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thesis entitled

Computer-Aided Capacity
Planning Model For
Facilities Management

presented by

Piyarat Nanta

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COMPUTER-AIDED CAPACITY PLANNING MODEL
FOR
FACILITIES MANAGEMENT
By

Piyarat Nanta

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF ARTS
Department of Human Environment and Design

1998

ABSTRACT

COMPUTER-AIDED CAPACITY PLANNING MODEL
FOR FACILITIES MANAGEMENT .

By

Piyarat Nanta

This Computer-Aided Capacity Planning Model for Facilities Management
focuses on the simultaneous optimization of the resource utilization ratio and user’s
waiting time in a shared space environment. The study was conducted in an open campus
state university computer lab which is considered a shared space environment. The data
collection protocol followed a prescheduled set of observation periods designed to
capture a representative sampling of expected usage during one semester. In a
perspective, this study employs the same device with two different models of workload
characteristics (the IBM compatible section and the Macintosh section). For the
Macintosh section, misinterpretation of the data arises from the discordance of the system
behavior and the instrumentation along with the design for data collection. By the same
token, the problem dueito the instrumentation occurs with the waiting time data collection
for the IBM compatible section. Further investigation to validate this method, should be
done by applying it to different kinds of shared resource environments such as hoteling or
workplaces that use similar strategies, thus demonstrating whether the methodological
results are reproducible in different work environments. Information obtained from the
users should be collected in order to compare the results of the resources utilization ratio
at each step to verify the strategy being used at the time. Time-lapse video is another

unobtrusive tool that can provide a further perspective on patterns of behavior.

To my beloved parents.

ACKNOWLEDGMENTS

I could not have begun this thesis without the guidance of Dr. Timothy Springer;
my debt to him is great. I began to formulate the idea of this thesis when I taking his
“Alternative Officing” course in summer 1996. His expertise in this area was my
inspiration. My profound thanks goes to Dr. Linda Good for her encouragement, and
who always found time to look at my thesis material. Dr. Charles Severance shared with
me his wisdom, helping to sharpen my wits and teach a new way to analyze the data. To
Mrs. Jeanne Halloin, with special thanks for her support.

With his kind spirit and patience, I am profoundly thankful to Dr. Natawut
Nupairoj, my best friend who helped me with excellent advice and expertise in computer
simulation. Wipada Wiwatana and Dr. Vance Chonhenchob are true friends who never
abandoned me, and spent nights and days volunteering their help in the laborious
collection of data. Andrew J. Mullard help editing drafts saved me from many
difficulties. I was given encouragement and friendship from Jeff Hodges who also read
parts of my thesis. My sincere thanks to Eric Boatrnan, my best friend in the ID & FM
program who shown his support throughout.

Moo-dang & Mod-dum, my dogs, they faithfully cheer me up and help me
through difficult times.

Special thanks to Piyada Nanta, my litter sister and friend.

I am profoundly grateful to my beloved parents, Mr. Boonrat and Mrs. Pimolporn
Nanta for their caring and supportive throughout. They are my inspiration and give me
energy and conviction I needed. I could not come this far without their unconditional

love and unfailing support.

iv

TABLE OF CONTENTS

 

 

 

LIST OF TABLES .................................................................................................. vii
LIST OF FIGURES ................................................................................................ viii
INTRODUCTION -- .... . ............. 1
CHAPTER 1
Description of Research Design - 5 A - A ..... 11
Simulation Model and System Components ........................................................ 12
System Capacity ............................................................................................. 14
Queuing System and Simulation Model Implementation .................................... l4
Queuing Models and Simulation of Queuing Systems ................................... l4
Queuing Notation ................................................................................................. 16
Queue Behavior and Discipline ..................................................................... 18
Arrival Process and Interarrival Time (A) .................................................... 18
Service Mechanism and Service Time (S) ...................................................... 19
Resource Utilization (p) ................................................................................. 20
Waiting Time (W) ........................................................................................... 20
Relationship of Resource Utilization (p) and Waiting Time ("0 ................... 20
CHAPTER 2
Data Collection 25
Environment of the Data Collection .................................................................... 25
Study Location ............................................................................................... 25
Workload Characteristics .............................................................................. 26
The Operation Cycle ...................................................................................... 28
Devices ................................................................................................................. 29
Customized Visual Basic Programs ............................................................... 29
Customized JA VA Program for Simulation ................................................... 31
Observers ....................................................................................................... 33
Data Collection Schedule ..................................................................................... 34
Period of Observation .......................................................................................... 34
Data Collection for Statistical Analysis ......................................................... 35
Sampling Method ........................................................................................... 36

CHAPTER 3

 

 

 

 

 

 

 

Data Analysis: Methodology 19
Data Analysis for Constructing the Simulation Model ........................................ 39
Estimation of the Data Distribution ............................................................... 40
Kolmogorov-Smirnov Test ............................................................................. 42
Data Interpretation ........................................................................................ 43
Cluster Analysis ............................................................................................. 46
Comparison of the Results ................................................................................... 46
Data Collection for Verification of the Computer Simulation Results .......... 47
The Computer Simulation for Queuing Model ............................................... 47
Output Analysis (Paired t test) ....................................................................... 51
CHAPTER 4
Results & Discussion <4
Field Observation and Workload Characteristic .................................................. 54
Cluster Analysis ................................................................................................... 56
IBM Compatible Section ............................................................................... 57
Macintosh Section .......................................................................................... 59
Trend Analysis ..................................................................................................... 69
Simulation Results ............................................................................................... 41
Application ........................................................................................................... 85
Summary .............................................................................................................. 93
CHAPTER 5 96
Research Contribution ......................................................................................... 96
Further Investigation ............................................................................................ 99
APPENDIX A 101
APPENDIX B 104
APPENDIX C 107
APPENDIX D 108
REFERENCES 109

