grade reporting and student scheduling output function. Figure 7 records the percentage utilization of the computer. Aside from.the two functions of grade reporting and student scheduling the loading by week has little variance; a low of twenty percent and a high of twenty-four'percent. The effect of grade reporting and student scheduling is vividly'demonstratcd as is the interaction‘betveen these two operations beginning in the forty-first weak. The peaks reach points ranging from forty percent to fifty-three percent but still could he considered safe. New applications should avoid cycles that would place heawy'burdens on the systam during these peaks. These peaks should be confirmed in an operational system and trends established so that ‘ management decisions involving the upgrading of equipment vould be timely. ' ’ Appendix c is organized alphabetically by district. For discussion of facility utilization, it is appropriate to divide them into three groups. The first group; consisting or Birmingham, Farmington, Pontiac, Royal Oak, Southrield, walled Lake, and Waterford each have high speed lino printers. .These terminals originate and receive in return all transactions involving their on local district data processing. In addition, they receive transactions from.ncighboring smaller school districts roprcscnting outputting functions of grade reporting and.student 100 NNNNNNNNNNHHHHHHHHH omuombumwoomnomewmu UM v-oo 32 w p m menace noecwuuum u N Oomqom uN~Oomvom u b b (fl 3... mm #U mm ow WEEK Figure 7 CENTER PERCENTAGE BY WEEK. 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O.\ I" \I I‘ s'l J4 s'4 a'4 I. ~I4 a‘4 s‘a ~‘4 s'4 ).l ' n'4 5.4 ~l4 ~' Q'4 a» s'a \la 4.~ 4" 4“ 4p 3‘. 4“ 4p 4p 4,» 4I- p . 4" 4'» 4" 4‘~ ’.§ l.‘ I“ q. . J n 1 +35 * >3 >4: 3% 31: =3 =1~ >1: 74: =3 *- >3 31‘ =4: =§= >3 =3 2‘ =31 “ s‘4 ~‘4 a“; «'4 \‘a ~I4 ~‘4 4" 1.! 4" 4'5 4“ ah 4" J4 J0 44 J4 slr J4 \'4 Jo J4 ~14 J4 J4 ' + g: :3 oh J4 J4 s'o 04 J4 ::: "v \" do on do s'r J4 J4 \9 J4 ’I‘ ’I‘ "Q q‘ ’.§ ¢ 4“ II. I“ 4r :,1 .I 1" 4's 4" 4* 4'. or I“ ~I l I g . I «3 >.< =3 =3 =. =.< 2: =I< ii: =.'< 4! ‘4: * =3 =3 * =§~ 3.: 3’5 3;: 44 I v o I, .I a *¥***¥*¥****m%**4¥*4 *4 J: l< >14 a'a s'4 «I— ~'u '4 J— .2 J4 “a \‘4 s'l J4 s'o s'd eh ~|4 \ 4' 3' l‘ 4,. 4'5 4‘. 4's ).~ 4" 4' 4" 4‘s 4;. a" 4'5 0" 4f; 4" 4.- ' al4 \I‘ do J4 J1 alt "4 J4 Jo \‘r sh §‘f J4 \I4 al4 ~' J4 )Io "- J: 4.. a‘ 4'\ 4“ a" 4' a“ 46 4.. 4“ 4r 4‘. 4'\ a" 4" fi‘ If .s l" I‘- +~|4 ~‘4 J4 U4 \‘4 a" J: ‘II )‘4 ‘9 J‘ 0 J \I4 a‘t ab 44 sh ~‘v ’V‘ ‘V‘ ’0‘ ’l‘ ‘1‘ '0‘ ’I‘ ‘6‘ I‘ '1‘ W ’I‘ ' 'l‘ 'l 'l‘ 'I‘ 'I‘ 'I‘ '7‘ I , .I +¥*****4************* ~54 4 s a 4 ‘14 \ e .0. I I **~*tt+e$*#****¢m$x* 4‘ *e J4 ~'4 J4 J4 o'o ‘54 J4 §|< \‘4 \‘4 J4 J4 a’4 s'o *4 J1 J4 n'4 + 4‘ s I" 4" 4" r" 4.\ 4" 4" 4' 4's 4" 4'- 4's a" or a 1'- 4p 4“ +*****$** ***=$***$** * +* '**************s*** **.**$***2$********* +***'***$************ +*******************$ +******************** +*************** ***** +****************M ** +***************** ** +**** *t**** ******** +*****:**** **%<** **** +** *************** +*************$****** +* *$*********** $***‘ +******************** +*********‘******* +*******************. +********** ******** * +************‘*****$$ +********‘$*** ****** +** $******‘*** '***** +*#******* +****** ***k********* +** *********** ***‘** +******************** +* *********** *** *** +****# *#**** ******* +*****»***********=** +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ PERCENT 10 20 are 4‘. q. * :3 0 J4 :I“ do it do "F 5’4 J4 do a" t" or J I '*¥«"ra‘ J4 4“ \" n ** * * J4 J4 \Io q. \‘4 4's W***$*' ** 0" ~" :' :5: 44 do 'I‘ 5‘ 44 J4 4‘s a" 490 = 4" * I ,1: 3:: J4 vc *** 4. a. -~—o~ ** =‘.=** *** *** *** ** .1. a. 'v tr *** *=* web.» rm'r *** **** **: s" 2: :k ..: ‘0. \‘f 4's do 4.. d. 4.. 'ch 4" 30 m:~*s J4 4" ‘I' "‘ Jo 5'4 I'~ do or J4 ’.. ~‘4 al- J or. Jr 4'. 9'4 "§ * s'4 ‘I‘ ’I‘ * J w~---~~ '********** 44: ~b a" ******************* 4's s‘o 4" J4 fl.\ \'4 4" \I 4 - I‘ hi4 of .I' :9 .I. a" p s‘o ‘14 J ‘I‘ '1‘ a fi~ J4 a" s.— as \‘4 4.~ 04 "~ 3!: ~‘J 4" Jo Ar oh 4’ .o 'r \‘4 “I * ‘I4 4" 30 4" 04 ‘.~ J4 4'. NI! re .5. er ‘.4 4.~ * J4 oh ‘I‘ J: ‘P a. - «‘4 4.~ slo or ‘9 O \‘4 ‘I‘l x: * Q.' 4 J4 '1‘ ~34 'r .9 veer 04 4'5 ‘b q. do '7‘ I, at. s 4" ~'4 h'r ~‘4 .I, ‘I, \‘4 ~la 9, 4r 0" =:: 4.. 4‘ 4. FACHJTYtflWLIDHWONo 40 +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ :: :Q.’ J4 J4 U4 J4 't a 4“ t“ 1" 4 J4 J4 u: 3“ 'v 'I‘ '4 J4 04 J4 J4 \ ". f'fi fl. "‘ I I *¥*= ‘4 04 d4 Jo \ Op 4‘s 4" ~\ .,. z: ::: :1: :fit'” .,. J4 Jr O ::< of "§ 40 +++~+++++~++++~++++-h++++s~+++++~+++++~++++4~++++ o ++++++++++++++ m F) () 44 oh do do I‘ o.\ a" 4's 1“ 71 scheduling (see Table 3). The profiles of utilization of each of these seven demonstrate the sensitivity to grade reporting and student sched- uling functions. All appear within a safe range even during peaks. Royal Oak.management might wish to weigh the advantage of doubling printer speed or ruling out other districts gaining access to their printer. The problem is highlighted in the discussion on queuing. The second group to be considered includes Berkley, Bloomfield Hills, Ferndale, Hazel Park, Oak Park and Rochester. Each of these districts was assigned fifteen line-per-minute terminals. The profiles of utilization for these districts indicate considerable variance from week to week although all remain in a safe range. This variance to- gether with growth in volumes and the addition of applications might soon push utilization beyond a safe point. Also, as modeled, these terminals do rely on neighboring fast terminals for volume printing. This printing volume plus current levels of utilization suggest the need to consider upgrading terminal power for these districts. The balance of the smaller districts or the third group all ap- pear in a safe range. The reconfiguration suggested in the previous paragraph would even have a favorable influence for this group by pro~ viding additional printing power for the entire system. Queuinngesults Each week from fifty to eighty units of traffic originated at each terminal in the system. The time of origin of each type was dew pendent upon the controls on that type in the model. Some were at quite specific times, others were almost completely at random and there were many degrees of control in between. The probability of a unit of traf- fic being serviced immediately was dependent upon the demands being made on the terminal. Is it in use? If so, how long? Are other units of traffic waiting to be serviced? If so, how'many; how long; what prior- ity? During the first fifty-two weeks of the simulation, approximately 100,000 units of traffic were serviced at the terminal facilities. Table 8 records the distribution of waiting times for these transactions. TABEE 8 DISTRIBUTION OF TERMINALHHAITS FOR.APPROXIMATEEY 100,000 TRANSACTIONS Minutes $ Cumulative $ Less than % 21.8 21.8 1 1i no.8 62.6 1;2% 10.6 73.2 2?..3 6.1 79.3 3 A; 3.0 82.3 h 5 2.2 8h.5 5 6% 1.9 86.1: ‘ 7 1.8 88.2 7 2% 1.2 89.11 2 1.8 91.2 10% 1.1 92.3 1 11,: .9 93.2 132:1} .9 91.1 12?].3; .7 91+.8 13?.1141? .6 95.14 1h—-15- .h 95.8 15 1 .6 96.h Over 165 3.h 99.8 Approximately 62,600 of these 100,000 transactions gained access to their respective remote terminals in less than one and one-half minutes. .About 96,hOO gained access within sixteen and one-half minutes. Over 3,hOO transactions waited in excess of sixteen and one-half minutes. Would this be acceptable? Closer examination of the output data reveals 72 73 isolated waits of two hours or more. Further analysis of queue statis- tics reveals that the transactions waiting in queues are predominantly file inquiry and network communication transactions. A fair share of other transactions are waiting but in an operational environment would be under greater control. Critical file inquiry and communication trans- actions would be given.priorities in an operational environment to ease this prdblem. The above arguments are presented as ways of accommodating re- strictions. More appropriate to the present is the evidence for suggest- ing different facility specifications in certain parts of the configur- ation. The queuing prOblems of the districts with fast printers could be eliminated by the addition of limited purpose typewriter terminals. The small terminals could be dedicated to Job rated applications such as file inquiry, summary reports and communication. The queues developed at the terminals of the medium size districts indicate a need to examine alternate facilities. A product gap in printer devices prevents speci- fying any particular printer speed at the present time but industry announcements of new equipment would indicate improvements are ferth- coming soon. Application queues were recorded at the terminals and at the com- puter for several of the applications. Queuing at the computer does not appear to be a.prdblem. beimum waiting lines rarely contain greater than two transactions, the exception occurring at grade reporting time when the length reached six on one occasion. Sizeable application queues do develop at the district terminals for the three applications of pur- chasing, file inquiry and communications. Each of these are daily appli- cations and this queuing could be expected to develop at heavy batch 7h processing times. These queue lengths emphasise the need for controls on accessibility and