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I” “I H “II II “T ' I'll lil”|”"| "H1; 1 :II “I I I "II III; I.I ’; I . ' I l;' IT ' ““I: I' 'I' 0 ' ml I” 1% ‘.I "”10,“ fl ’ I“ I: ‘.I?!” IIIIIIIIIIIQ‘i :1.“ III 2. [IR l n.” J III I.“ I... . I II...<.-I . I..III fin. .I‘IJ : III-IIWISI-Iu‘.“ '(fl‘fiw "" In!“ MI? I $1 ATM. I ' Will H I "ll." I‘ +|Il| IA ll‘ll WESTS This is to certify that the thesis entitled Development of an Intersection Turning Movement Predictive Model presented by Bruce L. Floyd has been accepted towards fulfillment of the requirements for M.S. 1133,6631 Civil Engineering (Emoflmm Major professorU Date 121/ l 6/ E/ 0-7639 ‘l’! nix}; ~. ram! OVERDUE FINES: 25¢ per day per item RETURNING LIBRARY MATERIALS: M- Place in book return to remove charge from circulation records DEVELOPMENT OF AN INTERSECTION TURNING MOVEMENT PREDICTIVE MODEL BY Bruce L. Floyd A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Civil and Sanitary Engineering 1981 ABSTRACT DEVELOPMENT OF AN INTERSECTION TURNING MOVEMENT PREDICTIVE MODEL BY Bruce L. Floyd An intersection turning movement estimation technique is developed using multi-variate regression analysis. The intersection is modeled by develoPing regression equations for the turning movements using the machine—counted ingress- egress volumes as independent variables. A computer program written to deve10p and test the model using the necessary field collected data as input is described. Using data collected from four intersections in Michigan, the regression theory is tested by develoPing actual intersection models. Analysis of these models shows the possibility of utilizing the regression technique as standard practice in turning movement estimation. The thesis concludes with an overall analysis of the theory and recommendations for future study. ACKNOWLEDGEMENT S I would like to express my sincerest gratitude to the numerous individuals in the Traffic and Safety Division and Computer Services Division, Michigan Department of Transportation and the College of Engineering, Michigan State University, who have aided me in completing this thesis. I would especially like to thank Dr. James Brogan, my advisor, and the other members of my committee, Dr. William Taylor and Dr. Adrian Koert for their assistance. The views, conclusions, and recommendations contained herein are the author's and not necessarily those of the Michigan Department of Transportation. The author is solely responsible for data and analysis accuracy. ii TABLE OF CONTENTS Page ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . 11 LIST OF TABLES . . . . . . . . . . . . . . . . . . . v LIST OF FIGURES . . . . . . . . . . . . . . . . . . ix CHAPTER ONE. INTRODUCTION , , , , , . , . . . . . . . 1 TWO. LITERATURE REVIEW . . . . . . . . . . . . 10 THREE. BASIC THEORY OF THE MODEL , . . . . . . . 15 PROBLEM STATEMENT . , . . . . . . . . . . 15 COUNTING ERROR . . . . . . . . . . . . . 19 DATA COLLECTION PROCEDURES. . . . . . . . 20 MODEL BUILDING THEORY AND APPLICATION . . 23 THREE-LEGGED INTERSECTION MODEL THEORY INTERSECTION TEST PROBLEM . . . . . . . 46 FOUR. CASE STUDIES , 61 FOUR-LEGGED INTERSECTION CASE STUDY , , . 64 APPLICATION OF THE MODEL , , . . . . . . 73 LINCOLN-LUDINGTON COMBINED DATA MODEL THREE-LEGGED INTERSECTION CASE STUDY . . 85 MAIN-FRONT COMBINED DATA MODEL , , , , , 93 FIVE. CONCLUSIONS AND RECOMMENDATIONS . . . . . 102 LIST OF REFERENCES 0 o o o o o o o o o o o o o o o o 107 iii APPENDICES O O O O O O O ._ O O O O O O O A. TURNING MOVEMENT MODEL COMPUTER PROGRAM.. FLOW CHART AND LISTING , . . . . . . TEST PROBLEM INTERSECTION MODEL . FOUR-LEGGED INTERSECTION MODEL DATA . THREE-LEGGED INTERSECTION MODEL DATA iv 109 109 170 194 204 Table 10 ll 12 13 Results of Results of Results of Estimation Movements. Results of Results of Estimation Movements. Results of Estimation Movements. Results of Estimation Movements. Results of Results of of Main-Front 7/78 Turning Movements Results of Results of Estimation Results of Estimation Results of Estimation Movements. LIST OF TABLES Test Model. . . . . Lincoln-Ludington 6/74 Model, Lincoln-Ludington 6/74 Model, of Lincoln-Ludington 7/76 Turning Lincoln-Ludington Combined Data Model Lincoln-Ludington Combined Data Model, of Lincoln-Ludington 6/74 Turning Lincoln-Ludington Combined Data Model, of Lincoln-Ludington 7/76 Turning Lincoln-Ludington Combined Data Model, of Ford-Newburgh 5/76 Turning Main-Front 10/75 Model, Main-Front 10/75 Model, Estimation Main-Front Combined Data Model, Main-Front Combined Data Model, of Main-Front 10/75 Turning Movements Main-Front Combined Data Model, of Main-Front 7/78 Turning Movements Main-Front Combined Data Model, of Grand River-Golf Club 2/77 Turning Page .48-49 067-68 . 75 . 81 . 82 . 86 .89-90 0 92 .94-95 . 96 o 97 . 100 Test Matrix (A), Ingress-Egress Manual Counts. . Test Matrix (B), Ingress-Egress Machine Counts . Test Matrix (M), Ingress-Egress %Error Matrix . Test Matrix (C), Adjusted Ingress-Egress Machine Counts Test Matrix (D), Adjusted and Balanced Ingress- Egress Machine Counts. . . . . . . . . . . . . . Test Matrix (Ml), Second Ingress-Egress %Error Matrix . . . . . Test Test Test Step Test Step Test Step Test Step Test Step Test Test Actual vs. Matrix (T), Statistical Statistical l O O O O 0 Statistical 2 O O O O 0 Statistical 3 O I O O 0 Statistical 4 O O O O 0 Statistical S O O I O 0 Matrix (E), Manual Turning Movement Counts. Analysis Variable Relationship. Analysis of Step-Wise Regression Analysis of Step-Wise Regression Analysis of Step-Wise Regression Analysis of Step-Wise Regression Analysis of Step-Wise Regression Regressions Coefficients Matrix Page 170 171 172 172 173 174 175 176-177 178 179 180 181 182 183 Statistical Analysis of Step-Wise Regression, Predicted values 0 O O O O O O O O 0 Test Matrix (F), Estimated Turning Movements . . Test Matrix (TE), Turning Movement Estimation Error 0 O O O 0 Test Matrix (G), Estimated Ingress-Egress Movements. . . . Test Matrix (H), Ingress-Egress % Error. vi 184 185 186 187 188 Page Test Matrix (P), % Turning - Manual Counts. . . . 189 Test Matrix (PP), Estimated % Turning . . . . . Test Matrix (GGG), Chi-Square Ingress-Egress Estimation O O O O I O ' O O O O O O O O O O O 0 Test Matrix (TTT), Chi-Square Turning Movement Estimation . O O O O O O O O O O O O O O I O 0 Test Matrix (PPP), Chi-Square % Turning Estimation O O O O O C C O I I O I C C O O O O Ingress—Egress Manual Counts, Lincoln- Ludington Intersection. . . . . . . . . . . . Ingress-Egress Machine Counts, Lincoln- Ludington Intersection. . . . . . . . . . . . Manual Turning Movement Counts, Lincoln- Ludington Intersection 6/74 . . . . . . . . . Regression Coefficients Matrix, Lincoln- Ludington Intersection 6/74 . . . . . . . . . Ingress-Egress Manual Counts, Lincoln- Ludington Intersection 7/76 . . . . . . . . . Ingress-Egress Machine Counts, Lincoln- Ludington Intersection 7/76 . . . . . . . . . Manual Turning Movement Counts, Lincoln- Ludington Intersection 7/76 . . . . . . . . . Ingress-Egress Manual Counts, Ford-Newburgh Intersection 5/76 . . . . . . . . . . . . . . Ingress-Egress Machine Counts, Ford—Newburgh Intersection 5/76 . . . . . . . . . . . . . . Manual Turning Movement Counts, Ford-Newburgh Intersection 5/76 0 O O O O O O O O O O O O O Ingress-Egress Manual Counts, Main-Front Intersection lO/75 . . . . . . . . . . . . . . Ingress-Egress Machine Counts, Main-Front Intersection 1.0/75 0 O O O O O O O O O O O O 0 Manual Turning Movement Counts, Main—Front Intersection 10/75 . . . . . . . . . . . . . . vii 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 Page Ingress-Egress Manual Counts, Main-Front Intersection 7/78. . . . . . . . . . . . . . . 207 Ingress-Egress Machine Counts, Main-Front Intersection 7/78 I O O I O O O C I O O O O O O 208 Manual Turning Movement Counts, Main-Front Intersection 7/78. . . . . . . . . . . . . . . 209 Ingress-Egress Manual Counts, Grand River-Golf Club Intersection 2/71 . . . . . . . . . . . . 210 Ingress-Egress Machine Counts, Grand River-Golf Club Intersection 2/77 . . . . . . . . . . . . 211 Manual Turning Movement Counts, Grand River-Golf Club Intersection 2/77 . . . . . . . . . . . . 212 viii Figure 10 11 12 13 14 15 16 LIST OF FIGURES NETSIM - Turning Movement Input Form. . . . Typical Machine Counter Configuration . . . Typical Vehicle Count Summary Sheet . . . . Intersection Flow Notation. . . . . . . . . Ingress-Egress Counts - Matrix Format . . . Turning Movement Counts - Matrix Format . . Linear Regression Model Theory. . . . . . . Regression Coefficients - Matrix Format . . Linear Regression Matrix Equation . . . . . Typical Three-Legged Intersection . . . . . Typical Hand Count Volume Sheet . . . . . . Typical Machine Count Volume Sheet. . . . . Lincoln Road and Ludington Road Intersection Ford Road and Newburgh Road Intersection. . Main Street and Front Street Intersection . Grand River Ave. and Golf Club Dr. Intersection ix Page 16 21 22 24-25 31 32 44 62 63 65 84 87 99 Chapter One INT RODUCT I ON Highway engineers and planners often have a need to know the directional flow of traffic within a highway intersection. An American Association of State Highways and TranSportation Officials (AASHTO) publication, for example, states that "The pattern of traffic movements at the intersections and volume of traffic on each approach, including pedestrians, during one or more peak periods of the day are indicative of the type of traffic control devices necessary, the widths of pavements required, including auxiliary lanes, and, where applicable, the degree of channelization needed to expedite the movement of all traffic." (1, p. 675)* One key to understanding an intersection's flow characteristics is a knowledge of the vehicular turning movements at the intersection. Turning movements are thus a main ingredient in almost every traffic intersection study. For example, the Federal Highway Administration's network simulation model, NETSIM, (4) requires that either turning movement counts or turning percentages be given. This data is entered in "NETSIM Card 7 - Link Turning Movements", a copy of which is shown in Figure l. *Numbers refer to The List of References (0 "A; 0") ‘ moo: 1' AHVIOOVIO wmm 'm u A!“ 0mm; ‘3!» u now omm'u Len A u 0' CM‘ 0. "KII' 0’ VI'”CK(3 ' Ioou Av ul‘ 0mm 1°“ 1| .. *\ 00' 100‘ avatmo 17:00“: ‘ soon- JV Humid cum-m woo-u u 5"“ Dim-n1 Moo: u nun; M-SIAVIA "0L!“ 0. ”KT!" 0' vimtf‘ '300. AV ul‘ 9mm: J I! it” 60 no- nvuuwoo In." :0 I00. twink" ' 300'- AV nan-09m mmnm FTLE: ‘.OO'U AV AHD‘I WW1 woo. AV flat-u om‘MVIA E x 5 8 3. Y 1' 5 3 'IOO~ A! All‘ ONMA I' ll an ”‘ ”0' "VHLIW N a man no ' noo- nvlukfl ‘IOO‘ " nut-coma can-um 'Iomu 5v Am Odom; ' soon it Riva nnum COUNV O. “Kl-V a! “mu noo- 17 “I1 001an O l' 1 um 00' non-imam II nwwnlnoumuum 123.567.. NETSIM CARD 7 — me TURNING movemems Figure 1 NETSIM - Turning Movement Input Form The signal optimization program, TRANSYT, (9) also requires intersection turning movement data in order to estimate link flows. Highway capacity analysis, signaliza— tion studies, conflict analysis, accident analysis and signalization phasing studies all require turning movement knowledge at the intersection under study. Planners, as well as engineers, may use turning movement information in checking origin-destination studies and in network analysis. There is, therefore, a large demand for inter- section turning movement information. At the present time, relatively simple procedures are used by transportation agencies in collecting inter- section turning movement data. In most cases, a crew of one or more people is dispatched to the intersection and a pneumatic tube or some other type of mechanical counter is placed at each entrance and exit of the intersection. Figure 2 shows a typical configuration. The machines then count the ingress and egress traffic of the intersection, typically for a 48 hour period with tabulations every 15 minutes. There are thus four counts per hour. At some time during the two days, usually during the AM and PM traffic peaks, crews hand count the turning movements within the intersection using a tally sheet or hand-held counter. These turning movement counts, like the machine counts, are tabulated every fifteen minutes. (The period of tabulation may vary from study to study or from agency to agency, but fifteen minutes is relatively standard.) 