on.priorities. Program.Applications Getting a Jab completed within a reasonable time period is a concern of the school employee charged with a specific responsibility. There are appropriate times for each of a number of steps in the init- iation, preparation, processing and completion of any given batch type job. It is extremely important in this mathematical model to determine if, in fact, the various phases were completed within appropriate time elements to serve a real life situation. Figures 8, 9, and 10 do reveal this evidence for three of the critical repetitive applications. The simulation calendar (Figure h) supports this evidence and reveals evi- dence of meeting deadline dates for student scheduling and grade report- ing. One of the applications where time is critical is payroll. Nine o'clock Rednesday'morning is marked as start time. Preferred results 'would be to complete the processing within the balance of the day. Figure 8 illustrates that this happened in the model about one-half of the payroll days. During the other weeks payroll processing overflowed to the next day, incidentally, conflicting with the daily 8:30 atm, net- work communication application. .Although overflow of the application occurred this often, only the computer and one or two terminals were involved by the overflow; The mean transit times for payroll batches varied from a low of one and one-half hours on the thirty-fourth week to three hours on the fourteenth and thirtywthird week. Input specifi- cations to the model set a .100 factor as probability of failure. In X 3:: MONTH JULY AUG SEPT OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY Figure 8 DISTRIBUTION OF STATISTICS OF PAYROLL BATCH PRICESSING 14 BATCHES PER WEEK AVERAGE TRANSIT TIME Z - 90 PERCENT COMPLETED ELAPSED TIME FROM FIRST BATCH ARRIVAL TIME TO COMPLETION OF LAST BATCH *5 TO THE RIGHT OF 7 1/2 HOURS OVERFLDWED TO THE NEXT WEEK bumucoxonbumH o—Ig-nt-‘HH Nme—IHHH .HOOmuom H O U R S l 2 3 4 S b 7 8 9 10 ++++.+++.+++.+++.+++.+++.+++.+++.+++.+++. + I + + X Z I * + + X Z I * + + X Z I + + X Z I * + + X Z I * + + X Z I t + + x Z n I + + x Z I + + X Z i I + + x z ' + + X Z * I + + x Z t I + + X Z I + + Z I + O O O O O O O O O O + X Z l * + + X Z *1 + + x Z I + + X Z 1* + + X Z I + + X Z I 'r + + X Z *1 + + X Z I + + X Z I + X Z I + X Z I + X Z I * + O O O O O O O O O 0 + X Z I * + + X Z * I + + X Z I t + + X Z I + + X Z I * + + x Z I + + X Z I + + X Z * I + + X Z I + + X Z I + X Z I * + X Z I + X Z I + O O O O O 0 O O O O + X Z * I + + X Z a 1 + + X Z I a + + x Z * I + + x Z t I + + x Z I s + + X Z t I + + X Z *I + + X Z * I + + X Z s I + + X Z * I + + X Z t + + X Z s I + + X Z * I + + X Z * I + + X Z * I + + X Z I * + + I + ++++.+++.+++.+++.+++.+++.+++.+++.+++.+++. 1 2 3 4 5 6 7 8 9 10 H 0 U R 5 DAY 75 Figure 9 DISTRIBUTION OF STATISTICS OF ACCOUNTS PAYABLE BATCH PROCESSING 3O BATCHES PER MONTH X-AVERAGE TRANSIT TIME 2-90 PERCENT COMPLETED M I N U T E S 60 120 180 MONTH ++++++.+++++.+++++.+++++. WEEK OATCHES + + JULY 1 24 + x Z + 2 6 + X Z + 3 + + a + + AUG 5 21 + X Z + 6 9 + X Z + 7 + + 8 + + SEPT 9 10 + X Z + 10 20 + X 7 + 11 + + 12 + + 13 + Z + O O O O 0 OCT 14 27 + X Z + 15 + + 16 + + 17 + + NOV 18 14 + X Z + 19 16 + X Z + 20 + + 21 + + 22 2 + XZ + DEC 23 28 + X Z + 24 + + 25 + + 26 + + O O O O 0 JAN 27 18 + X Z + 28 12 + X Z + 29 + + 30 + + FEB 31 10 + X Z + 32 20 + X Z + 33 + + 34 + + 35 + 4. MAR 36 22 + X Z + 37 8 + X Z + 38 + + 39 + + O O O O 0 APR 40 8 + X Z + 41 22 + x Z + 42 + + 43 + + MAY 44 a + x z + 45 26 + X Z + 46 + + a7 + + 48 + + JUNE 49 13 + X Z + 50 17 + X Z + 51 + + 52 + + JULY 53 9 + X Z + 54 21 + X Z + 55 + + 56 + + + + .+++++.+++++.+++++.+++++. 60 120 180 M I N U T E S Figure 10 DISTRIBUTION OF STATISTICS OF DAILY PURCHASE ORDER BATCH PROCESSING ISO BATCHES PER WEEK X-AVERAGE TRANSIT TIME Z-9O PERCENT COMPLETED MONTH JULY AUG SEPT OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY S m um 71 HHpF-P NF‘OOZDNOUIp wmuoomuompwm 23 M I N U T E s 5 10 15 20 25 +++++.++++.++++.++++.++++.++++. + + + X Z + + x Z + + x Z + + X Z + + X Z + + x z + + X Z + + X Z + + X Z + + x Z + + X Z + + x Z + + X Z + O O O O O O + X Z + + X Z + + Z X + + X Z + + X Z + + x z + + x Z + + x Z + + X Z + + X Z + + XZ + + x z + + X Z + O O O O O O + x Z + + X Z + + X Z Z + + XZ + + x Z + + XZ + + X Z + + X Z + + X Z + + X Z + + X Z + + X Z + + XZ + O O O O O 0 + X Z + + X Z + + x Z + + X Z + + XZ + + x Z + + X Z + + X Z + + X Z + + X Z + + x Z + + x Z + + X Z + + X Z + + X Z + + X Z + + X Z + + + +++++.++++.++++.++++.++++.++++. 5 10 15 20 25 M I N U T E S 77 78 fifty-two weeks seven hundred eight payroll batches were processed; an estimated seventy-eight failed once delaying or prolonging process time. Seven or eight might have failed twice, perhaps one failed three times. These occurances would help to account for the few batches re- quiring five or more hours and for some of the overflow to the next day. Figure 9 indicates the flow of the accounts payable batches through the model. This application was given a.priority and would have to vie only with payroll for access to facilities. There is no apparent evi- dence that servicing of this application caused any significant pressure on the system. Most accounts payable batches entered and cleared the system in two hours or less. The daily purchasing activity (Fi 10) rarely required more than fifteen minutes even during the summer months when data transmission was heavier from this application. Summagy The computer output from the simulation run contained over five hundred pages of printed tables. The graphs and tables in this chapter and in Appendix C are summaries from many of these tables. Man months, if not man years, would be required to interpret these results in de- tail. .At this point in time and preciseness of environmental descrip- tion, spending that amount of time is not warranted. Further interpre- tation of these printouts will.be helpful in arriving at a new config- uration for resimmlation purposes. Each district could weigh how the present configuration would perform for them, weigh the advantages of 79 other facilities and arrive at a facility specification tailored to meet the local district requirements. CHAPTER‘VII CONCDUSIONS AND RECOMMENDATIONS Introduction The rate of development of the technology of automation is so rapid that possibilities considered remote at the beginning of this study nine months earlier show promise of becoming reality within the period of the next one to two years. The Teleprocessing Feasibility Study involving seven of the larger local school districts of Oakland Schools was con- ducted during the months of September through December of 1965. During the months of January through.March, eleven of the remaining districts conducted similar studies involving the same applications but on a smaller scale due to their smaller student enrollments. Four additional districts are in the process of conducting independent studies to deter- mine the feasibility of involvement in the teleprocessing network. At this writing each of the local districts is in various stages in its decisions to commit resources to the development of the teleprocessing network described by the mathematical model. Some, at least five dis- tricts, have passed board resolutions and included resources in the next fiscal budget to prepare for the establishment of the network. Other districts have board resolutions pending and still others are awaiting the outcomes of staff studies. The appropriate timing of this study is self-evident. This initial simulation run presents significant data, not to make the final decisions 81 but at present to better realize the factors in the decisions that need further study and analysis. Conclusions Mathematical model building and simulation in the field of educa- tion is in its infancy. This model of a teleprocessing network to serve an educational environment is but a sample of one. Extreme care should be taken not to generalize based upon such limited experience. Never- theless, the complexity of the decisions facing today's educator and educational administrator mandates using more sophisticated techniques to clarify the issues. As stated earlier, data presented. in this study represents the out- put from a first simulation. Results should not be considered conclusive in every aspect, but the relationship between the parts can be tested further even if input data are only estimated. The first refinement of the model would adjust terminal power to overcome certain observed pres- sures in the system as determined by the first model run. The further refinement in the model would focus more closely on applications. Evie" dence from the computer output indicates that grade reporting presents one of the most significant pressures on the system. A series of ques- tions might be asked. Should power of facilities be boosted to account)- date one problem application? Should constraints on accessibility be applied or increased? What are possible options and their respective costs? Further refinements in the simulator program to run the model could test the appropriateness of suggested model changes. The cost of using the present simulator program to simulate the environment for full year cycles is relatively high. New programs pro- 82 mised by industry and new generation computers Will diminish..this_gproblem but for the inmediate future some attention should be given to building the model to study the environmental behavior in more detail over a shorter cycle. The present model develops weekly statistics for fifty- two weeks. This is needed to describe the cyclic activity that occurs relatively few times within the year. To supplement this overview, a. technique to focus attention on the hour by hour or even minute by min- ute enviromnent is needed. 3 The above statements refer to only a few conclusions that can be drawn from an analysis of the data generated by the model. Overall, the data generated verified that all program branches were functioning as specified and that transactions were being processed in an orderly fash- ion, given the various conditions assigned to each type of transaction. The importance of this can be emphasized by relating an occurance of one 'bad' run. The simulator program has a capacity of containing a max- imum of one thousand transactions in all blocks at one time. In this particular 'bad' run, one type of transaction was entered prOperly but was held in a loop of Just a few blocks in the flow diagram because of erroneous coding. Since these transactions could not leave, they con- tinued to accumulate until the maximum of onethousand halted entry of any new transactions into the system until others had left. This occurred sometime in the simulated month of December. For the balance of the year one thousand transactions were in the model continuously. Output from that point, forward was obviously had, but the simulator continued to operate the model with these restrictions. The final run did yeild out- put that described the environment that the builder expected. Conclusions related to individual districts, applications and con- 83 figurations would necessitate involving local district personnel. Ex- pectations of performance based on the present model, readiness to utilize program.applications and budgetary considerations of each local district- would contribute to conclusions and recommendations for each district. Prdblem.Areas The electronic components assumed in the mathematical model are available from the computer vendors at the present time. The systems support to implement such an operational environment is also available at the present time. The commitment of industry to establish an imple- mentation schedule will be a part of the bid specifications when invita- tions to bid are submitted to the vendors. This is a basic problem. Industry has not as yet committed technical staffs to developing pro- grams oriented toward accommodating the needs of the education community in teleprocessing. Computer programs to simulate mathematical.models of the complexity of this model are not user oriented. Too much time elapsed between the beginning of model building and the computer simulation. Progress is being made in this area. School administrators in general lack knowb ledge, training and experience to exploit scientific management techni- ques as tools in management decisions. Industry provides technical training fer top and middle management to exploit the advances in tech- nology. The single fact that industry is producing at an all time high rate while maintaining low inventories attests to the success of their management training programs. The lack of a similar commitment to train school administrators to an understanding of the potential of automation in school.management is a significant problem. A related problem is the lack of adequately trained specialists to staff new roles that are currently developing in educational data process- ing. Many of the problems are related to the single observation that technology as related to equipment is advancing at a rate faster than the consumer can implement. If the consumer is to gain ground a greater comitment to accomplish this end is needed. Recommendations For the inmediate future, Oakland Schools and its constituent disc tricts have available a scientific management tool that has the potential of aiding in the definition of a configuration of equipment to achieve the ends defined in the mathematical model. Modifications should be made in the model reflecting these new estimated and other known information. Better estimates of volumes are now available. Additional applications are needed in the model to accommodate the constituent districts. Also for the imediate future, effort should be applied to upgrade sinulation as a tool. First, to enable the user to prepare input with much less effort; second, to supplement the detailed computer output of the simulation run with sumnary reports. It would be especially valuable to have reports graphically displayed. The educational comnunity, including state departments of education, colleges and universities, intermediate and local districts should give : attention to an apprOpriate training experience for present and future educational leaders in education. Even before the mathematical model becomes in fact an operation model, it 18 known that it must remain fleXible. It must be readily 85 adaptible to changes in volumes, organizational patterns, new appli- cations and any other influences on the environment. Data to build this model were difficult to obtain, some of the data are best estimates. This does not have to be the case in the future. The operational model can accumulate data relative to its own behavior, store that data, and periodically'project what its future behavior will be based upon simul- ation runs using automatically accumulated precise historical inferna- tion. Systems design personnel should include such plans in the compre- hensive control program in the operational model. .3292! Simulation has been demonstrated as a mathematical analytic tool for decision making. It has not been demonstrated that a solution can be feund to a given problem but that mathematical.model building can provide a vehicle fer clearly defining the various factors of the prdb- lem. It can'be used for testing the interrelationship of these factors, and fbr testing the sensitivity of behavior when changes occur in the various factors. This demonstration has been conducted in an educational administration environment. The demonstration has presented evidence that a teleprocessing network can.bring the advantages of present day technology to children in school districts whether large or small. The demonstration has further presented evidence that this same technology can.provide tools for management decisions in education as readily as other governmental agencies or business and industry. APPENDIX A FIDW CHARTS OF THE MATHEMATICAL MODEL: A 'I'EIECOMMUNICATIONS NETWORK FOR DATA PROCESSING IN SCHOOLS 87 NEI‘WOM COW’IUI‘IICATIONS E“ e ”l 7.78 Ito Born NEIwosK COMMUNICATIONS (continued) 125 7W @ 134 m Zol Macaqu: 202.. 105' FIIE INQUIRY .2 (a 240:0 89 PURCHASE ORDER OUTINE of 56Pr— A mu. 90 91 PURCHASE ORDER ROUTINE (continued) 334 guns 33f 336 50/ 21800» 111400, ,c I {3! Bar” PAYROLL ROUTINE 92 PAYROLL ROUTINE (continued) 93 91+ PAYROLL ROUTINE (continued) 95 PAYROLL ROUTINE (continued) 96 PAYROLL ROUTINE (continued) J69 551 1 557 l 6’58 #6 o F [ at! 556 _ 97 PAYROLL ROUTINE (continued) ACCOUNTS PAYABLE ROUTINE loo:Fsz. bl! 98 99 ACCOUNTS PAYABLE ROUTINE (continued) 626 *7 O *8 539 ACCOUNTS PAYABLE ROUTINE (continued) ® ‘37 [10:0 0‘00 m * a m . 631 a lOO lOl MASTER FIIE UPDATE ROUTINE ‘ 5‘6 18200: to 102 MASTER FILE UPDATE ROUTINE (continued) STUDENT SCHEIIJIING ROUTINE l‘h K30 2w 7.1; 1% 103 10h STUDENT SCI-IEDJLING ROUTINE (continued) 105 STUDENT SCHEDULING ROUTINE (continued) 175' “520: Pu I STUDENT SCEEIIJIING ROUTINE (continued) 106 107 GRADE REPORTING ROUTINE 50 In 120 6': I L’s- no Born 5:. GRADE REPORTING ROUTINE (continued) 108 109 GRADE REPORTING ROUTINE (continued) llO GRADE REPORTING ROUTINE (continued) l7! i3 lll SUB-ROUTINES 7o [£0313 mm Ca.) 24: 573 $5 $"§?:§‘m "7'? 5’: "7 112 TIMEKEEPING ROUTINE 113 TIMEKEIEPING ROUTINE (continued) Q 7? 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PERCENTAGE BY WEEK. PERCENT 10 20 30 4O 50 +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++S++++ +* +* +* +* +* J; ... +* +* +* +::: +* +* +* +::: 2: :1: :,‘: :1: :1: ::: ::: :}: ::: z}: 2:: :1: + :3: 2:: ‘4: >:: :t: 2:: ::: :I: :{z \'o l.‘ * 7: 4% y. .31. ‘9 pp s'o t.‘ ** % . .l 3:: -l< a: >i= >§= =1: =’.= 3:1 >{< #1 * Jo .,. +* + ::: +* + at: 2:: 2:: :i: :5: :fi: :1: :1: :2: ::: +2: ::: ::: :;: :t: ::: :1: :;: :1: :fi: :1: ::: + ::: do a. +* +* +* +* * a: 2:: =:< z: ::: =:: 2: >1: =:: ::= 2:: +****** +* +* +* +* +**** ************* +********* +*** +***************** +********** +****** +** +****** +*** +*** +*************** +******** +* +* +* +* +* +* +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ PERCENT 10 20 30 40 o ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ m 160 161 FACILITY UTILIZATION. AVONDALE 01 PERCENTAGE BY WEEK. 30 4O 50 WEEK +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ 20 1 () PERCENT :7 Jo .9 4' u o'. 4" ’0‘ 's o" o. 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II II II II II II II II II .I II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II nu II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II 1; II II II II II II II II II I II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II I II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II I. 