6) 6) Machine Counter with Pneumatic Tube =<: >_' ' Figure 2 Typical Machine Counter Configuration All of the data is tabulated in an intersection turning movement report. Figure 3 shows the graphic summary of one such report. This sheet gives the intersection description and location, the final counts of the total time studied, and when the counts were taken. Subsequent pages of the report give more specific information, such as the machine counts, 15 minute tabulations, any unusual incidents that occured during the study period, and so forth. The method just outlined is labor intensive and thus costly. Since there are many users of intersection in- formation, transportation agencies are hard pressed to keep up with the demand for information. If all requests are to be fulfilled within a reasonable time, a large labor force is required. If a large labor force cannot be hired because of budget limitations, a backlog of requests usually results. Because of the long wait associated with obtaining intersection turning movement data, many users estimate this data or simply do without it. If a method can be deve10ped by which intersection turning movement informa- tion can be estimated with sufficient accuracy three major benefits will result. First, more intersections can be studied at approximately the same cost of the present method. Thus, potential users who would like to have information, but do not request it because of the time delay or cost to their unit, will now be able to do so. 1763(1/781 TV?” VILLAGE OR CITY INTERSECTION 0' DAY Wednesday counvv US-ZL [IS-41, Delta VEHICLE VOLUME COUNT GRAPHIC SUMMARY SHEET Study #203 TIME Escanaba szszn M-35(Lincoln) @ 12th Ave.N. TO 9A 1 r7 A 11ATo 1p “7 2P 6? TO 05-2, 03-41, M-3S(L1nc01n) 8 Hr. Total INDICATE NORTH _—> 11847 «___. 12th Ave. N. 12th Ave. N. -- 5763 6084 ___ 19 5880 135 k\ j 43 \J 193 11 ///,, 297 139 / 107 222 11 346 \ 228 W q r -————> 192 5613 101 REMARKS —————— INDICATES PEDESTRIANS CROSSING AT INTFRSECTION C - CHILDREN A - ADULTS P- ALL PEDESTRIANS ;> 12153 5906 6247 05—24 05-41. M-35(Linc01n) Figure 3 Typical Vehicle Count Summary Sheet The time delay to users will be shortened because hand counts will be taken at only those intersections which require it. Second, the estimation should allow study of the intersection turning movements on a twenty-four hour basis. If a technique can be developed which does not require constant human attention, night-time Operation studies, which are now generally cost prohibitive, can be made. Finally, if an estimation technique can be deve10ped and applied to large volume intersections, little accuracy may be lost and the accident potential associated with hand-counting Operations may be lessened. Therefore, if a method can be developed by which an accurate estimation of turning movements can be made quickly from the machine counts, the need for information may be met and the aforementioned benefits realized. This thesis deve10ped just such an estimation procedure. The estimation technique was based on statistical analysis and utilizes a large computer for rapid processing. The procedure which the thesis deve10ped is outlined in Figure 4, on page 16, which shows a typical four-legged intersection in which U-turns are not allowed. The nota- tion used throughout the study is shown in Figure 4 and is as follows: The numbers represent the major compass directions: North or Northeast, East or Southeast, South or Southwest, West or Northwest. waH I = Ingress traffic, the total traffic entering the intersection from a particular direction (vehicles/time unit), E = Egress traffic, the total traffic exiting the intersection to a particular direction (vehicles/ time unit), The traffic entering from the I th direction and exiting to the E th direction (vehicles/ time unit) XIE As can be seen, the values of the turning movements, (XIE's), are dependent on the values of the ingress and egress traffic (1's and E's). This research proposes that an estimation of any of the turning movements can be made from its relationship with the ingress and egress variables. A linear model was suggested as the first possible approach, with the dependent variables the individual turning move- ments and the independent variables the ingress and egress volumes. The following regression equation type was thus proposed: xIE = bOIE + bllE (11) + b21E (12) + b3IE (I3) (Eq. 1-1) + b4IE (I4) + bSIE (El) + bGIE (E2) + b7IE (E3) + bBIE (E4) Where the bIE's are regression equation coefficients and the Ii's and Ej's are the ingress and egress volumes respectively. The basic objective of the thesis was to develOp and test such a regression model using actual intersection data. The following procedure was used. First, a literature search was made to determine the present theoretical "state-of-the-art" of intersection counting procedures. The present field operations for collecting intersection data have already been described. The literature review thus focuses on recent efforts relating to the estimation of turning movements from flow volumes. Second, a theory of the intersection model development is presented. This chapter explains how the proposed inter- section model(s) were developed and tested and what results were expected. Analysis of expected error is also dis- cussed in this chapter. Third, in order to test the regression model, actual intersection data was used from previous traffic studies conducted by the Michigan Department of Transportation. The descriptions of these locations is given in the chapter on case studies. Both four-legged and three-legged inter- sections were studied. Finally, conclusions and recommendations are pre- sented. This chapter discusses how well the model(s) worked, what degree of error was present, and where future study should be directed. Chapter Two LITERATURE REVIEW A literature search produced little previous research on the subject of turning movement estimation from known ingress and egress movements. Most articles and publica- tions reviewed assumed that turning movements at inter- sections were hand-counted. For example, according to the Institute of Transportation Engineer's "Transportation and Traffic Handbook": "Intersection counts are usually Conducted manually. Low-volume intersections may be counted by one person, but heavier volumes are usually counted by a team of two or more observers." (2, p. 408). Recent articles in "Traffic Engineering & Control", however, discuss turning movement estimation. After a brief explanation of terms, a review of these articles will follow. In this thesis and in the recent articles, the following definitions and constraints (using the notation of Figure 4, page 16) apply: 1) The only intersections considered for study are those in which storage, the retention of vehicles within the intersection, is not allowed. Thus, the sum of the ingress counts equals the sum of the egress counts: 4 4 z Ii = Ej (Eq. 2-1) i=1 j=l 10 11 If this is not the case for any collected data, the source of error must be identified, and the data "corrected" to satisfy this constraint. 2) The only intersections considered for study are those in which U-turns are not allowed. There- fore, equation (2-2) holds. X11 = X22 = X33 = X44 = 0 (Eq. 2-2) 3) A solution is a set of numeric values which are assigned by some method to the turning movement variables, X12, X13, X14, and so forth. 4) A solution is defined as feasible if the values of X's are non-negative and meet the following constraints: I1 = X12 + X13 + X14 (Eq. 2-3) lg = X21 + X23 + X24 (Eq. 2-4) I3 = X31 + X32 + X34 (Eq. 2-5) I4 = X41 + X42 + X43 (Eq. 2-6) E1 = X21 + X31 + X41 (Eq. 2-7) E2 = X12 + X32 + X42 (Eq. 2-8) E3 = X13 + X23 + X43 (Eq. 2-7) E4 = x14 + X24 + X34 (Eq. 2-8) Il + 12 + I3 + I4 = E1 + E2 + E3 + E4(Eq. 2-9) 5) A symmetrical intersection flow is defined as one in which the ingress volume of any direction equals the egress volume to the same direction. Thus, 11 = E1, 12 = E2, I3 = E3, and I4 = E4. 6) A symmetrical intersection turning flow is defined as one in which Xij = X'i for all 1's and j's. Thus, X12 = X21, X13 = E31, and SO forth. The particular problem, as will be discussed in detail in Chapter 3, to which other recent research and this thesis address themselves is that when only ingress and egress volumes (link flows) are known, there is no unique feasible solution. There is, instead, a finite set of feasible solutions. The goal of finding a technique to determine the most appropriate feasible solution is common to the other recent studies and this thesis. 12 Martyn Jeffreys and Michael Norman, British transporta- tion consultants, have shown that using linear programming and matrix algebra, the finite set of solutions can be defined. (7) They also contend that as an intersection reaches saturation flow, the intersection flow matrix approaches symmetry. Given symmetrical flow, they develOp techniques for finding a unique solution. M.L. Marshall, a British planner in Dorset County, has shown that it is not necessary to count all turning movement flows, (XIE's), in order to determine a unique solution. (8) He also explains that if probabilities are assigned to the correct number of turning movements, an estimated solution can be reached without any observers. These probabilities are to be assigned assuming an "a priori" knowledge of the intersection's behavior. Ali Mekky, a lecturer at Alfateh University in Tripoli, has developed an iterative technique for updating an intersection flow matrix from a base year knowledge. (10) This technique involves using a Lagrangian equation which minimizes the distance between the base year turning movement matrix and the unknown turning movement matrix. The equation is solved iteratively using either the Furness method or the biproportionate method. H. VanZuylen has deve10ped a similar technique using "a priori" probabilities of turning. (13) Again a Lagrangian equation is solved using an iterative process.