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()23 ()lt C) 55 ()(3 7890123456789012345678901234 OOO1111111111222222222233333 02 WEEK 0C) NH O (1) HO OOOOO \OmflONflRURM‘OOGLQOm¢WMVFCMO NOWNEN OJ uuquNNNNNNNNNNHh‘HHHt-IHi—IH O‘ PUNHO b JMPPmOHd M 9 Nuoomq U1 ¢¢¢p¢ a omuom w meHMflm U’IPQJNHO m 0 WEEK BERKLEY FACILITY UTILIZATION. PERCENTAGE BY WEEK. PERCENT 10 20 30 4o 50 +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++S++++ +**********************# +************ +********** +********'********** +******z**~** +********************* +*#**************$ +********* +**=¢=* II ~=:=='.==:< +*********$******<***** +********* +******************' +****** ##IIIIIIIII +************** +****************** +******=*****$***~* +******************** +************** +*******$**** +****$******** ****“ +********** +*******#***************** +***~* #****************I*** +********** +*******$***********'I* +****#****** +********** +********~************ +***************** +**** **'*********#*** +*******#************* +************* +******************* +********** +************I*****I** +********************* +**********#******* +*#***************** ***** +********* +****************** +*************** +***************************** +********** +***************** I +************* +#****************** +******** +****************** +**************** +****#********************* +********** +***$**************** +************* +****************** +********** +*****************$‘** +++++S++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ PERCENT 10 20 30 40 o ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ m 162 J“;- 9% “f 03 NNNNNNNF‘HHHHHHHH Owkumwoomqombump 27 ,+*********** BIRMINGHAM FACILITY UTILIZATION. PERCENTAGE BY WEEK. PERCENT 10 20 30 40 50 +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ +*#********* . +********** +********** +*****#*** +************ +********************* +************ +******* +*********** +************ +********** +********* +*********** +***#***** +********** +*********************** +******** +**#******** +*********** +*********** +********* +******#****#******** +************* +************ +*********** +********* +********** +********** +**************#********** +*******#** +*********** +**#****** +********* +********* +********************* +********* +********* +**##******* +************ +*********** +**********#* +*****************#*** +**#*****#******#****** +********** +#********* +**#******* +********* +********* +***#**************** +*#*********#*** +************ +**#**¢*****#**** +********* +********** +********** +++++s++++ ++++5++++ ++++s++++ ++++s++++ ++++5++++ PERCENT 10 20 3O 40 o ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ CI 15.3 04 X NNNNNNNHHHHHHHHHHOOOOOOOOOm ombumpoomflom¢umpoomqom¢umwm 27 BLODMFIELD HLS FACILITY UTILIZATION. PERCENTAGE BY WEEK. PERCENT 10 20 30 40 50 +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ +**************** +********************* +************ +***************#*** +************************ +************ +********************* +*****#**** +********** +*************** +*****:********* +*********** +********* +********************* +****************** +*************** +****************** +*********** +********************* +********** +******************* +************$*** +********************** +********** +********** +***************** +********* +************************* +***************#******** +********** +*********** +********************** +***************** +******** +**************** +****************#***** +********* +******************************* +********** +******************* +***********#****** +******************* +*#*************** +****************** +************** +******************** +*********** +****************** +*******************#***** +************* +********************* +#********* +*******# +********************* +****#*** +*#***************** +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ PERCENT 10 20 30 40 ********* **$$ 0 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 01 16h OS 08 NNNNNNNNNNHHHHHHHHHp—ao \OmfloWfihmfihdooahflwmhUNM‘OO pxxpwouxwounwouuw fVHO¢flDQOUMMMUHO aa bu hpppc omqom mm HO munnmm OWWPNN WEEK BRANDON FACILITY UTILIZATION. PERCENTAGE BY WEEK. PERCENT 10 20 30 4O 50 +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++S++++ +**************** +*********** +*********** +********* +********** +::< :3 :3: :,’: >:: ::: ::: :;: :1: a}: :',: 2: +1: a." . :',: 2;: =4: z}: >3 ::: 3:: ****$$*** +* 2:: =2: =:< 2; ::= :3 =3 =:: ::= a: 22 +::: :4: 3;: ::: 3:: :3 2;: ::: >;: ::: :;: :1: :1: :k :3 ::: z}: ::: 3:: ::: :;: :3 :;: :1: +********** + :3 :k :;: ::: :fi: :k :3 :;: a: :i: +>:< x: 2:: 2:: a': =:: ::= =:< a: 2:: 4: =:: =:< *********** :k 3': :k :1: 3;: 3:: =2: :.',: ::: :.': :;: +********** * *******¢ do ~b ' \‘l «'4 Jr b J. ‘r J s'r \‘4 on» *‘r‘fl‘ - K‘» 3v «"9 4‘ +********** +2: 3:: 3;: 3;: :3 :;: ::: ::: ::: +:;< 3:: :,‘: 3;: ::: :1: 2:: :1: :‘,: :;: ::: +* 3|" 3k 2: * 'r * * 1:5 :3 :l: * ’t‘ :,': :4: 2:: :;: :i: :3 g: >:: * x: :{z +*‘**$*** +********* .9 "t 40 'a I, sh \‘o \‘r '1‘ 6‘ n~ 3» ’u- '1‘ +*************** +************** +******** +********$ +*°*******~4: +********* *****2** I +*:******* +********* +********** *********x U 0" a" A: I a! a. o I \ I n \ * s" '0 %* +********** +******** ******* +********** +******** +** ******* +**************** +*********** +********** +********** +******** +******* $** +************ +**z********* +************ +************** +********** +********* +*********' +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ PERCENT 10 20 3O 40 o ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ m 165 06 N“NVNRHDNHthHH»Mdequ Om¢uN~O©mflOm9uNHO© 27 CLARENCEVILLE FACILITY UTILIZATION. PERCENTAGE BY WEEK. PERCENT 10 20 30 4o 50 +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ +:k :: 2: ::< :k 3:: >:< 2: :3 :;: >3: :1: ::< +***************$*** +******$*** +3.‘= 3%: "4: =3 3:: =4: =4: =:= :3: *2: =1: =i< =:= ** +*************** +*********$*** +********* +::< >;: 3:: 2:: :‘,: :;: at: >:: z}: 3:: :1: ::: :;: :fi: 1:: ‘4: :‘.< z:: :1: :2: ::: :1: ::: ;:: :;: +* 3;: a}: >:: zit :z: 3:: :k ::: 1:: :i: ‘4: ::: :;< +********** +************** \b 'a do Jr s'a s“ s" \‘O J. Jo -'o U. do .9 do ~' i.’ '0 «lo do s'l \' J! u’; Jr \‘5 +vv~ '5'P3v'r'u‘fi‘fl‘ ‘v'r'r'u- +$*****$*$$****** 3:: *****5':* 9133303 I . +*****‘*$* +* =k >:: at: 3‘: 2: =:: 3:: z.‘= =:= =:= 9.: 2:: =:= =3 =:: +******$$******$ +********x I +************* +********$***$ +********$**** ~'— s. .a \‘o g'a ‘- ~'r 04 ‘1‘ sin .Ip +* * 0" I" :p 9“ a.» >I‘ 4" OP 0" 0" If .‘a \I; J: Jv s'a .‘o ~‘o a" s'c .‘p .31 0" qt 0" p" o" a... cf 1" fi\ 4's 4" ’f‘ +* 'I ~‘ .‘o ~'a s'a J" J. \’a s'o \" \‘0 x. 4 O" 0" o" .s t" 4.. 4“ on 5" ~" d; Jv J: J! s‘v do do J. J; \‘v "a "Q ‘I‘ or v... q. of as o" q. ‘ 'O‘ v.5 t" ‘. \ ‘3? ‘X‘ I +*<****$******* +*********$******* +********* ********$* +***************** +********* +******* ****** +******:* +*************$***“ +************ +******** ***** +********* +******************** ****$******** +********************** +*********** **** +********* +********** z: +********** ***** +**********#**** +******** +******************** +******** +**************** +************* +*********# +****************** +********** +**************** +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++S++++ PERCENT 10 20 30 40 \ o ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ m 166 07 WEEK 00000 meNH 0000 OQNO NNNNNNNHHHHHHHHHH OmwawoomqombumHo 27 CLARKSTON FACILITY UTILIZATION. PERCENTAGE BY WEEK. PERCENT 10 20 30 40 SO +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ +****************** +********** +2: 2:: 2:: :3 >’.= %: =:< «~ :3 ::< >:: =:: =:< x: =4: +******** +*********$ ' +**********$*“***** +*******“* +*************** +******** +*************$******* +***********$***** +*****$$* +******** +*****$**$* +********$¥ +********** *******$ +****************** ******* +**$*******¥****** +$$$$$$$$$$$$$$$$ +*****=<** +*********$***********<** +**'**** **********“ +*** ***$** +*********' ********** +**********‘ +********** +**$******* ***‘******= +*********$* +******** +************** +**********#**** +************* +*** *******#************* +******* +*******#****$*** +*************** +************** +******************* +******** +************* +************** +*********** +#**************#* +*********** +********************* +*************** +****#****** +**************** +************* +*************** +********** +++++S++++ ++++5++++ ++++5++++ ++++S++++ ++++5++++ PERCENT 10 20 3O 40 w********* ************ I ~ . I \ \ a \ l - - .‘L s g n' "3" * ’o \ fl \ W \" k \ '*** 'n' * **** *% *%* a; * * k m 0 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 167 08 01 v‘OOOCHWDOO (DOWQOWWPuN (”WU-10.! NNNN NNNN NNHHHHHHHfi—IH wmwocmwomhwmwoomuompump mm mp puwwm Oomuo 0103014594}? ##9## NHOxOOEflO‘UI-PQINH WUHDW OWPWU WEEK CLAWSON FACILITY UTILIZATION. PERCENTAGE BY WEEK. PERCENT 10 20 3O 40 50 +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ +>:==c:*=:<*>:<:'s:.~.::=* 2: x: +* ***************** +:;: * 3:: z}: :;< :'.: :,‘: :t: 2;: :1: :;: :1: :k :;: ::: ::< +************ +*'************ +************* +********* ***********z** .‘1 \‘a 'a s'a \la a J; s'a J: "o I + * u‘o "c \‘v ~|o ~‘a s" ‘9 sh \‘5 ~’- s‘a ~' s'v “0 sf fir '9 '.