- 13 Finally, Norman, Hoffmann, and Harding describe three techniques that can be used to determine a unique feasible solution. (14) These techniques are non-iterative and are based on using "a priori" knowledge to change a non- constrained flow matrix to a constrained flow matrix. These techniques are compared to an iterative technique, the Entropy-Maximization solution. Although the goal of both previous research and this thesis is the same, the sc0pe is quite different in nature. Whereas previous studies were attempting to solve the turning movement estimation problem primarily in order to update flow networks to be used in transportation planning, in this thesis the estimation technique was developed to fulfill a traffic operations need for turning movement information, such as for the NETSIM and TRANSYT computer programs mentioned earlier. Therefore, this thesis developed a technique that is much more specific in nature than previous research and therefore leads to several differences in the direction of future studies. Since most of the authors of previous studies are planners, their research reflects transportation planning needs. They are searching primarily for a reliable but inexpensive procedure to update traffic network flows so that they can be used for planning purposes. This goal has led them to develop iteration techniques similar to the "gravity" model to determine a solution. The time base is generally one year. Errors due to counting or to 14 minor changes in traffic operations are not studied since they are assumed not to be significant. The research in this thesis, because its sc0pe is directed towards intersection operation, differs from previous research in the following ways: 1) 2) 3) 4) 5) Tabulations were taken at shorter intervals, in order to describe variations in intersection behavior more accurately. Because of the shorter tabulation period, machine count error and Operations error must be described and compensated for. The intersection model should be able to detect changes in intersection flow using only machine counts. Collection of several tabulations will provide a data base for a linear regression technique, rather than using an iterative technique such as the gravity model which uses one set of data. Last, and most important, the linear regression technique should become a basis for developing "standard" estimation models. Data from inter- sections never before studied would be input into these models and the "best fitting" turning movement estimations used. In the next chapter, the theory of the linear regres- sion technique is fully described with a sample problem. References to previous research will be made where appro- priate. Chapter Three BASIC THEORY OF THE MODEL In this chapter the basic theory of building a linear regression model of intersection flow is discussed. First, the basic problem of turning movement estimation is analytically stated. Second, the problem of counting error is discussed and treated. Third, a step-by-step explanation of the model building technique is given for a four-legged intersection. Then, the theory of a third- legged intersection as a special case is presented. Finally, test data is used to build an actual intersection turning movement model. PROBLEM STATEMENT The basic notation and assumptions presented in the first two chapters are the basis for the problem statement. The notation shown in Figure 4 is used. The basic inter- section equations, as given in Chapter Two are: 11 = X12 + X13 + X14 (Eq- 3-1) 12 = X21 + X23 + x24 (Eq. 3-2) I3 = X31 + X32 + X34 (Eq- 3-3) I4 = X41 + X42 + X43 (Eq- 3-4) E1 = X21 + X31 + X41 (Eq. 3-5) E2 = X12 + X32 + X42 (Eq. 3-6) E3 = X13 + X23 + x43 (Eq. 3-7) E4 = X14 + X24 + X34 (Eq- 3-8) I1 + I2 + I3 + I4 = E1 + E2 + E3 + E4 (Eq. 3-9) 15 16 IH L ['.I I" X31 X21 fl a F__1 X14 \ E4 X24 >3 I.= X E . for each t=l,2,3,...n i=1 j=1 t3 Each row in Matrix (C) is thus balanced to meet this constraint. This balancing forms Matrix (D). The balancing technique assumes that the error is distributed prOportionally among the counts during the particular time period under consideration. The following formulas are used: (Eq. 3-19) 4 4 R = Z _ E E t i=1 Iti j=1 t] (Eq. 3-20) dtl = Ctl " E Ctl for 1 3,23} 2 4 :1 ti (Eq. 3-21) C11:1 = Ctl +_§_‘.‘—_ Ctl for 55203 4 ~—-- _ where: Rt = balance error for the t th row, dtl = the numerical entry in the t th row and 1 th column of Matrix (D), and Ctl = the numerical entry in the t th row and 1 th column of Matrix (C). 29 The adjusted and balanced machine counts of Matrix (D) are compared to the hand-counted ingress-egress volumes of Matrix (A) using Equations 3-12 through 3—15. The mean percentage error should be zero for all ingress and egress volumes. The more the mean percentage errors deviate from zero, the less successful the error adjust- ment. If the deviations from zero are unacceptable to the model builder, the error-adjustment process can be iterated until acceptable deviations are obtained. The intersection data can also be studied for time-varying dependence or for any violations of the machine count assumptions stated in this chapter. The level of tolerable deviation from zero mean percentage error is dependent upon the users' needs. In this study, the error process is iterated if the absolute value of any of the mean percentage errors is greater than five percent. The iterative process is cut off when the acceptable tolerance is reached or after five unsuccessful iterations. If the adjustment process is unsuccessful, the data should be reexamined. Assuming that the error adjustment has been successful, the hand-counted turning movements, Matrix (T), and the balanced and adjusted machine counts, Matrix (D), are used in regression analysis. The regression equation for each of the 12 dependent variables (the turning movements) is of the form: 30 (Eq. 3—22) xIE - be + b1 11+ b2 12 + b3 I3 IE IE IE + b I + b E + b E + b E + 418 4 51E 1 61B 2 7IE 3 b E 81B 4 The coefficients are calculated using a step—wise linear regression computer program (11), and are placed into a 9 x 12 matrix, Matrix (E), as shown in Figure 8. The model is tested by multiplying Matrix (E) and Matrix (D*) as shown in Equations 3-23 and 3-24, (Figure 9). Matrix (D*) is Matrix (D) with a column of dummy l's added. The dummy 1's are the coefficients of the intercepts. Matrix (F), the estimated turning movement counts, is the result. 31 AmvvmAmvvmaflvvavmvavamAHmvaONvammvmAHNvmavavmfimavm ANHW v a a a a n n n n n h h h m . . . . . . . . . . .fimavbn mm . . . . . . . . . . .Amavmn mm . . . . . . . . . . .Amavmn Hm . . . . . . . . . . .nmavan 4H . . . . . . . . . . .Amavmn mH . . . . . . . . . . .ANHVNQ NH . . . . . . . . . . .Amavan HH AmvvohmvvohawvohvmvohmmvowamvobvmvowmmvohHNvONOHVOMMHVOQANHVOQ .HCH max vi flax vmx me me wax mmx me wax max max - Matrix Format Icients Figure 8 Regression Coeff 32 fimva MNQQ wag MHWQ mag; 80 Q Io Q So Q So on a. wfifl FCC ma @HU BHU mHU mHU vHU MHU NHU HHU E 7 J lm4cc Imvcc lave: Avmcc lumen Eamon 148cc Ammo: lance Ivar: lmficc Emacs mmvvamANvVHmAHvVHmfivmVHMANmVHmAHmVHmAVNVHuAMNVHmAHNVHMAOHVHHAMHVHMANHVHH L Figure 9 Linear Regression Matrix Equation (Equation 3-24) 33 (D*) X (E) = (F) (Eq. 3-23) n x 9 9 x 12 n x 12 Comparing the actual turning movement matrix, Matrix (T) and the estimated turning movement matrix, Matrix (F) creates the turning movement percentage error matrix, Matrix (TE). The following formula is used: (Eq. 3-25) where: TE the turning movement percentage error in t1 the t th row and the 1 th column of Matrix (TE), Ftl = the estimated turning movement in the t th row and the 1 th column of Matrix (F), and Tt1 = the actual turning movement in the t th row and 1 th column of Matrix (T). The mean and standard deviation of the turning move- ment percentage error is computed for each Xij. These are measures of how well the model is calibrated. The means and standard deviations would equal zero if the model were perfect. The further from zero means are, the more imperfect the model. Applying the intersection equations, Equations 3-1 through 3-9, estimated ingress-egress volumes can be computed from the estimated turning movements contained in Matrix (F). The results are placed in Matrix (G). 34 Comparing Matrix (D), the adjusted and balanced machine counts, with Matrix (G), the estimated ingress- egress counts, an error matrix, Matrix (H), is computed using the following equation: (Eq. 3-26) where: H = the percentage error in the t th row and 1 th column in Matrix (H). th = the estimated ingress or egress movement in the t th row and 1 th column in Matrix (G), and Dtl = the adjusted and balanced machine count in the t th row and 1 th column in Matrix (D). The mean error and standard deviation are also computed and are shown in the last two rows of Matrix (H). The mean values of Matrix (H) provide another verification check of the model. The closer to zero the means and standard deviations of error matrix, the better fitting is the model. The estimated turning movements matrix, Matrix (F), can be adjusted to reduce the mean errors of Matrix (H). For each value XI of Matrix (F), there is an error E from the I component and an error from the E component. The values of the (F) Matrix are adjusted to give a new (F) Matrix by the following equation: 35 Ftl new = Ftl old + (I where: Ftl new = the new value column of the F old t1 the old value column of the IiGDE the error in matrices = Ii i = 1 when l i = 2 when 1 i = 3 when l i = 4 when 1 EjGD = the error in matrices = Ej j 1 when l j = 2 when l j = 3 when l j = 4 when 1 From the new (Fl) matrix, are computed. For this study t until all mean values of (H(n)) absolute value or a maximum of The next validation test is the comparison of the actual turning matrices. The percent counted data is placed in Matri iGDE/3) + (EjGDE/3) (Eq. 3-27) for the t th row and 1 th new Matrix (F), for the t th row and 1 th new Matrix (F), Ii between the (D) and (G) (D) — Ii(G), = 1,2,3 = 4,5,6 = 7,8,9 10,11,12, and Ej between the (D) and (G) (D) - Ej (G): 4,7,10 1,8,11 2,5,12 3,6,9. new (G1) and H1) matrices he process is repeated are less than 5.00% in five iterations is reached. Of the model calibration and estimated percent turning of the hand- x (P) and is calculated as 36 follows: (Eq. 3-28) kk where: Pt1 = the percent turning in the t th row and 1 th column of Matrix (P), and Tt1 = the number of turning in the t th row and 1 th column of Matrix (T), if 1 = 1,2,3 k = 1, kk = 3 if 1 = 4,5,6 k = 4, kk = 6 if 1 = 7,8,9 k = 7, kk = 9 if 1 = 10,11,12 k =10, kk =12. The mean percentage turning and the standard deviation are computed and placed in the last rows of Matrix (P). Matrix (PP) is the estimated turning percent matrix and is com- puted in the same manner as Matrix (P) except using Matrix (F) instead of Matrix (T). The closer the estimated percentages are to the actual percentages, the better the model is. The maximum allowable magnitude of error is a choice of the model builder. However, since these values are a primary output of the model, as described in Chapter 1 (for the NETSIM computer program), careful consideration should be given to their acceptance. For this study, the model is con- sidered acceptable if the estimated error percentages are not more than 2%. 3/~ The final validation tests are chi-square tests for the goodness-of-fit of the turning movement estimation, the percent turning movement estimation and the ingress- egress estimation. (3) The general form of the chi—square test is: (Eq. 3-29) 2 x z n _ _ 2 — (oi Bi) 1=1 E. l where: 2 X = the total chi-square value, 0 1 = the observed or estimated value for cell i, and E i = the expected or actual value for cell i. This test measures how well the model's output fits the actual intersection performance and is, therefore, an important test of linear fit for an intersection. Since the cells are the time periods and are considered inde- pendent, the degrees of freedom for the test equals the time period sample size. The autocorrelation coefficients and the residuals can be checked to determine the degree of time dependence. 38 The chi-square value for ingress-egress estimation is computed from Matrices (D) and (G) for each movement for each time period and placed in Matrix (GGG) using the following equation: (Eq. 3-30) GGth = (th - Dtl)2 Dtl where: GGth = the chi square value for the t th row and the 1 th column of Matrix (GGG), th = the estimated ingress or egress volume for the t th row and the 1 th column of Matrix (G), and Dtl = the adjusted and balanced ingress or egress volume for the t th row and 1 th column of Matrix (D). 39 The total chi-square values are computed using the fol- lowing formulas: (Eq. 3-31) 2 n X 2 GGG for 1 l 4 11 = :1 t1 -: .5.- where: X2 = the total chi-square value for the Il ingress from direction 1. (Eq. 3-32) 2 = n X Z (36th for 5 :1 :8 E t=l (1-4) where: E = the total chi-square value for the X2 (1-4) egress to direction (1—4). The level of confidence at which the estimation is accepted is obtained from a chi-square distribution table, (3, pages 600-601) using n, the number of time periods as the degrees of freedom. Note that the balanced and adjusted counts are used in this test in order to measure the error introduced by the linear regression model. If the model is perfect, the chi-square value for each movement will equal zero. 40 The chi-square values for the turning movements are computed in same manner using Matrices (F) and (T) as follows: (Eq. 3-33) TTTtl — (Ftl - Ttl)2 Ttl where: TTTtl = the chi-square value for the t th row and the 1 th column of Matrix (TTT), Ftl = the estimated turning movement for the t th row and the 1 th column of Matrix (F), and Ttl = the actual turning movement for the t th row and the 1 th column of Matrix (T). The total chi-square values are computed using the following formula: (Eq. 3-34) ‘X2 n = Z TTT Xij t=1 t1 where: 2 )( X =, the total chi-square value for turning ij movement from the ith direction to the j th direction. If the model would estimate each turning movement for each time period perfectly, the chi-square value would 41 equal zero in all cases. In a similar fashion, the chi- square values for the turning movement percentages are calculated using Matrices (P) and (PP) as follows: 2 (Eq. 3-35) PPPtl = (PPtl. - Ptl) Ptl where: PPPt1 = the chi-square value for the t th row and the 1 th column of Matrix (PPP), PPtl = the estimated turning movement percentage for the t th row and 1 th column of Matrix (PP), and Ptl = the actual turning movement percentage for the t th row and 1 th column of Matrix (P). The total chi-square values are computed using the following formula: (Eq. 3-36) = P x Z PPtl where: the total chi-square value for the x%.. turning movement percentage from the i th 13 direction to the j th direction. If the model's estimated turning movement percentages are exact, the chi-square values are zero. The level of confidence of acceptance is determined by the chi-square 42 distribution table using the number of time periods as the degrees of freedom. If the model is validated by all the tests, the error matrix(ices), Matrix (M), and the regression coefficients matrix, Matrix (E), are stored for future use. Any new machine count data is placed in a new Matrix (B). The model's error matrix(ices), Matrix (M), is (are) applied, giving an adjusted machine count matrix, Matrix (C). Matrix (C) is balanced giving an adjusted and balanced matrix, Matrix (D). The new Matrix (D) is multiplied by the model's regression coefficientS' matrix, Matrix (E), which produces the estimated turning movement matrix, Matrix (F). An estimated ingress- egress matrix, Matrix (G), is computed from Matrix (F). Matrix (D), the balanced and adjusted machine counts, and Matrix (G), the estimated ingress-egress counts, are compared, giving an error matrix, Matrix (H). A chi- square test is also performed using Matrices (D)and (F), producing Matrix (GGG). From these two matrices, the user can determine if the intersection has changed significantly since the model was developed. The larger the mean percentage errors in Matrix (H) or the chi- square values are, the more variance has deve10ped that is not explained by the model. Matrix (F) can be adjusted, as was discussed previously in order to attempt to reduce the Matrix (H) error. 43 If the model is validated only by the overall per- formance tests, but not by the chi-square tests, the user may still be able to retain and use the model. However, the model cannot be relied upon to give an actual estima- tion for any particular time period, but may be suitable for an estimation of overall performance for several time periods. A FORTRAN computer program was written which builds and stores an intersection turning movement model and can apply it to new data. A flow diagram and listing can be found in Appendix A. The model building computer program has a statistical output Option for the evalua- tion of the step-wise linear regression. This output includes the covariance matrix, the correlation matrix, total sum of squares, the improvement of unexplained variance for each step, analysis of variance, and a t-test value. The user can trigger this option and analyze any of the turning movement regression equations. THREE-LEGGED INTERSECTION MODEL THEORY The basic theory of the three-legged intersection is similar to that of the four-legged intersection. In fact, a three-legged intersection is simply a special case of a four-legged intersection. Figure 10 shows a normal three-legged intersection where there is no southern leg. The direction of the missing leg is arbitrary, but for this discussion the intersection of 44 X42 £2 Figure 10 Typical Three-legged Intersection 45 Figure 10 will be used. The same theory applies regardless of which leg is missing. All previous assump- tions and constraints on the four-legged intersection also hold for the three—legged case. Since the southern leg is missing, the following equation holds: (Eq. 3-37) 13 = E3 = X13 = X23 = X43 = X31 = X32 = X34 = 0 The following intersection equations also now hold: I1 + 12 + I4 = E1 + E2 + E4, (Eq. 3-38) 11 = X12 + X14 (Eq. 3-39) 12 = X21 + X24 (Eq. 3-40) I4 = X41 + X42 (Eq. 3-41) E1 = X21 + X41 (Eq. 3-42) E2 = X12 + X41 (Eq. 3-43) E4 = X14 + X24 (Eq. 3-44) There are 6 unknowns, 6 independent equations and l redundancy. Therefore, there is 1 degree of freedom. Thus, if one turning movement count is known and the ingress-egress volumes are known, the intersection is determinate. The matrix form of the independent equa- tion is: 46 (Eq. 3-45) F . FX X 0 0 0 0 l I 12 14 1 0 0 0 0 X41 X42 X l = I4 0 0 X21 0 X41 0 1 E1 X12 0 0 0 () X42 1 E2 X 0 l4 0 X24 0 0 1 E4 _ .J .J - J A linear regression approach, using knowledge of previous performance, was used exactly like the four- legged intersection. Therefore, the equations, which are simply the special case of the four-legged theory just discussed, are not presented here. To build the model, hand-counted intersection data and machine-counted inter- section data were used. The ingress-egress machine counts were adjusted and balanced. The regression equations were developed and turning movements are estimated. The model was checked and accepted or rejected. If accepted, the model was stored for future use. INTERSECTION TEST PROBLEM To better illustrate the linear regression model building process, intersection test data was used to build an example model. The input and output data are found in Tables B-l through B-24 in Appendix B, and will be referred to in the following step-by-step explanation. 47 As in the case studies of the next chapter, only a summary table will be presented in the text. The summary table for the test problem is presented in Table l on the next two pages. First, the intersection field data was collected. The hand-counted ingress-egress counts are placed in Matrix (A) as shown in Table B-1. The machine counts of the ingress-egress movements were placed in Matrix (B) as shown in Table B-2. The hand-counted turning move- ments were placed in Matrix (T) as shown in Table B-7. The headings show the movements using the notation of Figure 4, with the time periods numbered in the left column. These three matrices are the necessary input data for the computer prOgram. Using Equations 3-12 through 3-15, the error matrix, Matrix (M), is computed. To illustrate the calculation of the mean percent error matrix, the error for 11 during the first time period, (t=l), is as follows: %eI = 132 - 125 x 100 = 5.60% 11 125 where: 132 is the entry of the first column and first row of Matrix (B). It is the machine count for 11 for time period 1, and 125 is the entry of the first column and first row of Matrix (A). It is the actual count for 11 for time period 1. 48 TABLE 1 RESULTS OF TEST MODEL gm mh.m vv.Hl av.oa HN.oI om.mH mm.v mN.OH mm.H o.vH N.vm OmHmU nfieoa Hm «H MH NH HH ZOHBflSHBmm mmmmwMImmMMGZH mom Emma mmdDOmleU AOUGV mo.h mh.¢ Ho.m Hm.m HH.NH uzmam mv.o mo.0I mo.o mm.o mm.o "24m: Hm vH MH NH HH mommm onemzHemm mmmmomnmmmmozH Amy mm.ma ma.m me.oa mn.ma mm.ma uzmem Hm.m em.m mm.» mm.m mo.~ ”24m: Hm 4H mH NH HH nouns m Ase 49 TABLE 1 (CONT'D) max ¢.m m.HH max h.oa m.ma o.m H.HN m.v m.v max Hex emx OmHmU HdBOB m.vH m.v b.m N.m w.m mmx me vmx mmx me wax max max ZOHBfiEHBmm mwdfizmummm Bzmzm>02 UZHZmDB Emma HM4DOmIHmU Amflmv m.NN vi b.0N o.mw NVN m.mH b.~m vi N.mN m.mH ¢.om h.vH m.NN o.mH b.0H ¢.ma o.mH H.¢H OmHmU Hex h.ON v.mN HVN emx H4908 mmx me «Nx mmx me sax max wax ZOHBfiZHBmm Bzm2m>02 wZHszB BmflB mmoz oszmoe omaazHemm Ammv h.m v.mH m.NN m.N >.HN m.m N.b N.m HZ¢Em ~.mH N.mm m.mm w.ma 5.0m m.mH v.hm h.mN u me me VNX mmx HNX vax max max mwdfiZMUmmm BZMEM>OZ UZHZfiDE 44D90¢ Amy m.mm H.HH o.mH o.mN m.mH «.mm h.HH m.mH uZ¢Bm m.H v.o m.H m.N h.ol m.H N.0I 5.0 uz¢m2 me me vmx mmx me wax max max mommm onemzHemm ezmzm>oz oszmoe Away 50 If this calculation is made for all 20 time periods, then summed and divided by 20, as per Equation 3-12, the result is §E§;, which is 2.09%, as entered in Matrix (M), found in Table B-3, first column and first row. The standard deviation for the percent error in II, as calculated with Equation 3-13 is 15.28%. To summarize, from Matrix (M), we know that for the ingress movement from the North, 11' the machine count is on the average 2.09% high with a standard deviation of 15.25%; for the egress movement to the North, E1, the machine count is, on the average, 3.62% high with a standard deviation of 15.73%, and so forth. Matrix (M) is an important model matrix and is also found in the summary, Table 1. To adjust the machine count error so that the mean percent error is approximately zero, Equations 3-16 and 3—17 are used. This produces Matrix (C), the adjusted counts matrix, as shown in Table B-4. To illustrate the calculation of Matrix (C), the adjustment calculation for 11 for the first time period is as follows: 129.34 C = 132 - 132 x 2.2.42.9. 