~ 'r ‘0‘ '- “w vu~ '0 v» 'r- '1‘ an m - Q C o +xx***z******~** +*********2* '1 do J; Jr s" 0. J J; +>w- vr as 'r 4- '5 or +***********%******* +* zit 3;: g: 1;: :3 :1: a}: 2:: :9: :k z}: ::: ::: +*************** +**** *** +************** +**********$*** +************* ************* +********$$** +*******$*****$** +*****<$*$ +********* +**'*****-**** +*******$******** ********¥* +*$*$$***-***** ************=* +**'*~******* +************ +***** *******=* +********* +********¥****$********** "a ‘5 s'r \" Jo \ §.a \’o "a .‘a ' v¢¢v¢k$$$¢¢wm ****$****** +************** +** ******=*'*** +*******$*** +*****$* ****** +‘************“*W*** +**************** +*********** +************ +************** +***<***** +************* +*'**** *** +************ ********** +********* ****** +************* +****************** +******* +*******‘** +************** +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ PERCENT 10 20 30 40 o ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ m 168 11 wNNNNNNNNNNHHt-‘HHHHH Ocmuoubmmwoomqmm¢um 31 DUBLIN PERCENT 10 +++++5++++ +******$**$ +******** +********* +******** +********* +*$t****** +******** ********* +***’*****$ +*‘****** +£= 2: =' 3:: >3 =3 =1: +********* +2: a“: 351 :{z g: z: ::: :{z :j: :;; +******* +***$**** Ql s" ‘ 'o \h J» \‘4 d: s'd "f 'p 0‘ q >'§ 0" A" v‘a v's a" a" s'v 5" sh fit 'a ~‘l U. .‘n ~ . Q'! ~~ 'r '1‘ fl‘ 35‘ 'v 'r- 'v '.~ to .0 \‘a J4 \' Q" J s'o Jo "a ’9 op q. op 05 "s 9" ap s'a s55 xiv \‘n '- sh Jr \II 5'. s » fir q~ a" A" 3'. q. 4'~ 0's a" 4" ~" ~'— s'a s'a s'r ~'. J! a. fi‘ ’fi I" of o“ r'\ \‘p \’ \II ~'p \‘o .‘n J: ~‘4 \U )‘a \‘r s'a s" s'a ~‘a s.’ \‘o s" '\ 4" 7" a. if. —.- 9'» I.\ I.‘ \‘l “v * .9. n'» \‘a \‘o 'l‘ a“ s 4'\ r.‘ 0'» 1.. \‘t 4’ \‘I s'0 x" J; \‘o d. \‘1 fi‘ q. Op f'h r'§ a" 'l‘ Alfi r.\ ‘V U: ‘Ir J0 «'- 4: Ala ‘11 .‘u r ~ 9" r.» or a... o'. op 9" v9 o's 0" v + 3;: 9,: 3:: :;: z}: 2: :;: :;: + : z: * :i: :3 :1: 2:: :;< +2.: z}: :f: :;: ::: >1: :;: ::: +25: 3;: 3:: z}: :1: )fi: :1: ::: ********* +******** * ******** +********** +******* +******** +*=******** +**>::=.‘==::**>:=::=>:= +********* +******* +********** +******* $ +********* +********* +*** **** +********** +******** +******** +******** +****** +******** +******** +******* +********* +******** +**#***** +******* +++++5++++ PERCENT 10 FACILITY UTILIZATION. PERCENTAGE BY WEEK. 20 30 4O 50 ++++5++++ ++++5++++ ++++5++++ ++++5++++ :.~ "I ~': If I“ ++++5++++ ++++5++++ ++++5++++ ++++S++++ 20 30 40 o ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ m HQ 1 IO NNNNNNHHHHHHHHH mkwmwocmqombwmw 26 FARMINGTON PERCENT 10 FACILITY UTILIZATION. p ERCENTAGE BY WEEK. 20 30 40 50 +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ +********$*** +**********$** +************* +*********** +************ +********$** +*************** +*#**$**$*** +********* +*********** +***********$ +*********** ******$** +******<*** ** ***** +#**$******$** +********** +*********¥ +************* +********** +************ $$$$$$<$$$ +****$*******$ +********$** +************* +******** +************* +********** +********$$***mwfl +*********** +********* +**** **** +********* +******** * +******** ***$ +********’** +*********** +********** +********* +*********** +*********** +************* +***************' . . .Ia g'o s'r J; In 4" § h +******** +********** +*********** +***********~ +********* +************* +********** +*******'******* +******** +*******'* +******* **** +*********** +********** +++++5++++ ++++5++++ ++++S++++ ++++5++++ ++++5++++ PERCENT 10 '1 do \" ~'n q. as do ~'o r o" "s a" ** * .V. n ~|v s'o I'- t.‘ s’r s" ** 4"0 "P ”‘4‘ T'C‘T'I‘ Jo Jo ‘ .§ 0" r" or q. pp >3 ** 333:0? ** :********* ‘I0 J) s'o s'o s'l Jr J! in ft s‘o qs 4" a" yr 'l‘ I" o“ s .s o" s'a s" ~‘o 5.; J4 sh bdodo*=¢:¢: ************************* o ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 20 30 40 m 170 11 muUwuwwwwuNNNNNNNNNNHHHHHHHHHHOo omflOmbuNHOOWQOmbuNHOQEflOmbumwoom P4P HO PPPPPPPP omqompum WWUI NHO WUHHW 0m¢Nfl WEEK FERNDALE FACILITY UTILIZATION. PERCENTAGE BY WEEK. PERCENT 10 20 30 40 so +++++5++++ ++++5++++ ++++5++++ ++++S++++ ++++5++++ +******* ***¢**** +****************** +*********** +#***'***z********~* +********* +*********************** +********************* +******** +********~*$**z* +************$ ** +******$******$**** +********** +******‘**'** +*********************** +**********$*$~****=********$ +*********** +********** +***********=*****2****** +**********$******* +*********** +******** ********************* +********$*******$***** ***$*** +********* +**********:*$******* +** ****** +**$********=4***** +****$******** +******** ****$*** +***************** +************* +* *************‘=***** ******************** +******** +*#*******$************ +*******************‘ +* ********* +***************** +**#************** +********#* +***************************:*** **** +***************** +********** +********** ******* +************ +************* **** +******** +***************** ***************** +************ ** ******* +*********** +****************** +**************** ** +**********'$ +**********#******* +******* +++++5++++ ++++S++++ ++++5++++ ++++5++++ ++++5++++ PERCENT 10 20 30 40 o ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ m N1 82 12 NNNNNHHHHHHHb-b PUNHOOWNOmPNN NNRHUN omsuhm P UHAWUUHUWNUHU H OWNO‘U‘I‘PNNMO ##9## Pp P omuom mm o p p UHMfimm PuNu-OO mm mm WEEK XXX FACILITY UTILIZATION. PERCENTAGE BY WEEK. PERCENT 10 20 30 40 50 +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ +********** +* ******** +********* +*******'*** +*****$** +********* +******** +********** ******* +******** +******** +** ***** +******** +******* +******* +********** +********$*** +******** +>::*=:=:k::=*=:<" =:< +******* +********* ********* ********$ +******* +***** *$ +******~* +******* +*******' +**$***** +***4****** +******** +******* $ +****** +******** +******** +*****#** +******** +******* +******$** +*******'* *******‘** +******* +********** +********** +********# +****#**** +********* +********* +*******#** +********** +****#** +*#******* +********* +********** +******** +***** +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ PERCENT 10 20 30 40 a“. \‘v 9.5 *‘3? o ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ m 172 1 ‘— P?" 13 WEEK 01 02 ‘03 O4 05 06 O7 08 O9 10‘ ll 12 13 14 15 16 17 18 19 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 4o 41 42 43 44 45 46 47 48 49 so 51 53 54 55 56 WEEK HAZEL PARK FACILITY UTILIZATION. PERCENTAGE BY WEEK. PERCENT 10 20 3o 40 50 +++++S++++ ++++5++++ ++++S++++ ++++5++++ ++++5++++ +************** +***********#******* +********** ******* +****** **** +************************ +******** +******************' +**#****** +********* +****: :*******xu =9* ***** +****** Kb*'.~':~= +**************** +********** +********************$ +******************* +********:***** +******* +*#********=kxwk******** +*****=€<*>‘.<>:<=:==::=:: +$*******$********* +***x=*=:=>:==:= +*******4=****$*$********* +**********zs*$* +******' <*****4=***‘= +*******$*****2t**$*$* +********** +**************=* +************‘****** * +*********** +****** ***** ************ +**#*** ***** +#************ ****** +***% **”“*****>«+~ +*********** +***********2:**x******** +************ +******** ******** **** *** ******* +********** +************ **fl=* +******** +************* +******* *****************$** +********** +*****$ '#***** ***~* *"*’W +**************=k= +**** ****** +**** *** **** +********$ ***‘***** +*******************'*$* *2<“*£ =*4< +*********** +*****************'=* +************ +********* +****************** **** +******** +**#************'** +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ PERCENT 10 20 3O 40 o ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ m 173 14 NNNNNNNNNNHHHHHHHHHHO OWNOmpuNHOCmQOmbuNHOO HOLLY FACILITY UTILIZATION. PERCENTAGE BY WEEK. PERCENT 10 20 3O 40 SO +++++S++++ ++++5++++ ++++5++++ ++++5++++ ++++S++++ +4444444444444444 +44444444444 +4444444444444 +44444444444 +44444444444444444 +4444444444 +4444444444444 +44444444 +444444444444 +444444444444 +444444444 +4444444444444 +444444444 44444444444444 +44444444 +4444444444444 +444444444444 +444444444 +* ‘4: * i: :,‘: ::: ::: :;: :,‘: ::: :1: 3:: " :1: +44‘4444 +44444444444 :3 2: 3:5 * ‘4: ::: ::: :k :2: ::: :;: +444444444444 + 444444444 +44 ' 4 4 4 4 4 4 4 +4 44 4 4 4 4 4 4 4 4 4 4444444z444444 +4'444444444444 +4444444444444 44444‘4444 4 444'4444444 +44444444 4444 +44 4 4 4 4 4 +4444444444444 +444444444444444 +444444444444444 +44444444444 +4444444444444444 +444 4444f +444444444444 +4444444444444 +*44444444444 444444444=444 44444444444 444444444444444444 Jo 0" s'r JO Jo \‘o J1 J0 J; :z \‘I W‘ 'P’Pq‘ ‘O‘W‘ 'l‘ 'P '3‘ 'I‘ +44444444444 +444444444444 +4444444444444 +44444444444444 +44444444444444 +444444444444 4 4444444 +444444444444444 +4444 444444 +4444444444 +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ PERCENT 10 20 30 40 o ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ m 174 09 OWPUNHOOWNOwaNHO 27 HURON VALLEY PERCENT 1 0 FACILITY UTILIZATION. PERCENTAGE BY WEEK. 20 30 40 50 +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ +*************** +******** ******** * * **** ****** +*****=**** +******** ~‘a '0 z}: 2:: z}: +*************** +**:***** ******** +******** ~‘a Jo Jo sh do "a sh or I" I" as l.\ 0" 0.. ******** +* o \‘v J; Jr “a J; it ’ 'r'r'r'r'r :0 Jo W q'a ~Iu u'a q'- \'u J + ‘T‘l‘fl‘fl"? ’1"!‘ o s'o s'o Jo . +***-»»~~ +******** +******** ** * *** +***$**** +*******$ J slob": - I’d +4'fizl"l‘**=l"r:'r O *x****** +*******$ '. ‘ +*k***$** 4. Jo .1. J J4 ‘Io da .4. if! O'~ as ’I‘ ff II! fi‘ fl. §'o \‘4 §b \‘4 Jr sla J: U "Q as o's of 0's —.5 q. *v :1: JD '0‘ J. q- 3;: 1.: ::< * x: do ”fl 4. 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PERCENTAGE [-EY WEEK. 20 30 4O 50 ++++ ++++5++++ ++++5++++ ++++S++++ 178 lO Ulwwuwmmmi“NFCNNNNHHHHHHt-opp prHO©$V3m¢wNHOLGQOprN~ MADISJN HTb FACILITY UTILIZATION. PERCENTAGE BY WEEK. PERCENT 10 20 30 40 SO +++++b++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ +29. ": :1: :1: :1: :1: :1: :1: :1: :1: :1: :1: :1: :1: :1: :1: :1: :1: a: ..: :1: :1: :1: :1: :1: :1: :1: :1: :1: :1: :1: :1: :1: .‘4 4 '4 .'4 .'4 .‘4 .l4 .‘4 .4 .'4 .l4 .‘4 .‘a .‘4 4.. . 3.. 4.. 4.. 4.. 4‘. 4'. 4_. 4.. 4f. 4'. 4'. 4'. d: 44 .I4 .I. :0. .0. .v. .v. a: J. >I. .I. .34 a. u. .I. I. "§ O'\ r.‘ 1.. d.‘ 4'. "- 1'. 0" .. I“ 4" fl'fi O.\ 1" .‘4 .I4 .‘4 .'4 .l- .‘r .‘4 '1 «'4 .‘4 J4 J4 J4 ‘P 'I. W‘ q. "‘ ’.‘ 9" 0" U.‘ "\ "‘ "§ t.‘ .‘4 .‘4 .54 .‘4 .‘4 J4 ~‘4 J4 J4 J4 4 '§ 1" 0.5 V.‘ \I4 ‘0‘ ‘1‘ 'l‘ ‘I‘ ‘I‘ ‘I‘ ’0‘ ’I‘ .‘4 )l4 .'4 .‘4 .‘4 .‘4 .‘4 -'4 '4 .04 fl‘ I" O" «Q I.‘ OI. tr. ;.5 "\ \‘4 .‘4 .‘4 .‘4 .l4 .'4 .'4 .‘4 .‘4 .'4 .‘v -'4 J4 .l4 ' ‘ O \ u I ‘ I' 4‘ [Q 4'. 4’ 4.. I. 4'. 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I‘ :1: >1: :1: +=*** ~**4~3.**** +********»*****¥~$4 * **** ~********* +*********** +*********$* +*************$*** +***'** ****** +****"******* +++++5++++ ++++5++++ ++++S++++ ++++S++++ ++++5++++ PERCENT 10 20 30 40 o ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ m 179 20 WEEK {,fibuf‘JHCCI'flO‘UL‘ri-d NNNNIJn‘sHHHHHwI—IHH NU V PERCtNT I 10 FACILITY UTILIZATION. PERCENTAGE BY WEFK. 20 30 40 ' 50 +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ s'a s'a v'\ I.‘ s'o "p q. q. ..l Q'- d“ o.\ s'o U; + a" I" ‘l - Q“ + 7" q\ Al- d, O.‘ fi‘ s'o s'a I“ 5.. dc s‘o O" "‘ c'a "a o I‘ ’r‘ "- 5'4 4“ '.5 U; . It r. u rls s'a ~' o 4'. fig d: .‘p qs a“ 0- d» 'l‘ "s J. J. A- «I. J. J. a" 4.. .I- \‘o G.‘ t" 5‘4 i'l -"\ "h ‘9 U: fi‘ 'I‘ d. a. . I‘ '1‘ s'a ~’a q. r‘\ J. .l. v.~ q~ 4'. a.b ,|. a . K‘d \'1 q. up Q't 0" a" ¢|~ d; d; 1.. q. s'v J, .I. q. up .I. .l. .I‘ ... AI. ‘1. a.\ ... s'a ‘I. .l. '1‘ \'v ~‘I o“ a" \l; q'a v's a" J. J; .u 'I sic a“ . 'a I" \‘n 4“ \‘l t.‘ a. 'r \'< " ‘b fi‘ Jr 1‘. "' as ~|r fl‘ \‘O Q. J. l.‘ ‘I' ‘.\ \‘o "\ J- a.‘ Q‘d a“ J; tr. «'1 I" .‘o .'~ .0, ' a" §lt — s ' to ~ r.\ \‘u 1'. h.- ‘v‘ .U 4" H, "s .1. J. 4.. d. .I\ .14 A.. \'d ‘ ‘I s.- a.‘ \'I ~ ’w or ’w «‘a s" +‘.‘ fl‘ +** J: J; +** ‘3’ \lfl a" or +** q. +** do s‘d fi‘ ‘l‘ ** :i: 3:: +=¢<>§= +2: :.'< +>:<* +** Jldv 't‘fl‘ +** +** +** ** +** +** Jada W‘fi‘ +** +++++5++++ ++++S++++ ++++5++++ ++++5++++ ++++5++++ PERCENT \‘a a.- :,‘< 3:: 2:: do O" ‘h 0 I‘ O I Jo '1‘ b a, do v9 Jo q~ :3 * 0 § * 3:: ~ a a'\ \‘n r.\ .0. . 'I ~'a ~ 4,\ ~‘n . ~ I 'u ‘|‘ Old ‘ ’I ~‘. u.‘ t" 'I‘ J; 4" \‘a v.‘ \‘a I.‘ 't -.~ J— - ~'0 \‘I n - "§ ' .l, a.» "l 4.. J. 'r .T, .q t.\ \‘d 0'. fi.‘ q. \‘a . ‘|4 "‘ Jo '.‘ "I 5" Q" r. If x‘p ' '\ ~‘v I“ >:: 2:: J a O|‘ J. I" ~h J‘s do fi.‘ \'4 fl. \‘p 4‘ Jo up Jv or \‘o ’0‘ J a i'Q do if s't "a \ a ’.~ \‘o r" s‘a 4-4 do ’I‘ * s'v q‘ #0 I.‘ * ‘IO ." »'§ 4“ fl \'; I ~ §.a v|~ ~05 Jo plx o" aaaaaaaaaaaaaa #4 fi‘ do or J; O.‘ J: v *=‘.<** **=§<=§< +****** * x: :3 do 'I“ a. v» x: J! '9 J' as Jo fl. Jo q. a h'o o .‘ ql. ‘U, C . l . P. \‘r "- r.~ a" «a.la ' ‘ a 1.. "x . .I. .n, v.‘ 'w 'l \.O I‘ ’I‘ le§’ up 5’! V'd V" * \ee*-*as*+sae* - \ ‘l r , v.\ .- ‘ x" J. \'4 ... ’I‘ sit \‘a r.~ 9's - I‘ I s l \I \‘a J; a" or "' ‘I; cl. as in s" s t.\ do 0' ..§ 0“ ‘1, J: r.§ 0.. do I.\ fi§ sh do fl‘ "§ Jo s'o a" J; 3 ‘3? '. \ d! fi‘ *3 s" :;< ** 9.: :3. 10 do a" J vIs ~°c a|s I ~— r |‘ .U U. .' ~'a ‘I‘ 4" . H. r" ~‘o ~lv 'n‘ J: 'r J: q‘ \‘o '0‘ \‘o , 5" '.\ a, or JO 0“ J; 0“ slo op 0» p.5 :,': p.~ s'o a . | \'a a s ‘ a" x b r.‘ \‘I as >:: J! "A do 1" s'l ’0 :k U. AI. s“ "' p. t" Up I \‘O V" 9" ' Jo §"§~ 4‘ vr ‘r 'r 04 ~'; ta 9" o ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 20 3O 40 U! 180 WEEK 01 O2 03 O4 05 HcomquDuNHOOIMOwme wounw mhwm ¢~.bbbbflflww # FUHO¢XBNO ##9## a omuOm w mm HO (fimm -bum mm om WEEK OAK PARK FACILITY UTILIZATION. PERCENTAGE BY WEEK. PERCENT 10 20 30 40 50 +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ *************************$ + :1: 3:: >1: :,‘: :;: ::: :t: ::: :1: ::: :fi: :1: ::: ::: >3: 3:: >1: gl; J; 2: J; «I; .0; \‘a J; .l; «I; J; ‘l; J; J; J; ‘1‘ J; J; J; \I; s‘; J; 9; 3'; ;'~ a.‘ ;'\ ;.~ ;.‘ ;'§ r.‘ q! ;'\ ;'~ I.‘ ;.\ I" ;‘§ ;. II\ 0.5 ;'\ r" If I“ .h s'; s'; J; ~'; ’- J; J; 0; ~'; -|; 5'; J; J: I" t.‘ r.‘ ;‘\ .‘ ;.\ ;.\ ;.§ ;.§ ;'~ ;.\ ;'§ ;. ~l; ~I; * x'; s'; s'; U: .‘n H. s‘; ~ 1 “a J; c'; 5'; J: ~'{ ‘1; 4; §" J; x; ‘3; * J; J; s'; s'; ;‘— ;.~ 'I‘ ;'\ 'g‘ ‘1‘ ;,~ t.\ ;I\ 'l‘ ;I~ ~- ;'~ 'I‘ ;' ;I ;.§ ;'~ ; ;'~ i «h 0.5 ’f‘ ;.\ ;.s J; \l; .l. s'; s'; Q; .|; 0; ~'; + 'U‘ 'I‘ ;'~ ;'\ ;'s ;.~ q» q. ’1‘ \Ir J; J; J; J; J; q'; u'; "; J; J; J; ;.~ ;.§ q. q. ;'s ;.\ ;" ;'\ fl. ;'\ ;.~ ;.~ \'. s'; \ ; s'; “; \'; ~'; ~|; ~'; -'- "- “; §‘; ~.; \‘r J; ~‘; 5'; sl; s'l ; l‘ a" ;'\ as ;'\ ;‘s a‘\ ;'\ ;.\ ;'~ ;.\ ;'s ;'5 ;‘\ fi‘ 0" I.‘ ;.~ 0" fi‘ \0 — I‘ d; \" \'; \‘; st; ~I; .V; .h J; C; J; s'; n'; J; '; ~‘n a]; «'O \.; ~‘( \I; J; )‘o ;.s ;'5 ;.§ ;'\ ;‘ ;.~ ;‘s «— ;'\ ;'\ r" ;.\ r" ’I‘ As I“ .s 4.5 ;'s o. ;.\ ;I\ p \'; s'; "; s" J; s'; \'I ~'; \'; ~‘; ~'; t'l \|; J; ;.u ;I\ ;‘\ "‘ ;,~ ;.~ 4'. a" ;" fis ;.\ ;.§ ;'\ as J; J; J; y'; J; U; \.; d- d; J. J. .I; J; J; J; .l, J; .< J; ~'; ~l; ;'\ q. ;.Q ;.~ ;,‘ q. 5" ;'\ ;'q ;'\ ;.- ;'~ ;'\ ;.\ ;.\ ;.‘ q» I. ;‘§ ;'\ 1's + ~‘v "; J; s'; “; \'; s'; s'; s'; ‘l; s r.\ ;" ;.‘ ;. ;'\ 5‘ ;‘~ ;.‘ t.‘ ;.w d; J; J; s'; J; J; U; s'; U; '1‘ q; ;.- ;I‘ ;\ ;,. ;.~ ;.s ;.~ J; .I. .0. .I. .I; .l; J. J, .I. A . u. . l~ q. ;" q. ;.u ”s ;|. -P ; . ;.. :l‘ L II J; x'; J; J; J; \’4 J; ; s‘; 0; s‘; "; n» J; s'; s‘; or .~ «~ vr 'v‘ - w .\l % ~ ; 5" «I; "; s‘; 5'; s'; \‘0 0; ~'; J; J; J; 3.; x'; 3‘; sl; ~'; q. ;'\ ;I‘ q. q. qh ;.~ ;.\ ;'s ;.~ ;'5 ;'~ ;'s s ;'s .s ;'u I.‘ l‘ 96 =§= >1: =3 =3< >1: =2: \l -- J; J; J; .l; \.; d; ~0- J; U; u'; ; ; .fi 1“ I‘ I.‘ 'l‘ 1" 1.5 I" 0" l \ J; ~'; 1'; .'; -'; J; ~'; s'; J; U- 4. ;.~ ~ ;.~ ;'~ ;,\ q. q‘ '1‘ o.. J; ‘I; .‘z ~ ; ; \‘; s'; d; s'; ; s'; ~ s'; N; J; s'; J; u; s‘; 5'; G; q. fl. fl. 1.. C.‘ "‘ 1" ‘I‘ 'I‘ ‘I‘ 'l‘ f.‘ '|‘ '.. q. I 'l‘ 1'. fl. ‘.‘ 'l‘ "§ C.‘ fl" 'I‘ J; ‘1' .l; s'; d; Q: s'; U; H; d; J; J; J; J; "; J; J; ~ ; \I; J; s’; J; .I, T 'I’ ;.- ;I\ ;.‘ ;" ;.~ ;.‘ ;'. ;'- r's ;.. ;~ ;,- ;.\ ;‘\ ;f§ ;.~ ;I‘ ;'\ q. 'I‘ o's K , J. J; ; U; ~'; ~'; -‘- J; J; J; J; J; \‘a J; J; J; -'; 3'; ;.~ '1‘ ‘I‘ "- ;.s ;.~ ;.- ;‘~ ;'. ;'\ 'I‘ 'I‘ ;I\ ;'. ;'~ ;‘\ ;'~ v.5 fl. 5. ;'u q; .\ .'. §'l -'- J; J. -'n ‘I; d; -'; -‘; J; J; J; u'; d; \l; J; “; J; ‘0; U; Q'; J; + A ~ ; . \ ; ~ I. I Ii I. fi" "‘ I. f" I‘ i.‘ "‘ 0" '.§ "§ "‘ 'r "\ ’.‘ fl" ‘I J; N; J; u; 0; J; U; U; U: ‘1. J; s‘; ~'; J; J; ~'; J; 0; J; O; J; s‘; ~‘; ’0 q‘ "\ I“ 1“ 7“ ’|~ 0“ I'. "‘ ’I. "~ fl‘ V.‘ "V "‘ ‘.‘ ’.‘ ’I‘ ’I‘ Q‘ 'I‘ ¢ 'fi ' A'. ~'; «I; .‘- .l; .1, .'. ~'; ~'; \‘; s'; \I; \'; ~'- 0; s'; \’; \'; ~'; ~'; ‘ ;.~ ;'\ ;‘\ ;.~ ;'~ ;.. ;|- ;'~ "s q. ;.\ ;.. .'. 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J; I. \’; s'; s'; H; J; .I’ "Q q‘ l.‘ ~§ ‘I‘ .". J; J; J; ~b J; 9; J; u'; s'; s‘; ;.s ;.s "s ;p ;'. p ;.- "s ;" ;'~ 1 +4; s‘; ~'; J; 4; * ~l; s‘; u'; 5'; q'; - ; T 'l“.‘fi"1‘-""l"f’ 'i‘ ‘l‘ +* +* J! qh :;: =:: z:: * >:: 2:: ::: :,': ::: 2:: :i: 9,: ::: :1: :2: 2:: x: =3 2:: ::: :fi: :;< :1: :3 2:: ::: ::: :1: ::: ::: ::: z:: +********* +***********$**$*$*$$$ J; J; J; s'; ~10 J; \'; \l; W Q. 'rcr'r'r'r'r'v—rfi-vc‘ $*******$* +=:=*** **=‘.<* +** ******* +* ******** +********************* *‘*********2*** +*****=*** +******************* +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ PERCENT 10 20 3o 40 50 I l\ I; ‘1 s' VI sl; ~'; ‘I, >l~ :.~ ;.‘ 4 ;.§ 0.. q. I * J; J; J; Q'; J; J: \l; U; \'0 J; ;.\ ;'~ 0" as q. o, q. ~ ;" as . \I; s'; s" \I; s'; J; ;I\ ;.u ;.~ ;'s ;.s as y'; J; ;.~ ‘I l\ ‘ u I J; ‘P; ‘9 U; s'; ~|; J; J; J; .l, J; J; .b ' J; \‘l s‘; s‘; ; \|l s‘; Al; \|; §|I s'; s'- \l; J; s'; ~'; ;.~ 9" ;f\ a.‘ 5 q‘ ;‘~ 1" r.‘ fi‘ ;'\ ;'~ ;.~ I.‘ ;'~ I" ~ I J; Q; s'; V'P J; \‘a #0 i'l “I. ;'s qs ;.5 'l‘ ;r q. q. ;p ;'~ as ;'~ «s ;.Q q. ;‘~ as es ee 4% II l; d; s'; J; VI; J; ~.; J; k~ ;.~ ;.~ q~ q‘ 4". ;'u up \I - - l\ \l I\ I . :**x**#** *********z#** ************* J; W‘ *****,******** * +++++++++++++++++++++++++++++++++++++++++++++++++++++++ 181 I‘.’ r: t'. K (:08 wk)» OCCC “go-ab th-‘C'Cu— -n'\ u-" ch'xj3 ‘N-‘JPJFQVHHHHHHHHHHOO \ \ I I .' 4 ”v I rue LixJ \ .r , s I - 30 31 3?. 33 34 3b 36 37 38 39 4O 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 WEEK HXFUHH FACILITY UTILIZATION. PERCENTAGE BY WEEK. UbRCi:NT 10 20 3O 4O 5 +++++u++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ .I. do d; d; d; 4‘; a. o; J. .'- .1; c; o; J; J; ;.‘ ;" ;.~ ;.~ 1" ’I‘ ;.~ ;I‘ o“ ;|\ ;.‘ ;.‘ ;'- q. ;'Q s'; ~'; \'; \'; \‘; ~'; ~’; \'; ~ ; "Q ¢ 1" "‘ "\ fl. ’|\ J‘\ l.\ )I, .I, an, >I. .I, .0, .I. .I. .I. J. .I. '\ or '\ 'h "§ ;'u u'A ;'\ a]. o.‘ 0.. | .u u. d. u; .0. d. .t. a. u. .I. .I. J. d; 4‘s 4“ ;.u 4.; ; \ 0" ;.\ ; ‘ 1‘. ;'~ ;'~ ;‘\ 5. Q'D ~.; "; \I; ~'; ~'; .‘a A - \'; «'- 4 \ N l O O I. l‘\ l.‘ ;' ;I I. 0“ .! ;'\ |s s'; \.; .'; ~P. J; \'; J. 5 d; " U; ‘; ‘5; x‘; ‘.I ~'; + . . . ;.\ fl‘ ;'§ 1" ;.~ ;.g ;. ;|~ ; ;.~ 'I‘ '» ;'\ ;.\ ;.- ;'§ J; ~'; \'; s'; ~'; 4' .L ' ‘; .‘a ;'~ ;.\ ;'\ ;.