11 100 (rounded to 129) where: 132 is the machine count for Il for the first time period, column 1 and row 1 in Matrix (B), and 51 -2.09 is the mean percent error for 11' as is shown in column 1 and row 1 of Matrix (M). The negative error means that the movement was undercounted due to machine insensitivity or vehicles missing the tube. The adjustment is made on all the machine counts, making the mean percent error approximately zero for all ingress-egress variables. Next, the counts are balanced for each time period, using Equations 3—19, 3-20, and 3-21. This satisfies the constraint that there is no storage in the intersec- tion, that is, that the sum of the ingress volumes equals the sum of egress volumes for each time period. The adjustment for 11 for the first time period is as follows: First, the constraint error is calculated: 4 I. = 129 + 58 + 100 + 80 = 367, Z 1 i=1 4 ; Ej = 157 + 74 + 68 + 65 = 364, i=1 R1 = F E- ‘2 Ii = 367 - 364 = 3, 3 52 4 where: Z Ii is the sum of the ingress counts for i=1 time period 1 in Matrix (C), and 4 3-1 Ej is the sum of the egress counts for time period 1 in Matrix (C). The adjustment for 11 (t=1) for Matrix (D) is calculated next: 11 (t=1) = 129 - 3/2 (129/367) = 128.47 (rounded to 128), where: 129 is the adjusted count for 11 for time period 1 in Matrix (C), 367 is the sum of the ingress counts for time period 1 in Matrix (C), and 3/2 is R /2; since one half of the error is adjusted with the ingress and one half with the egress. The completed Matrix (D) is shown in Table B--5. From Matrix (A) and Matrix (D) a new error matrix, Matrix (M1), is calculated and shown in Table B-6. Matrix (Ml) shows that the mean percent errors of Matrix (D) are not greater than 5.00%. Therefore, the adjustment procedure has been successful. To illustrate the statistical output that is avail- able from the computer prOgram, only the linear regression 53 equation using X12 is used, since the output is quite lengthy. The output for the other eleven equations have the same format. This output is optional for the user and can be used to analyze and validate the linear regression equations. Tables B-8 through B-13 contain the data from the X12 equation. Table B-8 gives the means, the standard deviations, the covariance matrix, and the correlation matrix of the dependent variable X12 and the eight independent vari- ables. The total sum of squares error is also shown. Tables B-9 through B-13 show the step-by-step analysis of variance for the regression analysis. The stepwise linear regression computer program is very similar to the one described by Neter and Wassermann (11, pages 382-386). The procedure used in this study's program is a forward selection one, since once an inde- pendent variable has entered the equation, it cannot be removed. For a variable to be allowed into the equation it must explain at least 0.1% of the remaining sum of squares error. Each step of the regression can be studied to see if the parameters need to be changed. The procedures for analyzing linear regression are explained in detail by Neter and Wassermann (11). Intense statistical analysis of the linear regression equations is not done in this study, since the main objective was to demonstrate the feasibility of such a model. However, any statistical 54 value which indicates the lack of fit for the model, or is abnormal in any way, is presented and discussed. The final regression equation for turning movement X12, as shown in Table B-l4, is: X = 7.84385 + 0.13931 I + 0.11028 I4 12 1 + 0.12895 E1 - 0.05258 E3- 0.14424 E4 (Eq. 3-46) After all the dependent variables have undergone the regression procedure, there are twelve regression equations with twelve sets of coefficients. These coefficients are shown in Matrix (E) in Table B-l4. Table B-15 contains the estimated values for X12 using the regression equation and the data of Matrix (D). The residuals, the standard model error, and the r value are also given. The residuals can expose any time- varying dependency or any lack of normalcy error, as described by Bhattacharyya and Johnson. (3) Multiplying Matrix (D) and Matrix (E) with Equation 3-24 gives the estimated turning movements matrix, Matrix (F), shown in Table B-l6. Comparing the estimated turning movements with the hand-counted turning movements by using Equation 3-24 gives the turning movement error matrix, Matrix (TE), shown in Table l and in Table B-17. From Matrix (TE), the first validation check can be made. The only mean error greater than 4% is from X41. 55 Most of its error comes from a 300% error in time period 15. If the turning volumes are low, the percent error can be very large. For example, for X41, time period 15, the estimated count from Matrix (F) is 8. The actual count from Matrix (T) is 2, thus giving a 300% overcount. Therefore, with this high error explained, we can accept the validation check. Using the basic intersection equations, Equations 3-1 through 3—9, Matrix (G), the estimated ingress-egress volumes, are calculated using Matrix (F). Matrix (G) is shown in Table B-18. Using Equation 3-26, Matrix (G) is compared to the adjusted and balanced ingress-egress counts that entered the regression subroutine. The percent error calculation is similar to the other error calculation. For example, the count in Matrix (D) for 11 (t=l) is 128; in Matrix (F) it is 130. Therefore, the percent error in this movement for this time period is: 130 - 128 x 100 = 1.22% 130 The percent error is calculated for all movements and forms Matrix (H) shown in Table B-19. The second validation check is to look at the mean % errors of Matrix (H), as shown in Table 1. These mean errors are all less than 5.00%. In fact, they are all less than 2.00%. Therefore, the second validation check is acceptable. 56 The third validation check is the comparison of the estimated percent turning with the hand-counted percent turning. Matrix (P), shown in Table l and in Table B-20, shows the hand-counted percent turning as calculated by Equation 3-28, using Matrix (T). Matrix (PP), as shown in Table l and Table B—21, gives the estimated percent turning as calculated by Equation 3-28 using Matrix (F) instead of Matrix (T). As an example of the calculation of the percent turning matrices, X12 of for the first time period for Matrix (P) will be used. Looking at Matrix (T), X12 is 40 for the first time period. The sum of the turning movements from the North is X12 + X13 + X14 = 40 + 55 + 30 = 125. Therefore, the percent turning for X12 for time period 1 in Matrix (P) is: %P X12 40/125 x 100 = 32.00% as is shown in Matrix (P). Matrix (PP) is calculated in the same way, using Matrix (F). Comparing the mean values of Matrix (P) with those of Matrix (PP), we can see that there is less than 1.00% difference. Therefore, this validation is acceptable. The model can be accepted for overall performance. Next, the chi-square tests for goodness-of-fit are made. 57 The chi-square test for the ingress-egress estimation is calculated using Equation 3-30. The chi-square value for time period 1 for I is calculated as follows: GGG11 where: GGGll 130 128 (130 - 128)2 128 is the value of the chi-square test for the first row and first column of Matrix (GGG), Table B-22, the value of the first row and first column of Matrix (G), Table B-18. It is the estimated ingress volume from the north for the first time period, the value of the first row and first column of Matrix (D), Table B-5. It is the adjusted and balanced machine count of the ingress volume from the north for the first time period. The chi-square values for the other time periods and other movements are calculated in the same manner and placed in Matrix (GGG) shown in Table B-22. The total chi-square value is calculated for each movement, using Equations 3-31 and 3-32, and is shown in Table l as well as Table B-22. 58 The chi-square test for the turning movement estimation is calculated using Equation 3-33. The chi- square value for time period 1 for X12 is calculated as follows: TTT = (41 - 40)2 11 = 0.03 40 where: TTTll = is the value of the chi-square test for the first row and first column of Matrix (TTT), Table B-23, 40 = the value of the first row and first column of Matrix (F), Table B-l6. It is the estimated turning volume for X12 for the first time period, 41 = the value of the first row and first column of Matrix (T), Table B-7. It is the actual turning volume for X12 for the first time period. The chi-square values for the other time periods and other movements are calculated in the same manner and placed in Matrix (TTT) shown in Table B-23. The total chi-square value is calculated for each movement using Equation 3-34 and is shown in Table l as well as Table B-23. 59 The chi-square test for the turning movement per- centage estimation is calculated using Equation 3-35. The chi-square value for time period 1 for X12 is calculated as follows: pppll = (31.5 '- 32.00)2 = 0.01 32.0 where: PPPll = is the value of the chi-square test for the first row and first column of Matrix (PPP), Table B-24, 31.5 = the value of the first row and first column of Matrix (PP), Table B-21. It is the estimated turning volume percentage for X12 for the first time period, 32.0 = the value of the first row and first column of Matrix (P), Table B-20. It is the actual turning volume per- centage for X12 for the first time period. The chi-square values for the other time periods and other movements are calculated in the same manner and placed in Matrix (PPP) shown in Table B-24. The total chi-square value is calculated for each movement using Equation 3-36 and is shown in Table l as well as Table B-24. The summary table, Table l, is used to check the chi-square tests. For this model, the degrees of freedom is the number of time periods studied, which in this case 60 is 20. The maximum chi-square value for the ingress- egress estimation, Matrix (GGG), is 34.2 for 11' The The level of confidence for acceptance of this value is less than 5.00%. The maximum chi—square value for the turning movement estimation is 25.2 for X41. The level of confidence for acceptance of this value is less than 25%. The maximum chi-square value for the turning movement percentage is 21.1 for X32. The level of con- fidence for acceptance of this value is less than 50%. Therefore, the chi-square shows that the model is an unacceptable estimator for these variables for individual time periods, but is valid for estimating average percent turning. In the next chapter, the intersection model theory described in this chapter is used to build intersection models using actual data. The results is analyzed to see if this theory is valid in practice. Chapter Four CASE STUDIES In this chapter intersection turning movement models deve10ped with actual field data, using the theory described in the previous chapter and data from previous studies conducted by the Michigan Department of Transporta- tion will be discussed. Selected candidate locations were chosen to develop and test the models. The procedures for data collection used by the Department are similar to those described in Chapter 1. Figure 11 shows a typical hand-counted volume summary sheet. Figure 12 shows a typical machine count volume sheet. Note that the counts are tabulated in fifteen minute time periods. Despite the large amount of collected data available, only two intersection data sets were acceptable for study. The reasons for unacceptability are many: 1. Straight-through counts were not made, 2. Machine(s) failed during the study, 3. Hand-counts were not taken at the same time as the machine counts, 4. Volumes are so low that they cannot be studied without large error, 5. There was an accident or some other disruption during the study period, 61 (52 ONHNH NNN NOH HH OH HON HHH HH HOH H4NO HNN OHHH OHH HOHH H4 HHOH HOH .mumzH HOH H 4 O H O H H H HOH H HHH O OHH H NHH H NOO O N44 4 H H O ON NH H H O4N H NNN OH HHH H 4HH H H4 OHH 4 4 O O HH HH O 4 HHN HH HHH O HHH O ONH O OH OHH HN HN O O OH HH O H HHH NH HOH 4 HON H HH H NHHHH-H HH4 N O O N H H O H HNN HH OHN N HON 4 HOH 4 NOO H HHH HH NH O H HH H O H HON O 4HN H NHN N HHN H H4 HHH N H O H HH H O 4 HON O OHN H 44H O HHH H OH HH4 H H O O HH H O H ONN O HHN H O4N H 4HN H NHHH4-4 .MMH, O H H O HH OH N H NHN H NNN H HOH O HOH 4 HOO 4 HH4 H H O O O 4 O N OHN HH HHN H HNN H HHN H H4 OH4 OH O H O O H O O OHN H OHN H NHH H OHH N OH NHH 4N 4N O O O H O H 4HH HN HHH H HHH H NHH H NHHanH OO4 H H O O HH H O H ONN H OHN H OHH H HOH H HOO H ON4 H H O O H H H 4 HHN O ONN H HHH O 4HH H H4 HH4 H H O H 4H H O O HHN H NNN H HHH H NHH H OH HN4 4 H H O O H H O OHN O ONN H HHH H OOH H NHHHN-N O44 O H 4 O 4 N O N H4N H HHN H HHH 4 HHH H NOO H OO4 H N O H H N O H-11 HOH H HHH 4 HOH O HOH H H4 OH4 HH H H H H H O .~:tLTmOH H 4HH 4 NON H OON H OH OHH H H O O H H O N HON O HHH 4 HON H OON H NHHHNH-N OO4 HH H O H OH 4 O. .HH HHH O HOH- OH 4ON H ON H ZOO NH HHN H O O N H N O.I|1Tm- H4H H HHH H HHH H NH H H4 HHH O H H O OH H H N HHH 4 HOH H HHH O 4HH H OH HHH H H O O 4 4 O O OHH 4 4HH H 44H H 4H H Oh #19. >191.“ bum; adeh >29... rtoithm bun.— JCHO» HIGH! »:o_¢¢»m yum; JihOh ~29: $121125. >uui. 3:2 .63. fiNH s 3 .5... .034 fiNH s H .6... HH-2.H4.N-HO5H 8... HH-:.H4.N-HO 3 z .5... u...» mo 0... “N I .2 054 HAHNH 1% ndHOUflA—‘Ay ufiln (fidlwa JNlmz no 10:.uuqurl .: 2. <3 , abacmumm :5 so 311:»...3 .315 52:33»: 3 :3 cm 0... 