~ ;.. ;‘. ,p ;I. ~ ;‘~ ;'§ ~I l . I , -I, s'; .'. -'. . II. .‘. - ; ‘ - .'; El; J +;.,‘;....‘..........;., . I I I I I I - I I I O I‘ 0 .l. 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I. do s . .t. .‘p U; \'; s'; 0; ~'; 6; r . ~ I ;'. ;.‘ ;'\ ;. ;'. ;'. ;.\ fi‘ ;.‘ ’U‘ ;'s .I; .'; 4‘; ~'; "- J; .I; ~'; u'- s.- ;.~ ;I\ r‘s '1‘ A‘. ;'~ ;‘\ ;" ;‘\ ;.. )'; §'; s'; 4'; «I; \ll \'; \'< J; .I; §" I‘ ;'~ ;~ q. ;’u ;‘s ;.§ ;I Q‘ l,‘ ;r 4'; .'; ¢.; s'r s‘; s'; 5.; -'; ~‘; "; “’ .‘. “o 4'; c'; ‘.; \k “I ~I; ;‘s v.» fis r'\ r'\ A" 0'. ;'§ a‘\ 'I‘ ;‘§ q. ;.\ m ;‘§ v's ; ;.§ ;.§ \'; "' J; s'; J; \‘o 4‘ .‘- \’; ~'; ;.~ ;'§ ;'\ qs ;'~ ;.‘ ;" ;'~ ;'~ ;r\ .l; ‘l; s'; \'; J; J; 4'; I" ;.~ ;|\ 'I‘ ;.\ 9" ;.~ ;P s'; ~'; Q J; xl; s'; «I; ul; s'; s'; «'r \'; s'; \‘V J; \'; Q; ~'; J; s'; s‘; s'; \'; ~'; ~" s'; J; "; ~'; s'; "0 J; .'; g‘; * 'I‘ *x.¢;*~l‘ \I;*:lf:::< J; §'; **#********* '; s’; J; §.fl \K; s'; ~'; .9 Q; s'; s‘; '9 '0‘ ’9‘ ’1‘ 5‘ 'v‘ ’I‘ 'I‘ 'l‘ ’V‘ 't‘ ‘F J; ; J; \k J; J; J; "r d; d; J; J; J; - Q; 4; If ;|~ ;|\ ;‘\ ;.~ ;f~ ;.s ;‘\ ;f I" ;.~ ********** J J J; ; J; J; s'; ' J; +¢FOI‘*-***«~¢'I~R‘*- ¢;§l;**\b~bs‘;*s‘v Q‘ wybdo r4;~l;q';~|;*do*s';sk '9 «~ 'r I - .,. on "a ; J; J; J; \.; ~’; J; s’; s’; s’; ~l; Q‘ ‘ 'V‘ ’I‘ '7‘ fi‘ 'I‘ '0‘ 4‘ T 'I‘ ’i‘ I * +************* +** ****** +*************** ******* +********* ***** * +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ PERCENT 10 20 30 40 m o ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ o 182 23 WEEK 01 02 03 04 05 06 07 ON on 10 L". l V“ ’-‘ I I :L' /r ,.J ._ l ’\ I... 3 33 WEEK HINTIAC FACILITY UTILIZATION. ERCE NTAGE BY WEEK PPHCkHT 10 20 3O 40 50 +++++h++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ l'a ~b .‘n 5.: ‘I— J; J J. «'9 J; I“ up rls a.» a.» r.~ r" . . ¢.‘ .‘~ I .‘p ~|. .3. "a .'- J- .'. .I. \‘p 1‘. I“ v,§ a" a,» 1“ .l~ 7“ ’l‘ I u l ‘I, I ‘0 I, .‘ '9 q t . 1" . P v \ l d, .I. | v . A x I, l.‘ " a. r‘h 1' ‘l §§§§§ 1“ r. I. ‘ f.§ l‘ ‘l_ l {h'l‘ ‘ sl. I. ' I, u I I n . 0, a‘\ . a I ~ a” p .0. ‘ - ‘- ‘; 5'» < '- x - --‘< ~' \ s'; U. \‘n J ft \t .'r s'o J: v.. ..~ .,\ p‘- .l- or . — 1.. »,~ ..~ .I. 4.: 9.5 1‘. a“ 1" :,~ :5; ;:: 0.: 1.: 's A]. or aIs r's . . ~I. ' .I 9 .0. .I. .I. .I, # ....... u I ‘fl‘ ‘ ~ I I. t .1 L . _ u a. A, .u -I. u, .'. 5., d .. s'v a. '- . r .' A ‘ — ¢.\ 1'. 1.. rl‘ “- .’~ o,\ o.. fi~ '.~ 1" vs J Al I »c .|. ~'. .‘o E . \ —~ ~ . I d- I r . u ', .‘u _.- . a ‘ ’0 I I l I. -. ‘ ‘ . I 'L ' I I‘ ‘ v ‘| |‘ a" ‘y ' ‘ ' ' -- 7' A , A" '- u'o do Ur Na d; s'— ~"/\- - , . - -‘§ .4. . ~ ~ iii 1.. I.\ II. 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U ROCHE .s .H \I. .L rls «I .0 ‘. 4...: ,. J .' 9"» ;,~ ..‘. .0, ... 7‘. J, J. 4' o.\ o,\ .I I. +,, +x~ \" ’r + :2: + :;: .I. 1“ ~ ‘5 5 d,‘ ‘I’ II. + :1: +* +* :‘.: 4: «Q +* .‘a us I '|‘ ~I- v.‘ .I o.» .‘O ‘|‘ ‘34 a l‘ 4v q~ O.‘ ‘I' a" s. I ~ 0.. ‘I, o“ u'c ~' O'. * » "Q "' I'Q $3533.: 4. Jo sla -¢fl~ *ih'k * ." up do a.- +**** *** + 3:: +* \‘o vr * ‘9 o'. +**** \‘OJI*J¢ 'I"P‘I“P Jaw +* OP "Q +**** +******* +****** +******** +***** ST! i-t +******** +*********** +********* +++++5++++ ++++ I l .l— p... + a . .I, FACILITY UTILIZATION. PERCENTAGE BY 20 +++5++++ ++++5++++ ++++5++++ ++++5++++ . ‘lp U. do s'v fl.‘ "§ 0" 0“ ~ . .I, J, .0, .l. .I, v.\ o, -. a" ~‘n _I. ~' -'V- J- ~ ; J; '- ~‘l ~‘t \‘o ‘9 s'o \‘I \b §'a ’I‘ 1- 'I‘ _. —.. . ‘ ,.\ ’1‘ o.‘ v'\ o.\ v.s a“ r.~ o'- .3 I n, 'V , .. , \’ ‘ ' ‘- ‘p 'a 5‘. «I. n . .‘a q. ’. .‘ 'I‘ '. u. op l‘ I“ "O -.l .I I I‘ 0- . V- J: 'o ~'a s.» "a y’a A" s'a s'a ‘9 a" ' n. I‘ I“ 3 0.! o.~ c.» on 4.: '1‘ a" or .'- .2 . 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A. a" a“ a" do s 'r Jr '0 J; s" \‘a r.u p :'~ 4.. :I‘ 9.5 'P r“ ‘k * qla J. J. Jr * "a O. q‘ q. a" I" u 4 Jv s'a 5“ Jo "0 §" "a sh 3.0 s‘— ‘.I s'o do s'a 5'4 s" 0" r.- fir "s o" 0" 1'. o" I. a" o" q‘ I" as I" a" b c'a ~|o do )I, -'a s“ .I‘ Jo 3p '0. o|\ I" ‘s q. "s 4. '.~ §.a ~‘i s" ~‘o ~‘o ~‘a 5'. t9 ~51 \‘o \h s'p "o q‘ If I" 0” q. a" o" p'\ o‘- 1" a" 0.. 9'. sh W 3:- 3: J! Jo .9 ~b "a \‘4 ~‘o s" \‘a s" as up s 'I‘ «s a" 4.. cf- '3‘ q. up v” a" :‘o )" J; Q's P .- q. ' uh \‘I Jo ‘5. 3' do U; do .5 J: "1 4; Q” .l’ or 0' «Q ~\ " 0.. 1" r.‘ 0.- d.~ I" r" o" r“ s'o \‘o h'a \'l sic Jo ~‘n ~'o s'a ‘9 ~‘o o" 4‘. 0‘5 0.. a" “u a.\ r.§ a“ a'\ 1p 3" Q" do do )2 59 J4 J0 d: J: Jo 04 41 q. 0 . v” 'P 9.. o. I. or a“ of Jed-~54, ado Jo.b~|:~b.b~».u.b 0“ '.~ fi‘ 0.. 0“ fi‘ «I 'I o“ I" q. of r'\ ‘o n Jo s As a" 4‘ Jo .o 1 Jr J! J; '0 a 5. O.‘ on 5‘ if of a. . PERCENT 10 5++++ ++++5++++ ++++5++++ ++++5++++ 20 WT; EK o 30 40 ,l I l l I 3.: =3 a: a: 11' "s o.~ 'I‘ a" a" \U s'c O“ "‘ \b or o ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ o 30 4O 01 18h 185 25 ROYAL OAK FACILITY UTILIZATION. PERCENTAGE BY WEEK. PERCENT 10 20 30 40 50 WEEK +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++S++++ 01 +************* 02 +***=€=**>:<*>:<**=¥ 03 +********* 04 +********* 05 +******$****** 06 +********‘* 07 +**********$‘*****************$** +************ +*********** +***** ** +*** ********* +***$********#******** 08 09 +************ 10 +******$**** 11 +********** *** 12 +********** 13 +********* 14 +********** 15 +****#*****$** 16 +*#***************************$ *** 17 +*******m*** 18 +*********** 19 +*********** 20 +******* 21 +*********$* 22 +* ** *********** 23 *******$>*********************o*** 24 +******** 25 +******* 26 27 28 29 30 +******************$*********$****** 31 +************ 32 +************ 33 +******** 34 +**********$*** 35 +**************** ************** 36 +***$*#************ 37 +********** 38 +******** 39 +************ 40 +*#********* 41 +************** 42 +************ . 43 +***#*#***********'***********=**$**********=***** *+**** 44 +*********** 45 +************* 46 +********** 47 +*********** 48 +********* 49 +*********#* 50 +***************************************** 51 +********** 52 +***#***** 53 +********* 54 +************ 55 +******** +++++++++++++*++++++++++++++++++++++++++++++++++++++++++ 56 +**#********** WEEK +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ PERCENT 10 20 30 40 50 I 26 08 mbufiMAOQthOmwaVHO() NNNNNNNNNNHHHHHHHHHHO OWN“? wuwuuwwu NGmPNNHO ##UHM H000) p p 93333 an \OmflOWn UN mmUI NH0 53 meI omb- WEEK SOUTHFIELD FACILITY UTILIZATION. PERCENTAGE BY WEEK. PERCENT 10 20 30 40 50 +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ +*********‘ +*#********** +******** +******** +****** $* +*********** +**************$** +*****#*** +********* +**~******* +*********** +******=**** ******$** +******** +********** +*********$***** +********** + 2i: 3%: * =:= it >2: 3:: =1: =3 ::= $3 =£= +::: ::: :;: :1: :t: :4: :g: ::: :;: :1: ****$***** :fi: :3: :’,: :1: >;: :t: 3:: :1: :;: +****‘******************* z: ::: ::: :.'< :i: :fi: 3:: :;: :: ::: +***$**** +********** ::: 3‘: 2;: ' ::: :i: :t: x: :5: "' ************ +*********** +******$******$**$******* +********** +******* +********** +********* +******$***** +**************‘** +********* +* *******$* +*********** +********** +*********** +************* +********** +**#*********4 ** +******************** +************ +********** +********* , +******** $ +********************** +************* +**#****** +********* +********** +********** +*#****** +******** +++++5++++ ++++S++++ ++++5++++ ++++5++++ ++++5++++ PERCENT 10 20 30 40 o ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ m 27 \OmijmPuNHOcmfiO‘umNr-IOIO uuuNNNNNNNNNNHHD-‘HHHHHHHO NI—no N p PPPWNPPP¢JLPUNOMMM U \oqu‘mthI—Ooqu‘m OJ UHDWUHBW UIIPUNHO m 0 WEEK TROY FACILITY UTILIZATION. PERCENTAGE BY WEEK. PERCENT 10 20 30 40 50 +++++S++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ +444444444444444 +444444444444444444 +444444 444 H444444444 4444444 +4444444444444 +444444444444444 +44444444444444 +44444444 +4444444444 +44444444=44444 444 +444444444 +44444444444444>4 +4444444444 +4444444444444444 +4444444444444 +444444444444 4 4444 44 +4444444444444444 +4444444444444 +44444444 +444444 4‘ +~444444444444J +4444'4444444=4444444 4444 +44444444 44 44 ::444 444 444444 +4444444i44444444 +4444444444 +44444444444 444 444 +4444444444444 +4444444444 4444 +44444444444444 +4444444444 +4444444444444 4 +44~'44 44444 4444 4 +4444444444444 +4444444444444 4444 +444444444444 +444444444 +444444444444 +44444444444444444444 +44444444444444 +4444444444444444444444 +44444444 +44444444444444 +444444444 +4444444444444444 +444444444 +444444444444444 +4444444444444444444 +444444444444444 +4444444444 +44444444444444 +44444444444444 +44444444 +444444444444 +++++S++++ ++++S++++ ++++5++++ ++++S++++ ++++5++++ PERCENT 10 20 30 40 o ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ m H” 28 10 Om¢umwoomqombum~ 27 WALLED LAKE FACILITY UTILIZATION. PERCENTAGE BY WEEK. PERCENT 10 20 3o 40 so +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++S++++ +4444444444 +444444444444 +444444444 +444444444444 +44444444 +444444444 +4444444444444444444444 +444444444 +4444444 +44444444 +44444444 +4444444444 444444444 4444444 +444444444 +4444444444444=444444 +444444 =4444 +44 4444444 +444444 "444 44:444444 +4444444444 +444H44444444444 444444444444 +444444444=§d= +****~- **3n-*fl‘ +444=i=44:' 4 +4444444‘4444 +44444444 +4444 4444444 44444444444444444 444 +4444444444 +44 4444444444 +4444444444 +444444444 +444444444 +4444444444 +44444444444444444444 +44444444>. 