4N .21.: 2.: \..\....H|.H.1..r.a . uNUHU .3340. 2.: >¢<<¢¢ 321m) @flv HM.” HON... 3:5... 61.... Figure 11 Typical Hand Count Volume Sheet 63 P405 0 YRAFFIC PECORD PROGE‘" NO 16071 COUN'Y 03 NO «XLE Pt 01‘ N0 03300110N DELYA 21000 00.000 103‘ 500' “CUTE DESCRIP'ION 1ZYH AVE I00 FEE? £087 0' 03-2 USO“) H033 LINES IAN? OI CIOCCOVCI ‘LL LINE, 0" MON TUE DID THU FR! 807 DATE 07'?“ 07.25 07'26 07.27 07.20 07.29 END 1!»! AN PM AM PM An pH AM PM In PM AM PM 1215 I 13 1230 3 Z ‘2 !Z“5 2 0100-00.... 1 0115 0130 0145 1 0200......- 0215 0230 0245 0300......- 0315 0330 0305 I OQOG-I..... 0015 ‘7 0430 1“ 0445 12 0500......- ‘7 0515 0530 I 0545 000°..Cd... 0015 I 0030 0605 0700......- 0715 0730 07“5 0800......- 0815 0030 0805 0900......- p on OO“‘.“~°““Q..°— U o. woo—r ” N \lkflUQWUOO‘ on...” Q. tout-unanno- Nuomo COB — .- out ONflfluOiOOQHOUO too- " " WU O’CONUcOO‘ uno- ”NOGDSOBOUOBNO‘ p _ (”fit-‘ODCGOOOOUNOOO » anu~ Q... Figure 12 Typical Machine Count Volume Sheet 64 There was only one set of data at the study intersection. Two sets of usable data are needed, one to build the model, and the other to test the model. Of the two intersections with acceptable data for study, one is three-legged and the other is four-legged. Each was studied separately using the following procedure: 1. A model is developed, verified, and accepted using the older data set, The machine counts of the newer data set are used with the model to estimate the turning movements during its study period, The results are compared with the actual turning movements to see how well the model works, Combining both sets of data, another intersection model is created, The combined model is tested with a similar intersection's data set. Using two sets of data and a set from another inter- section allows analysis of the effects of change in machine count error and operation upon the model. FOUR-LEGGED INTERSECTION CASE STUDY The four-legged candidate location is the Lincoln Road (US-2, US-4l, M-35) at Ludington Road (US-2, US-41) intersection in Escanaba, Michigan. Figure 13 shows the 65 z - TH 5 F H. I E E 41 AVE N El QDDD IUDD ST ' IISOTH ST 29TH 'D-DD Emlflflfl Figure 13 Lincoln Road and Ludington Road Intersection 66 Vgeographic location of this intersection in Michigan's Upper Peninsula. The intersection is in an urban environment in downtown Escanaba, and was studied twice, in June, 1974 and July, 1976. These two data sets meet the requirements for intersection model study as discussed in previous chapters. Both Lincoln Road and Ludington Road are five-lane with exclusive left-hand turning lanes. The intersection is signalized with no turning prohibitions and no turn phasing. The first set of data was collected June 10, 1974 between 7:00 AM and 9:00 AM; and June 11, 1974 between 7:00 AM and 9:00 AM, 11:00 AM and 2:00 PM, and 3:00 PM and 5:00 PM. The second set of data was collected at this intersection on July 21, 1976, between 11:00 AM and 1:00 PM, and 2:00 PM and 6:00 PM. Thus, there are nine hours of study from the first data set, and six hours of study from the second data set. Appendix C contains the input and output data in the creation and application of the intersection model based on the June, 1974 Lincoln and Ludington intersection data. The input data is Matrix (A), the hand-counted ingress— egress movements; Matrix (B) is the machine-counted ingress- egress movement; and Matrix (T) is the hand—counted turning movements, Table C-3. Table 2 on the next two pages contains the summary results for this model. 67 TABLE 2 RESULTS OF LINCOLN-LUDINGTON 6/74 MODEL mm.m mm.HI 4m Hm.v mm.HI Hm OmHmU AdBOB onamzHemm mmmmomummmmozH mom Emma mmmaomuHmo Howey 55.4 mv.HI Nm mm.m mN.oI Hm HH.4 mH.mI 4H mm.m Nv.mm mo.m Hzmam HH.OI HN.OH O0.0 "zmmz HH NH HH mommm onHHEHemm mmmmomnmmmmozH Hmv om.5 mm.mm m5.m Hzmfim mH.m HH.mI N¢.m z¢mz HH NH HH HQEmH sz 68 TABLE 2 (CONT'D) 0.04 5.0m N.HN 4.Nm *«« 5.0 04x H4x 0.0m 5.H0 4.Hm 0.00 5.NH 0.0 40x 00% me 4Nx mmx me 4Hx max max ZOHBdEHBmm mwfifizmummm BZflZm>OS UZHszB BmMB mm4DOmleU 0.0H 0.0H 0.0m ««« 0.0H 0.00 0.Hm N.5m 0.0m 5.0m m.HN N4x H4x 0.0H 0.0 H4 4Hx NHx HHx 4Nx HNx HNx 4Hx HHx NHx onHHzHHHm Hzmzm>oz wszmOH Emma mmHOomnHmo N.N 0.4 0.0 0.0 0.0 0.0H 0.5 N.0 H.m 0.0 H.0H 5.05 5.00 4.0a 0.54 H.NN 5.04 0.0m 4mx me me 4Nx MNN HNX 4Hx NHX NHX OmHmU 44808 Ammmv OmHmU HdBOB ABBBV 2480 Zfimz mwdfizmommm Ezm2m>02 OZHZmDB DMB<2HBmm Ammv H.H H.O H.H H.O H4 0.0H NH H.H H.H ”25H H.H H.HH H.HH H.OH O.HH H.H4 H.NN H.O4 N.HN "zmmz 4Hx NHx HHx 4Nx HNx HNx 4HOH HHHH NHx mo¢ezmommm azmzm>oz oszmse HHDBUH HHH H.OH 444 H.H H.HN H.HH H.ON N.HH H.HH H.4H "249m 4.N 444 H.O O.H H.OH O.H H.O H.O H.O “24m: 4Hx NHOH HHx 4Nx HNOH HNx 4HOH HHOH NHx mommm ZOHBfiEHBmm BZMSM>OS UZHZMDB AMBV 69 The error matrix,_Matrix (M) is shown in Table 2. Most intersections have multi-axle vehicles traveling through them. Therefore, an overcount or positive error is expected. The intersection is typical of this positive error except for the ingress from the east, I2. This error has a mean of -5.11% and a standard deviation of 26.99%. This abnormal error can be caused by the machine or by driver behavior. Since the standard deviation is much larger than for the other movements, a time—varying cause would be suSpected. The model builder, when confronted by such a value may desire further testing, and/or new data. Since this data is the only available data, it will be used in this thesis for illustration. As will be explained in the concluding chapter, problems such as machine count inconsistency show the need for further research. It is also important to note the large size of all the standard deviations. This makes it extremely difficult to estimate accurately any single 15 minute turning movement count. For example, if it is assumed that the machine count error is distributed normally, then for 11 approximately one-third of the counts will be either more than 18.17% overcounted or more than 1.33% undercounted. The machine counts are adjusted and balanced to form Matrix (D). Matrices (D) and (T) then enter the linear regression program as described in the previous 70 chapter. Matrix (E), Table C-4, contains the regression coefficients. In analyzing the regression coefficients, it can be seen that the intercepts are not zero. These coefficients should be zero, since if there are no ingress-egress volumes there can be no turning movements. However, the linear regression model developed in this thesis, like other linear regression models is valid only within the range of values of the independent variables upon which the model is built. Since none of the regression models built in this thesis has low values, the extension of the linear regression equation to zero values cannot be expected to give a valid solution. This does not invalidate the model, since the regression equation should give correct estimates using intersection volumes in the range upon which the model is built. Therefore, an intersection model developed with medium volumes should not be expected to give correct estimations at very low or very high volumes. More discussion of this problem is given in the next chapter. Secondly, the signs of the coefficients are not unrealistic because of the interrelation between the ingress- egress variables. In the X12 equation, for example, all of the ingress coefficients are positive and all of the egress coefficients are negative. However, if any egress movement increases by 1, an ingress movement must increase 71 by 1. Therefore, the relationship of the dependent variable, the turning movement,can be either negative or positive with any of the independent variables, the ingress-egress movements. This topic will also be discussed in further detail in the final chapter. The estimated turning movements, Matrix (F) are produced by multiplying Matrices (D) and (E). The estimated turning movements are compared to the hand- counted turning movements to produce the error matrix, Matrix (TE). The means and standard deviations of Matrix (TE) are summarized in Table 2. This provides the first model validation check. Except for X23 and X32, all of the errors are under 5.00%. The extremely large error found in X32 and the 10.3% mean error in X23 are due to the small turning volumes which produce large percentage errors, as was the case in our test problem of Chapter 3. With this explanation, this model check is accepted. Using the basic intersection equations, (Equations 3-1 through 3-9), Matrix (G), the estimated ingress- egress volumes, is computed from Matrix (F). Comparing Matrices (G) and (D), the error Matrix (H) is computed and shown in Table 2. This matrix provides the second validation check. All of the mean errors are under 3.00% except 12. The 10.23% mean error comes primarily from the 290.42% error during time period 9. Looking 72 back at the collected data for I2 for the time period 9, the actual ingress volume from Matrix (A) is 31 and the machine count from Matrix (B) is 7. This has caused the abnormal machine count error in Matrix (M) and the high mean error for I2 in Matrix (H). Now the model builder must decide whether to delete the data from time period 9, accept the data as it is, or to reject the entire data set and collect new data. This study shall proceed with the data as it is, keeping in mind this source of error. This demonstrates the value of the validation checks and shows that the model analyst must understand the basic principles of the model building procedure. Using Equation 3-28, Matrix (P), the percent turning matrix, is computed using Matrix (T). Matrix (PP), the estimated turning matrix, is also computed from Matrix (F) using Equation 3-28. The means and standard deviations from these two matrices are summarized in Table 2. They provide the third validation check. Since none of the estimated mean values is greater than 2.00% in error from the actual mean values, the validation check is accepted. The model can be accepted as an estimator for the combined performance of several time periods. The chi-square tests are made using Equations 3-30 through 3-36, producing Matrices (GGG), (TTT), and (PPP), which are summarized in Table 2. Because of the very large chi-square values, the model's ability to estimate 73 individual turning movements and turning movement percentages must be rejected. All of the chi-square values for the ingress-egress estimation can be accepted at a 0.995 confidence level, with degrees of freedom equal to 24, except 12. The very high chi—square value of 12 can be attributed to the abnormally high standard deviation of the machine count error of I2. This demon- strates the effect that the machine count error can have on the model building process. Thus, the model must be rejected as an accurate estimator of turning movements during individual time periods. In this study, however, Matrices (M) and (E) are stored in the computer as the basic model, which will be used with the second set of data. APPLICATION OF THE MODEL Any new machine counts taken are adjusted by Matrix (M), and balanced, forming a (MODEL) Matrix (D). This Matrix (D) is multiplied by Matrix (E) forming a (MODEL) Matrix (F). From (MODEL) Marrix (F), an (MODEL) Matrix (G) is computed. (MODEL) Matrix (H) is created by comparing (MODEL) matrices (D) and (G). A chi- square test is performed on the ingress-egress estimation using (MODELS) Matrix (D) and (MODEL) Matrix (F), creating a (MODEL) (GGG). Matrices (GGG) and (H) give the only two validation checks for the performance of the model. A (MODEL) Matrix (PP) is computed from 74 (MODEL)Matrix (F). If the validation checks are accepted, the turning movement percent estimation is accepted and can be input for NETSIM or some other computer program. This is precisely what was done with the July, 1976 data collected from the Lincoln and Ludington intersection. The computer input can be found in Appendix C and a summary is given in Table 3 on the next page. The hand- counted ingress-egress movements and the hand-counted turning movements were collected and used in this study. Normally they would not be available. Tables C-5, C-6 and C-7 show Matrices (A), (B), and (T) of the 1976 study. Matrix (B) enters the model, is adjusted by model's Matrix (M), and is balanced to form (MODEL) Matrix (D). Comparing Matrix (M) of the model, with the 1976's error matrix in Table 3, we can see a large change in the mean errors of 11, I2, I3 and E3. The effects of this change in error will be evaluated at the end of this model production run. (MODEL) Matrix (D) is multiplied by the regression coefficients matrix, Matrix (E) producing.the estimated turning movements for the 1976 study, (MODEL) Matrix (F). Looking at the mean values of (MODEL) Matrix (H), in Table 3, there are two values greater than 5.00% in absolute value. However, they are approximately 5.00%, I1 being 5.31% and Il being -5.78%. The chi-square test for the ingress-egress estimation is made with the results in (MODEL) Matrix (GGG) in Table 3. With the degrees of 75 TABLE 3 RESULTS OF LINCOLN-LUDINGTON 6/74 MODEL ESTIMATION OF LINCOLN-LUDINGTON 7/76 TURNING MOVEMENTS o.m H.MH M4N H.4 N.m4 N4x m.4 m.N4 vi 0.0 0.50 H4 H.m m.44 H4N 00.0H 00.0 4m H.N H.OH 4Hx H.m 5.0H 4mx 0.H mm 04.N ma.0I Hm H0.0H N4.0 Hm O.N H.H O.H H.H H.H H.H H.4 O.H "249m m.NH 4.55 N.m4 H.0H 5.0m 0.0m 0.5m 0.HN HZNWE NHOH HHHH 4NOH HNx HNx 4HOH HHN NHx momezmommm azm2m>oz oszmoe omeoz oszmaa Hmseo4 Ame O.H 4.4 H.4 H.H H.HN H.OH OHHmo H4909 NM NM 4H NH NH HH onemzHemm mmmmomummmmqu mom Emma MHHDOHuHmo Hwoov HN.4 NN.H HH.H HH.N OH.H HO.H "249m 4H.H 4H.Ou OH.N HH.O- HH.H- HH.H "24m: Nm Hm 4H 0H NH HH mommm onemzHemm mmmmomnmmmmozH H00 HH.O HH.H H0.0H N4.NH 4H.4H H0.0 ”249m HH.H| HH.H HH.H NH.HH HN.4 HH.H: “24m: Nm Hm 4H HH NH HH mommm 0 A20 76 freedom equal to 24, all of the values of the chi-square can be accepted at a confidence level of at least 0.90 except I which was rejected in the original model building. Whether to accept these two checks requires the judgment and needs of the model analyst. (MODEL) Matrix (PP) is computed next. If the model production data is accepted, this matrix is the primary output. Matrix (P), which will not normally be available, was computed for the 1976 data. The means and standard deviationszof these two matrices are summarized in Table 3. Comparing Matrix (P) with Matrix (PP), the largest error in the mean values is an approximate 7.5% overestimation is the percent turning of X24, and X41. Since the operation of the intersection changed little, as shown by comparing Matrix (P), 1974 data, with Matrix (P), 1976 data, this error comes primarily from the difference in the machine count error. However, the error in the percent turning estimation is not large considering the magnitude of the change in the machine count error. The two mean values in (MODEL) Matrix (H), also indicated there would be some error in the estimation. LINCOLN-LUDINGTON COMBINED DATA MODEL The two data sets collected at the Lincoln and Ludington intersection were combined to form one data set from which a model was built. Table 4 on the next two pages gives a summary of the results of this model. 77 The error matrix, Matrix (M) shows the machine count error for the combined model. Matrix (TE) shows that only X32 has an estimation error greater than 5.00%. This is due, as was the case previously, to small volumes Vgiving a large percent error. With this fact in mind, the first validation check is accepted. Looking at Matrix (H), only the mean value of I2 is greater than 5.00%. The reason is, again, the data from time period 9 from the first set (1974). Note, however, that the mean values of Matrix (H) are much closer to 0. This should be the case if the sample size increases, and the sum of squares error does not increase due to non-linearity of operation. Again, with this fact in mind, the second validation check may be accepted. Com- paring the actual percent turning, Matrix (PP), with the estimated percent turning, Matrix (P), in Table 4, there is less than 1.00% difference. Therefore, this validation check is accepted. The summary of the chi-square test matrices, (GGG) (TTT), and (PPP), are found in Table 4. Because of the very large values of the total chi-square for (TTT) and (PPP), the ability of the model to estimate turning move- ments and turning movement percentages is rejected. The chi-square values for the ingress-egress estimation is unacceptable for 11 and 12. This was the case for the previous model. Since the first model's data is included 78 TABLE 4 RESULTS OF LINCOLN-LUDINGTON COMBINED DATA MODEL 0.HH 4m 00.0 5H.HI 4m Hm.m 04.0! Hm 00.0 00.0 Nm 0.5 Hm 4.4H 4H 0.0 0H NH HH OmHmU AdBOE ZOHBfiSHBmm mmmMDMImmmmeH mom BMMB mmmbamleU A0000 04.0 mN.H| Nm 00.5 00.01 m0.N 00.0I Hm 00.0 00.HI 4H 00.4 05.0 0H 05.44 H4.0 NH 40.5 0H.0I HH HZ£Em HZ¢WE mommm ZOHBOZ UZHZMDB BmmB mmdbOmleU ABBBV 4.N N.0 0.04 0.4 40 0.4 0.4 H.5 0.H 4.5 0.0 4.0 0.0 u 0.4a 0.05 5.00 0.4H 5.04 0.00 0.H0 0.0m HZNMS NHx HHx 4Nx HNx HNx 4H4H HHx NHx moHazmommm Hzmzm>oz oszmOe OmamzHHHm Hmmc 0.0 0.0 0.0 0.4 0.0 4.0 0.0 0.0 "ZdBm 0.4a 0.05 H.00 5.4H N.04 H.0N 0.H0 0.0m HZNMZ N0x H0x 40x 0Nx me 4Hx max max mwoz UZHszB AflDBUfl Amy «44 0.0H 0.0m 0.50 0.0H 0.5H 0.0H 0.0H HZNBm ««« 4.0 0.H 0.0H 0.N 0.0 0.0 0.0 HZoz oszmDe Hmev 80 in the combined data model, the same variables in (GGG) had high chi-square values. The 1974 data was run through the combined model in the first production run, (MODEL). The 1976 data was run through the combined model in the second production run, (MODELZ). The results are in the summaries of Tables 5 and 6. Since the data of these two sets are embedded in the model, it should accurately estimate the turning movements and the percent turning for both sets. Looking at (MODEL) Matrix (H), only the mean value of Iz is greater than 5.00%. This is true, again, because of time period 9. Comparing the estimated turning percent matrix, (MODEL) Matrix (PP) with the actual percent turning matrix Matrix (P), Table 5, there is less than 2.00% difference in the mean values. This is exceptionally good for a production run. Looking at (MODELZ) Matrix (H), Table 6, the only value greater than 5.00% is 11. The model will iterate without changing the percent turning, as was described in the previous chapter. The iterated values are important if you are interested in specific turning movements. They are not shown in the appendix. Comparing the estimated turning percent matrix, (MODELZ) Matrix (PP), with the actual percent turning matrix, Matrix (P), in Table 6, there is less than 2.00% difference in mean values. This is a considerably better estimation than was given by the first model, as should lie expected. The chi-square tests for ingress-egress 81 TABLE 5 RESULTS OF LINCOLN-LUDINGTON COMBINED DATA MODEL ESTIMATION OF LINCOLN-LUDINGTON 6/74 TURNING MOVEMENTS H.N 5.0 0.0 m.N 5.4 4.0 H.m 0.H N.0 0.0 N.m 5.0 ”248m 0.NH 0.04 4.H4 0.0 H.0H 0.05 5.50 0.0H 4.04 o.NN 0.04 4.0Nu24m2 04X N4N H4N 40x NMN me VNN MNN HNx 4HN MHx NHN MOANBZMUKWQ HZMZMKVOZ UZHZMDH. OmagHBmm Ammv N.4 4.0 4.0 0.0 0.0 0.0 0.0 5.4 0.0H N.5 H.5 H.0 «ZGBm 4.4H 0.04 0.04 0.0 0.0H 0.05 0.00 0.0H 0.04 H.NN 0.04 N.0NHZ¢MZ 04x N4x H4x 40x me me 4Nx me HNx 4Hx 0Hx Nax MUHHNEZMUmM—Hm BZHSMNVOE UZHZMDH. .H/NDBUAN Amy 0.5 5.5 5.4 0.4 0.0 0.0 0.H5 H.0N OmHmU QNBOB 4m Hm Nm Hm 4H HH NH HH onamzHamm mmmmomummmmozH mom Emma mmHDOHuHmo Hwoov NH.0 40.0 00.0 H0.0 40.0 00.0 00.00 00.0 "2090 00.NI 00.0: 05.NI 00.0! 0H.Nl 00.N 00.0H 40.4! Hz¢m2 4m 00 mm Hm 4H 0H NH HH mommm onamzHemm mmmmomnmmmmwzH Hmv OH.H H0.0 H4.H HO.H 4N.H OH.H O0.0N HH.O "249m HH.H OH.H HO.H O4.H HN.N OH.H HH.H| N4.H 24m: 4m Hm Nm Hm 4H HH NH HH mommm w 33 82 TABLE 6 A MODEL N-LUDINGTON 7/76 TURNING MOVEMENTS RESULTS OF LINCOLN-LUDINGTON COMBINED DAT ESTIMATION OF LINCOL 0.0 0.4 H.0H 0.04 mvx mvx 00.0H 00.0 0.0 0.0 o.N 0.N 0.0 0.H H.0 0.0 H.4 0.0 "ZdBm 0.04 H.OH 0.0H 0.05 H.04 0.0H o.44 0.4m 0.40 H.HN uZ¢m2 H.0 H.0 0.0 N.4 0.0 H.4 0.4 5.4 0.4 0.4 mwfifizmummm Bzm2m>02 UZHszB QBBGSHBMM Ammv ZflBm 0.44 5.0H 4.0H 0.05 0.00 0.0H N.04 0.4m N.40 0.HN uZ¢m2 Hvx 4mm mmx me me mmx me vHx me NHx mwflfizmummm BZmZm>OS wZHszB AdDBUd Amy N.H 0.0 0.4 0.0 H.0H N.0H OmHmU AdBOB ZOHBdSHBmm mmmmwmlmmmmUZH mom Emma mm¢DOmIHmU A0000 om.4 00.0I mm H0.0H N4.0 00.N H0.N 05.4 00.N 05.0 00.4 uz¢Bm 00.H No.H 0N.OI 0o.NI 40.0! N0.0 ”Z¢m2 mm Hm 4H 0H NH HH mommm onamzHemm mmmmwmummmmwzH Amy H5.0 00.0 Hm.OH N4.NH 40.4H Ho.m "2&80 55.HI 50.0 50.H N0.5H HN.4 50.0I uzm4002 4L U: B MARQUETTE A DART MOUTH A Figure 14 Ford Road and Newburgh Road Intersection 85 throughout the data as shown by the low standard deviation. There is also a mean error of -11.34 in 12, and a mean error of -l7.05 in I3. The chi-square values of the ingress-egress estimation, Matrix (GGG) are extremely high for 11, 12, and I3. The model based on analysis of ingress-egress estimation, is not suitable and the results should be rejected. Comparing the estimated turning percent matrix, (MODEL3) Matrix (PP), with the actual turning percent matrix, Matrix (P), in Table 7, the conclusion of the ingress-egress estimation analysis is shown to be correct. The estimation error varies from 1.30% to as high as 28.5%, (X31). An estimation error of 28% would generally be unacceptable. Therefore, from Matrices (H) and (GGG), the model analyst would conclude that either another model is needed or more data study should be made. THREE-LEGGED INTERSECTION CASE STUDY The three-legged intersection case study is Main St. at Front St. in downtown Niles, Michigan. The location of this intersection is shown in Figure 15. All three legs of the intersection are four-lane with no exclusive turn lanes. The intersection is signalized with no turn phases. The first set of data was collected October 8, 1975 from 2:00 PM to 6:00 PM and on October 9, 1975 from 7:00 AM to 8:00 AM. The second set of data was collected July 10, 1978 from 2:00 PM to 6:00 PM and on July 11, 1978 from 7:00 AM to 9:00 AM. 86 TABLE 7 RESULTS OF LINCOLN-LUDINGTON COMBINED DATA MODEL ESTIMATION OF FORD-NEWBURGH 5/76 TURNING MOVEMENTS 0.o m.N 4.N b.mH m.em s.mH max msx Hsm 04.NH nm.~ 4m N.m m.mm «mm m.m H.m o.~ m.o m.H m.v H.s m.m "249m H.Ns q.s~ m.mm m.mH ~.om m.¢~ “.44 >.om "24mm «mm me vmx mmx me vHx me «Hx mwdfizmumwm Bzm2m>02 UZHszB QHBflZHBmm Ammv 4.0 5.0 0.4 0.0 m.N 0.0 5.0 4.0 N.Hm 0.N0 0.05 0.0H 0.4H 0.0H O.H0 0.0m "2490 ”2mm: mmx me sax mmx me wa MHx NHx momezmommm ezmzm>os oszmDe qmseom Amy m.mH H.v m.om m.4OH m.