4444 +4444444444 +4444444444 +444444444 +44444444444 +444444444444444444444444444 +44444444444444 +444444444444 +444444444 +44444444 +444444444444 +44444444444444 44444 +4444 44444444444444 +44444444444444 +444444444 +44444444 +444444444 +44444444444 +444444444 +4444444 +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ PERCENT 10 20 30 40 o ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ m 188 29 08 Oomqomkumwoomqompumwoo U quNNNNNNNNNNHHHh-HHHHHHO k NH NUHMUUJ U ®®~Mfim (u 4>¢¢ NHO 4444444 om40m4w WUHmflmm UNROJNHO w 0 WEEK WATERFORD FACILITY UTILIZATION. PERCENTAGE BY WEEK. PERCENT 10 20 30 4O 50 +++++5++++ ++++S++++ ++++S++++ ++++5++++ ++++5++++ +44444 4:444 +44444444 +444444444=44 +4444444 4 +44444444 +4444444=44444444 +«‘************* ********** +4444444444 +4444444=4 +4444444444 +444444444 +44444444444444 +44444444444 +444444 444 44 +44<44 4444444444444 +44444 44444444444 4444444444444 +4444444444 44444444444444 +4444444444 +44444444 +444444 4444 +44444444444444444444 4444444444. +44444 W 4 44 44 4 +4444444444 +444444444 +44444444 +4444444444‘ 44 +*********.; +44444444444444 +444444444444 4444444‘4:44444 +444444 44-4 +444444444444 +4444444444 +44444444444 +4444444444444444444444444444444444 +44444444444444 +4444444444 +44444444444 +444444444 +4444444444444 +4444 444444444 +444444444444444444444444444444 +4444444444444 +44444444444444444 444444444 4.4 +44444444444444 +444444444444 +444444444444 +444444444 +44444444444 +44444444444444 444444444444444 +4444444444 +44444444 +4444444444 44 +4444444444 +44444444444444 +444444444 +++++5++++ ++++5++++ ++++5++++ ++++S++++ ++++5++++ PERCENT 10 20 30 40 o ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ m 189 30 NNNNN HHHHHHHHHHO m¢wNHOom40mbuNHO© N WEST BLOOMFLD FACILITY UTILIZATION. PERCENTAGE BY WEEK. PERCENT 10 20 30 40 50 +++++5++++ ++++5++++ ++++5++++ ++++5++++ ++++5++++ +44444444444444444 +44444444444444 +44444444444 +4444444444 +4444444444444444 +4444444444 +444444=4444 +4444444444 +4444444444444 +4444444444444 +4444<444444=4 +44444444 +444 444444 444 +44444444444444 +44444444 4444 +44444444444444 +4444444444 +4444444444 +444444444444444 +4444444444 +44444444444'4 +444=44 «444 +4444444444: 444 +44444 44444 +4444444444 +444444444444 +444444444 4'4444444 +4444444444 +4444444444444 +44444444444 +444444444444 +4444444444444 +4444444444444 +4444444444 +444444444444 +444444444444444 +4444444444444 +**35****** +44=444444444 +4444 4444444444444 +444444444 +444444444444 +44444444444444 +4444444444 +4444444444444444 +4444444444 +444444444 +4444444444444 +444444444444444 +44444444444444 +44444444444 +4444444444444 +444444444 +4444444444444 +44444444444 +444444444 +++++5++++ ++++5++++ ++++S++++ ++++5++++ ++++5++++ PERCENT 10 20 30 40 o ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ m 190 BIBLIOGRAPHY Books and Pamphlets Dixon, Wilfrid J. , and Massey, Frank J. Introduction to Statistical. Analysis. New York: McGraw-Hill Book Company, Inc., 1957. Evarts, Harry E. Introduction to Pert. Boston: Allyn and Bacon, Inc. , l96h . Good, Carter V. Introduction to Educational Research. New York: Appleton~Centu1y~Crofts, Inc. , 1959. Grossman, Alvin and Hove, Robert L. Data Processing for Educators. Chicago: Educational Methods, Inc. , 1965. Jennings, Eugene E. The Executive. New York and Evanston: Harper and Row, 1962. Lehrer, Robert N. Work Simplification: Creative Thinking About Work Problems. Englewood Cliffs: Prentice Hall, Inc. , 1937. Likert, Rensis. New Patterns of Management. New York: McGrawc’Hill Book Company, Inc., 1961. Lindsay, Frank A. New Techniques for Management Decision Making. New York: McGrawquill Book Company, Inc., 1963. Reed, Luton R. Data Processing Systems. Central New York School Study Council, 1961: . (PamphletT Schlaifer, Robert. Probability and Statistics for Business Decisions. New York: McGraweHill Book Company, Inc. 1959. Walker, Helen M. , and Leo, Joseph. Statistical InfereEEE. New York: Henry Holt and Company, 1953. Articles and Periodicals Baker, Frank B. "Use of Computers in Educational. Research," Review of Educational Research, mIII, No. 5 (December, 1963) Bliss, Sam w., and Kaiser, Dale E. "A Teleaprocessing Pilot Study Pro-_ posal," Educational Data Processing Newsletter, IV, No. 3 (March, 1965). 12-f6o 191 mutated, Alec R. ”The Role of Time Sharing in Educational Data Pro- CessingSystems," M__o___nitor, IV, No. 6 (February, 1966), h-S. Cartwright, Charles N. 'Nev York State EDP Survey," AEDS‘ Bulletin, III, so. 5 (May, 1965). 2-h ”Dissertations," Journal of Educational Data Processing, III, No. 2 (Spring. 1W Educational Data ProcessiggFNewsletter, 1962-1965. Edwards, Ward and others. ”Bayesian fiatistical Inference for Psycholog- 1;:1 Sgsearch," Psychological Review, xxx, No. 3 (May. 1963), 1 -1 Goldstein, Willard. "The County Office and What It Can Do for School Districts With or Without Their Own Data-Processing Equipment, Journal of Educational Data Process g, III, No. 1 (Winter, 1965-66), “-80 Grossman, Alvin and am, Robert 1.. "Regional Educational Data-Process- " ing Centers in the State of California," Journal of Educational Data Processing, II, No.h(Fa11, 1965), 127-155. Haussmann, Rudolph D. , and Bath, Gustave J. "Automatic Teacher Assign- ment- A GPSS Simulatibn,‘ Journal of Educational Data Processing, II, No. 3 (wer’ 1%5)’ 103-1%. Hove, Robert L. ”Det' s Get Together on Systems, Educational Data mcessggjmlater, IV, No. 1 (January, 196‘), 31,32, Hunter, G. Trman. ' ”An Information System for School Management, Educational Data ProcessingZNewsletter, IV, No. 6 (June-July, 1965) , 1-9 Johnson, M. Clemens. ”Adaptive Computer Model," Journal of Educational P cholo , LV, No. 1, 66-70. Kaimann, Richard A. "Educators and Pert,” Journal of Educational Data Processi , III, No. 2 (Spring, 1966), 13- 57. Oldehoeft, Arthur E. ”The Roles of Systems Analysis, Programing, and Operations in an Information System," Educational Data Process _n§_ Newsletter, IV, No . 1 (January, 1965) ,"l"'5'-'l'9". Pike, Arthur 11., "NUBUG for Decision Making," Business Autanation. XII, No. 10 (October, 1965), Ash-A35. Proaect on Information Processing Newsletter. 1963-1965. Reed, Wayne 0. "The Data Link,” American Education, I, No.. 6 (June, 1965), 31-32. 193 ”Report of Committee on Educational Data Systems of the Council of Chief State School Officers,” Monitor, N, No. 3 (November, 1965), 2-3. "Research Documentation Editor, Iowa Educational Information Center,” Monitor, IV, No. 2 (October, 1965), h-7. Silvern, Leonard C. "Synergism in the Training System," Business Automation, XIII, No. 3 (March, 1966), mans} "—— "Time-Sharing System Will Do Many Tasks Simultaneously," Data'Processor for Customer Management, VIII, No. 3 (June 25, 1965), 1:5. Trocchi, Robert. "The Role of Computers in School Systems," Monitor, IV, No. 5 (January, 1966), 6:9. TechnicaI Publications Distal Communications Concepts and Communications Facilities. White Plains: International Business Machines, Technical Pub .lications Department, Form Nunber E20-8158. Data Processor for Customer Management, I34. 1962:1965. Data Station - Remote Communication Terminal. Wellesley Hills, Mass.: Honeywell Inc. , Electronic Data Processing Division, 1965. Flowcharting Techniques. White Plains: International Business Machines, Data Processing Division, Form N‘mn'ber 02043152. General Purpose Systems Simulator II. White Plains: International Business Machines, Technical Publications Department, Form Number B20~63’+6. 1963. Glossary of Data Processing and Communications Terms. Wellesley Hills, Mass.: Honeywell Inc. , Electronic Data Processing Division, 1965. Modern Coding Methods. White Plains, New York: International. Business Machines, Data Processing Division. Form No. X21=3793. The UNIVAC Educational Marketing Department, A Univac Student Accounting System, A Case Study. New York: The UN'l'VAC Division, Sperry Rand Corp. , Market Development Services, 1961;.(Pamphlet.) Unpub ll shed Material Bibby, Dause L. ”Computers and World Leadership." Keynote address bea- fore the Eastern Joint ComPuter Conference, Washington, D.C., 1965. 194 Emerson, William J. "The Intermediate School District - Middle Echelon of a Three Echelon State System of Schools.” Paper read before the meeting of the National Professors of Educational Administration, Arcata, California, August 26, 1965. (Mimeographed.) Kytle, Calvin. ”Civil Rights andCybernation,” an address to the third annual convention of the Association for Educational Systems, ' M33” 19650 ‘ Learning Systems Institute, College of Education, Michigan State Uni- versity. "Simulated Statistical Inference." East Lansing, Mich. , 1961;. (Papers of the Institute #8 duplicated.) Michigan State University, Division of Engineering Research. ”A Pilot Systems Research Program in Socio-Economic Studies." Report on Systems Research. East Lansing, Michigan: November, 1965. Reed, Luton R. "Bibliography, Automatic Data Processing." (Duplicated.) The Research and Development Center in Educational Data Processing. ”Bibliography of Publications." Sacramento: Department of Education, State of California, 1965. (Mimeographed.) Waterford Township School District. "Instruction in Electronic Data Processing." Waterford, Michigan: Board of Education Staff Study, 1961;. (Mimeographed.) Williams, John C. "Report of Teleprocessing Study - Walled Lake Consoli- dated Schools." A staff study report, 1966. (Mimeographed.) Other Sources Gonzalez, R. F., Michigan State University, Department of Management, East Lansing, Michigan. Personal interview.