-H m.mmm omHmo qmeoe mm Hm 4H mH NH HH ZOHB02 UZHZmDB BMMB mmNDOmIHmU Ammmv 0.0H 0.0H 0.0H 0.0N OmHmU AdBOB HN 4H x x NH N x ZOHBfiSHEmm Bzm2m>02 UZHZmDB Emma mmNDOmIHmU ABBBV N.N N.N N.m N.m .zmam m.ns m.Nm H.Hv N.Nm "2mm: «Nx HNx «Hm NHx mwfiezmummm BZMSM>OZ UZHZmDB DflBflZHBmm Ammv 5.5 5.5 0.5 0.5 ”ZdBm 5.54 0.N0 4.H4 0.00 “24m: 4Nx HNx 4Hx NHN mwfiezmummm BZMEM>OZ GZHZmDB AdDBUfl Amy N.NH N.cH s.mH H.4H "zmam o.o N.o N.on m.o "zmmz «Nx HNx vHx NHx mommm ZOHBdEHBmm BZMEM>OZ UZHZMDB AHBV 91 will be a good estimator for other data. Matrix (F) was iterated to try and reduce the error in Matrix (G) to less than 5.00% for all mean values. It was unsuc- cessful in five iterations. Although the Main—Front model was unacceptable, and should have been rejected, it was stored. The second set of data was input into the model. The results are found in Table 9. Note that the error matrix of the second set of data, Matrix (M), is very different than the model's error matrix. Analyzing (MODEL) Matrix (H), there are four unacceptably high mean error values. Comparing the estimated turning movement percent matrix, (MODEL) Matrix (PP) to the actual turning movement percent matrix, Matrix (P), Table 9, the model did much better than expected. The x12 and X14 are approximately 7.00% in error. The other movements are less than 2.00% in error. Comparing the two actual turning movement percent matrices in Tables 8 and 9, show that the actual operation of the intersection did not change significantly. Therefore, the model building technique presented in this thesis may be less sensitive to changes in machine count error than it is to changes in operation. This may be why the model performed as well as it did, even though the machine count error changed significantly. The chi-square values of Matrix (GGG) in Table 9 are unacceptably high and should have indicated that the estimation obtained from the model would be inaccurate. 92 9 TABLE RESULTS OF MAIN-FRONT 10/75 MODEL ESTIMATION OF MAIN-FRONT 7/78 TURNING MOVEMENTS o.OH o.OH N.m N.m N.N m.m ” N.mN N.NN 9.04 O.Hm H.Hm m.mo ”24m: Nsx HHN va HNx «Hm NHx WO4BZmummm BZMSM>OS wZHszB QMBdEHBmm Ammv 0.0 0.0 N.5 N.5 H.5 H.5 uz¢Bm 0.45 H.0N 0.44 N.00 N.00 0.H0 «ZGMS Nam HHH HNx HNx HHN NHx mwdfizmummm BZMSM>OZ GZHszB HdDBUd Amv H 0.50 H.NN 0.0 0.00 N.NN OmHmU HNBOB N H 4 N H m m H H H ZOHB02 UZHZmD9 9mm9 debomleU Ammmv 4.00H H.N0 4.05 N.05 H.04 H.00 OmHmU H¢909 Nsx st sNx HNx «Hm NHx ZOH902 UZHZmD9 9mm9 mmOZ UZHZmD9 QM902 OZHsz9 HOE UZHZmD9 Am9v 96 TABLE 11 RESULTS OF MAIN-FRONT COMBINED DATA MODEL ESTIMATION OF MAIN-FRONT 10/75 TURNING MOVEMENTS 0.4 0.4 5.0 5.0 4.0 4.0 "z¢9m H.N5 0.5N N.54 0.N0 N.H4 0.00 n N4x H4x 4Nx HNx 4Hx NHx mwd9zmommm 9szm>OZ uZHsz9 Qm9¢SH9mm Ammv H.0 H.0 5.5 5.5 0.5 0.5 "2490 4.H5 0.0N 5.54 0.N0 4.H4 0.00 "ZNMS N4x H4x 4Nx HNX 4Hx NHx mwm9zmummm 9zmzm>oz wZHZmD9 H429Um Amy N.0H H.00 N.0H 5.4 H.40 5.0a OmHmU 44909 «M NH Hm 4H NH HH ZOH9¢2H9mm mmmmOMImmmmGZH mom 9mm9 mm02 OZHZmD9 Qm942H9mm Ammv 0.0 0.0 N.5 N.5 H.5 H.5 u2¢9m 0.45 H.0N 0.44 N.00 N.00 0.H0 ”Z¢m2 vi Hex va HNx «Hm NHx Homezmommm azm2m>oz oszmoa Hansom Amv 0.0H 0.00 N.N0 0.4H 4.00 5.04 OmHmU H¢909 4m Nm Hm 4H NH HH ZOH9 33 .. ‘ 2 : sou and. 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oooocvOOIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIU oommmvooI Zvvpmovomm omvmvuumw Iu ocevovooI map a» a vmxIvvuv oomemvoc xIvnv as on mm oomeovoo co~echOIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIU oooeovoOI wu4m vxuz homvum Iu oomeevOOIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIU oceeovoc acmeovoo coweovoo m~ av ow cavemvou mazv—zou om oooemvoo zuzuz commovoo mmuam me Omeovco om Iom Ime vumuomvuv ccvmovco nmvvn\~II~m>avuuum ooomovoo zIavIszzumv ccmmovoc zIranm>a oe ooemovoo . oe Icm Iom anxvavvuv acmmovoo vvvxmvuz 163 ooovhvoo zz2nvawI~vm—vx3 aeoawIUOv mv oomuovoo zzZAcowIsvm—vm: «moououov uv oowmovoo zzznaowInvm—vmz Awoowouov uv cavmcvoo zzzacmesvu—vmx Avoowouov uv cacao—cu owe 0— cu a-NIOMIQwavvuv ocmawvoo saw av vo avoouopmmozvuv caeuovou Iavxuvzu uamuvmga hmv~¢4:‘z=u mv anvaI a omIamvw2 4<=pu< no a camwovou uuzo¢mzv mv avvaI N amunvvwz< ocvmmvou :u‘uavzvg ooomovoo omuvm pxu‘ ‘v uummpgu mm vb boa w4m mu

Iu oo~m~v00I no wvm>4¢‘< mam u=4 vm‘a 1c mumxazoz.\- oowmIHoo .m.ov.. IIIIIIIIIIIIIInzov~o¢11voz.\- ooqm~voo.I.o~I.u IIIIIIIIIIIIIIIIIIIIIIIIIIummm4vcuamravo Na amxam>avucnm>avooafi~younwuuo fiInaufiVILufiH ca ma Ina Ioa armatfivum «a No Iem Iced aafivdauuu z+uranm>4 tIanh ecu on :Ixuzum>a amnvcnom :u‘¢n~|3w‘uczuam co"¢hucocc¢cuaa««¢a«c«Ica¢I«aIIa¢«a«III...«cacaaa¢¢tc«c¢acacaacaatI.¢«can.«IIIIU ooomsuoac pzuxuam 4~m m2» >m manawa «u oomwb~001¢aca«accaa«aa«u¢aaaccu¢6ccacuaca«¢o«acaa¢c«IIIIIIIIIIIIIaIIIIIIIIIIIIIU occmh—oo oo--oc ocean—cu oomw~woo 00¢mK—oo cemwhuoo ocwwN—oo cc~w-co ooow~uoo cem-—oo ocwhsuoo oo-buoo acousnoc camNK—oo ocessnoc Genus—co oowusuou oo--co ooo~buoo “mucus: ma‘upzou n~o "macaw no uhIIIIocupoh uuhamzou mu Amuh N auvmxauumuamvp occewwou FZmHHHIImou ‘u~wmm¢QUu 4<~p¢numuIH~Iu+aruv4um commence ~‘2I~n>~ mww co 00¢mw—ou Navmz< n amquvm om“ oomwm—oo cowmc—OUIIIIcqccacacacaIIIIIIIIII«I«IIIIIIIIIaacaicaiaaIIIIIIIIIIIIII«I«IIIIIIIQ comma—co. mac; 3pn- «mu mpzuuquImUo oz< pmuuumpz— :hmz Auv owa .zuo om zou m~.wN Im Ow.MN~ I” 177 TABLE B-8 (CONT'D) econ meow: "N.00 mm.ot mkoo mm.u| mNoo N¢.uu Imoo Nax we.01 co." m~no «woe oMIOI «moo «coo mwoo owco em u~.o| o~oo OGIN no.9 No.01 Nmoo umIO No.o mw.0 mm wm.ou «N.0 No.0 Geog onion ca.o mm.o mooo OHIO Nu IIuI II.I- II.I- II.I. II.I II.I- II.I IIII- II.I nu IIII.IIII "IIIIIII II III IIIII cm.o1 umco N~.o wa.o c¢.ou ecom cc.o aw.c md.o qH mm.o a¢.o umuo mm.o o¢oo ceoo co.“ aqoc Naoo mu N¢.01 mace Nc.o mmco amocl mmoo acoo ocoa NN.O NH ~m.o oNoo mwoo Oa.o Nm.o mH.o h¢.o Nwoo co." In xumh hm<4 mo mumtzz mzouhIZNImwhuo NAN—~42: Io hzumu~uImou umuhm m—zp up emuaomm mmm ouz~<4mxuza Io hzwzm>ommzu uwmm<=um Io tam onwmumomm N u muhm max 179 TABLE B-lO TEST STATISTICAL ANALYSIS OF STEP-WISE REGRESSION STEP 2 ¢m-Nouu cwmo.ou ammmmco ~amo.m« Nnmm~.o «mmMIee NNeo.¢mN Nu mew—m.o o~ohonumu memo.o «NNm.am ammo-moo IIIIIIIIIIIIIIlIIIIUIIIIIIII))IIIIIIIIIIIINIImummbza '5"--- I '53-}- "hzuwummumou c N uam 1):-711111111nunuuunuu-uquIIII II IIIIIIII IIIIIIII uuwb hm¢4 Io mmmzzz "ZONPIZNINmeo u4m-azz Io hzmuuumumou umuhw wmzp op omuzawm mumcacm no tam wp<42t2u unuoaumm mmx<=ow mo xam 4 omz~<4uxuz= Io pzmzu>ommtu umu¢ "mommu Io up hm¢4 Io mumzaz I nzoub¢zmlmuhuo mamwhaaz Io hzuwuuuuuou "muhm wmzp o— amuamwx mmm omz~ommz~ umum<=um Io tam zoummmmwmm m u mupw me 181 TABLE B-12 TEST STATISTICAL ANALYSIS OF STEP-WISE REGRESSION STEP 4 IIIII.I IIII.I IIIIN.I IIII.II IIIII.I IIII.I~. IIII.III m— n mommk.o owma.¢qma NNNOIQ oom¢.¢m Nw¢Noomm 1'"..' I nhmuumuhzw nbzmwummmwou I I wam "momma Io uh bm<4 mo awmzzz "zouh«z~;muhuo mam—~42: Lo pzwmuHIImou umwbm aux» up ouunowm mmm ouz~<4mxmza Io pzwxm>ummz~ umum<2uw no 23m zowwmumoum 4 a awhw Nux 182 TABLE B-13 TEST STATISTICAL ANALYSIS OF STEP-WISE REGRESSION STEP 5 momcw.N ono.oa IwNncwm NONm.o~ ONccmoo emumcmN mmnN.mIc ca asmo~.o hqmm.Nmm~ choo.o «omm.~ moomoofim Hummumuhzm "hzuHUHIImou h a u4m<~m<> "mommw Ia up hm<4 mo mumzaz uonb‘zmzmubuo mammpan Io bzw~u~umuou umwhw warp up cmuzaum wmm<=am Io ram u— cmz~<4mxuzn Io pzwru>ommx~ "IIIIIII II III IIIIIIIIII m a mth Nux 183 TABLE B-l4 TEST MATRIX (E) REGRESSION COEFFICIENTS MATRIX N0m00.0 0H~M0.0 Nm000.0 ~00Mw.0 esomm.01 0HONw.0l 0~M0~.0I 0N00~.0I ~0Nm0.0 M0x Mm000.0 00000.0 00000.0 mNINM.01 00000.0 00000.0 m0mMN.0 00000.0 NN000.0« 0Nx 00000.0 00000.0 00000.0 N0M~N.0I NO0N0.0 00000.0 00000.0 NMO0M.0| 0000M.0M N0x NO0N~.0 mmm~«.0 000M0.0 0N0-.0 00000.0 mN0—N.0I 000M0.0| m000~.01 acufim.M me 00000.0 0M0ma.0 00000.0 oMMN0.0 0~000.0 ~0N-.0| 0-00.0I 0M-0.0I M0~m0.hun ~0x M000~.0I Inucu.0 00000.0 ~N0m0.0 MO0M0.0 0-M~.0) 00000.0 N0~m~.0| 00mmo.m HNx m—00N.0 00000.0 00000.0 00000.0 00m00.01 m0000.0 mNM00.01 00—00.0I m~00m.0 0Mx 0000N.0 ouh0—.0 00000.0 000N0.0 00000.0 N000N.0I 0~MOI.0) NwMN0.01 ~0MM0.~—I 00x 00000.0 NNO-.0 0000N.0 00000.0 0MOMN.0| 00000.0 00000.0 00N00.0I mdamm.dun NMx 0MN00.~ N000M.N NO0H~.N ~0NON.N 00000.NI nonmN.N1 Nmmmh.~) 0~m00.NI M0~0m.m« de 000N~.0- 00000.0 00000.0 00000.0 00000.0 cmmom.0 00000.0 MM000.0¢ 00MNM.0N qu 0NO0I.o- Imwmo.o- 00000.0 mIINI.I INIII.0 00000.0 00000.0 ImoMI.o m0m00.I me no No IN no am a0 nM Aw AI am am an am am n0 Am Am n0 184 TABLE B-lS TEST STATISTICAL ANALYSIS OF STEP-WISE REGRESSION ACTUAL VS. PREDICTED VALUES X12 TIDE PREDICYED ACTUAL RESIDUAL PER. 1) 40.00000 41.92196 ‘1.92196 2) 31.00000 33.755C3 '2.75503 31 32.00000 31.94491 0.05509 4) 26.00080 3C.16165 '4.16165 5) 35.00000 31.41365 3.58695 6) 45.00000 44.36254 0.63746 7) 50.000C0 46.05971 3.94029 8) 53.00000 46.98644 6.01356 9) 45.00000 39.21218 5.78782 10) 32.00000 43.20118 11.20118 11) 29.00000 27.28937 1.71063 12) 20.00000 24.20321 '4.20321 13) 26.00000 18.57067 7.42933 14) 26.00000 26.79321 5.20679 15) 14.00030 17.33815 '3.33815 16) 19.000C0 23.42329 ‘4.42329 17) 28.00000 3C.48793 '2.48793 18) 34.000C0 3C.28571 3.71429 19) 32.00000 34.36302 '2.36302 20) 28.00000 29.22677 “1.22677 STANDARD EEQDR (MODEL # 1) 15 5.43281 185 TABLE B-16 TEST MATRIX (F) ESTIMATED TURNING MOVEMENTS um «N NN Nu NN em hm on mN mm ~— mg QmWO€°QQ m¢x mud mum cam mmu N:— hw— mm— gun hmu emu uu :— «a on ow an om me ~m a: we mc om m— an ow em «cx ma a“ ha ~— cm Nm 6m mm aw ow nu ~— hm Mn fig an a— «mg on me ~M mm mm «M cu su «m an @— ca NN ~— ~— 0— cu mmx as Ns em em «N me N~ um um am am an N—u ca um ~m ~m ac °~ as unx sad eq— cod cuu sea New and MN— -~ me" o: Nm we o¢ q¢ cw nN om mm «N :NX «N um um ow cm mm c~ mu cw NM o— cu @— n— N— N— N «a mmx - mu mu Nu an au ¢~ nu ma KN mm mm mm mm mm Ce mm on on we umx ca en sa an em m“ o“ NN um NM an cc on Km ~— nu ma ad gm ¢ux m~ - sm no - m¢ m4 an en am mm am no as ¢m cN no em ~n cm mgx am cm on an MN ~— cw n— «N NN me am ~c me «a am on an mm a: Adm .ou .c~ ANN .0“ an“ .¢_ and .- ._~ “a" .a .9 a~ Ac .m A: .m .N .g .mmm N_x wrap 186 TABLE B-l7 TEST MATRIX (TE) TURNING MOVEMENT ESTIMATION ERROR co ha a oN s as ¢ eN a NN u «a c a" o oN n ma e. NN h. an N.N: an 0. cu m 3 «a: o 0 hat 0 on hm- 0 mm @- mm: cN o mN cm- mex w.c o"! N— NI NI 0— N a! a Mo 0 Owl m cu: «an on 0 mm flu! emu mm qu m.m o c NI 0 a! can mml he- a {I N Nut #0 s NI ma c 0 W! G! ~¢x m m o a 9 ml MI no «at on: ~u cm. “a. an. mm mm mc emu @ a «NI 0 mN cl cu: m... O¢ «as o dd: N cut an- an N; ms ml mNu o om: me :.o c an ad! ¢ n— ma dul.. out m N'. as m... mu N m. uul NN m an a: amx c a an om w: was N m- fin o ms «t mm- m mun Nu mm a Na: mm- mm - ch N N o ml 0 m.- c mg m ¢NI 0 m0 "ml cm out ch mu: m cm eel Mal c— mwx on N 0 on m: an 0 mm: out :1 on N N. mu 0 am at ON: ¢N N- "Nx mod -I Na Mg NNI c mm o u:0 C... 9 m0 auu mi a~ ml «M Na N Nu! m ¢ax Noun m.m« Noon No0 us ¢ m c “an Nal c N mu “N N: “N N MN: am: am: cu 0N N NI m cm mu! m~l can «a! NI can 0 N: o« «ml a“- mu 0" ml Nu m m m mdx Nux uz¢~m «24w: noN aauu an" Asa am“ am“ Ac" and RN“ Ada no— an Am as no Am a; an RN nu .mmm uxmh TIME PER. 1) 2) 3) h) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 187 TABLE B-18 TEST MATRIX (G) ESTIMATED INGRESS-EGRESS MOVEMENTS II 130 109 100 106 118 165 162 170 150 163 157 120 79 73 79 124 104 134 125 112 12 13 14 E1 :2 78 94 so 159 an 63 90 33 126 51 63 as «e 123 64 64 \ 71 ac 104 59 76 66 as 117 59 117 119 9a 190 102 11a 123 95 200 104 127 151 as 225 101 123 118 109 17a , 117 120 128 102 206 104 247 117 241 113 238 221 121 196 91 212 155 91 132 67 146 166 135 191 96 207 183 122 159 96 165 227 129 184 121 193 167 91 '213 81 238 207 108 244 83 275 181 161 238 107 282 175 129 214 99 250 E3 77 69 '67 78 86 111 104 107 111 113 171 127 88 90 95 129 100 137 119 115 E4 62 SA 43 40 43 92 91 103 94 90 240 228 156 172 187 221 133 198 177 166 188 TABLE B-l9 TEST MATRIX (H) INGRESS-EGRESS % ERROR .: m~.m “c.0u caoul uNoOI so.¢u MN.cn mmomu swam- N«.Nu ¢m¢Nu w¢o NI mwoON um.ou Hm.m cm.o mN.N| NmoNI o—.m~| um.o 0N.o No.91 uN.M—I No.0 Nm.-n meow: mq.o No.u| ad.” mm. on 60.6 cc.Mu m~.o «eon: «o.mu «N.N mm.mu mm.o mw.on om.o msom— em.au om.o. ~Nomu oNom~ #m mu N~.~ mm.“ MN.oa MMool N~.¢1 «N.m1 mm.m1 omom mmuo co.on m¢.NI mN.MH meomu coco mo.wl N~.oa Noc¢ moon Naomw T¢Noo aN-OHI ¢~.m~ Nu macs m¢.o muoo m~.¢ mm.ou mm.¢ {moan mmoNl owoau ooomul cmomul ¢M.N1 no.0 Nwoo um." mu.N opoN em.N mN.o MNJm mac”: Nuoo nu m~.q «0.01 _m.m- ao.m- -.m- No.N- om.~- m~.~ om.” mm.o- o¢.m- m”.~ no.“ mo.d o¢.w- mo.m- co.n- _~.m o~.o_ ao.e‘ em.~- mm.c :— Ho.m mo.o mo.o cm.c1 eoom oaom 05.0 m~.al m~om1 0¢om N¢.o Nm.N1 om.wl N~.m1 «h.m1 oe.m1 cNomI mc.o~ ooum ~n.m N~.m wsoml mm «woo no.0 mm.ou NNosl oNohI w¢oo once: sm.o mmom enoo c¢.MI «cud N~.OI mo.mn “Coal O¢on «coo amoen o~.~ «hood ocom mNomm NH «H.Nu uz