 

vi

LIST OF TABLES

Table 1: Data Collection Periods ............................................................................ 37
Table 2: Periods in Spring Semester Based on MSU Academic Calendar ............. 38
Table 3: Frequency of the Data Collection (Stratum) ............................................. 63
Table 4: Distribution of Stratum Within Different Clusters ................................... 64

Table 5: Distribution of the Data Sets in the Scatter Plot Using Coordination
of the Actual System’s Resource Utilization and Overall User’s

Waiting Time ............................................................................................. 86
Table 6: Comparison of Historical Outputs and Model Outputs:
Utilization Ratio (IBM Compatible) ........................................................ 104
Table 7: Comparison of Historical Outputs and Model Outputs:
Resource Utilization Ratio (Macintosh) .................................................. 105
Table 8: Comparison of Historical Outputs and Model Outputs:
Waiting Time (IBM Compatible) ............................................................ 106

vii

LIST OF FIGURES

Figure 1: Notation of System Components ............................................................... 13
Figure 2: The Queuing System of the Union Building Computer Section ............... 15
Figure 3: Simple Queuing Model (Source: Banks & Carson II (1994) .................... 16
Figure 4: Modified from Banks & Carson II (1984) ................................................ 17
Figure 5: The Relationship between the Users’ Waiting Time (w)

and the Resource Utilization Ratio (p) .................................................... 21
Figure 6: The Study Plan Flowchart ......................................................................... 24
Figure 7: GUI of Interarrival Time and Service Time Recording

Program on Visual Basic ......................................................................... 30
Figure 8: GUI of Queuing Recording Program on Visual Basic .............................. 30
Figure 9: GUI of Queuing Recording Program on Visual Basic .............................. 30
Figure 10: GUI of Simulation Results ...................................................................... 32
Figure 11: Input Measure Menu ............................................................................... 32
Figure 12: Graphic Display of Users’ Waiting Time and

Resource Utilization Ratio ..................................................................... 33

Figure 13: Cluster Analysis for IBM Compatible Section (Full Scale) .................... 57
Figure 14: Cluster Analysis for IBM Compatible Section (Close Up) ..................... 59
Figure 15: Cluster Analysis for Macintosh Section .................................................. 60
Figure 16: Cluster Analysis for Macintosh Section (Close Up) ............................... 65

Figure 17: Proportion of the Data Set in Each Cluster of

the IBM Compatible and Macintosh Section ......................................... 65

Figure 18: Distribution of Different Periods of Day of

the Week within Cluster A of IBM Compatible Section ....................... 66

Figure 19: Distribution of Different Periods of Days in the Week

within Cluster B of IBM Compatible Section ....................................... 66

Figure 20: Distribution of Different Periods of Day in the Week

within Cluster A of Macintosh Section .................................................. 67

Figure 21: Distribution of Different Periods of Day in the Week

within Cluster B of Macintosh Section .................................................. 67

viii

Figure 22:
Figure 23:
Figure 24:

Figure 25:

Figure 26:

Figure 27:

Figure 28:

Figure 29:
Figure 30:
Figure 31:
Figure 32:

Figure 33:

Figure 34:

Figure 35:

Figure 36:

Time Series Plot of IBM Compatible Interarrival Time ......................... 70
Time Series Plot of IBM Compatible Service Time ............................... 70
Comparison of Historical Outputs and Model Outputs:

Resource Utilization Ratio (IBM Compatible Section) .......................... 74
Comparison of Historical outputs and Model Outputs:

Resource Utilization Ratio (Macintosh Section) .................................... 74
Comparison of Actual Service time and the Service Time

Used as inputs for Model ........................................................................ 80
Comparison of Historical Outputs and Model Outputs:

Waiting Time (IBM Compatible Section) .............................................. 74
Scatter plot of IBM Compatible Section’s Resource Utilization

Ratio and Average of Overall Users’ Waiting Time .............................. 87
Number of Computer Stations versus Resource Utilization Ratio .......... 90
Service Time versus Resource Utilization Ratio ..................................... 91
Interarrival Time versus Resource Utilization Ratio ............................... 92
Comparison of Historical Outputs: Interarrival Time

(IBM Compatible Versus Macintosh) .................................................... 10]
Comparison of Historical Outputs: Service Time

(IBM Compatible Versus Macintosh) .................................................... 102
Comparison of Historical Outputs: Resource Utilization Ratio

(IBM Compatible Versus Macintosh) .................................................... 103
Comparison of System and Model Outputs when using Identical
Historical Inputs ..................................................................................... 107
Percentage of the Students t Distribution ................................................ 108

INTRODUCTION

Competitive economics of the late twentieth century have driven the recent
acceleration in changing work patterns of business and industry. In order to keep pace, a
company’s workplace strategies, including the office environment require adaptations to
efficiently provide the task requirements of the company’s employees. Hence, large and
small organizations must reevaluate their strategies related to re-engineering, customer
service, quality control, outsourcing, vastly improved communications networks and
access to worldwide information systems. These organizations must be concerned that
they restructure their business practices in a manner that will lead to success in new and
foreseeable business environments, and that maintain flexibility towards new alternatives
in the operation of their organization so as to accommodate future requirements.

The new business imperative tends to favor smaller and more flexible
organizations; which invariably means fewer, smaller and more flexible employee
workspaces (Brill, 1993). To meet these demands, new strategies grouped under the title
“alternative officing strategies” have been implemented to create environments that suit
the tasks and needs of changing work patterns. In 1995 the IFMA (International Facility
Management Association) Foundation and Haworth Inc. conducted research on
alternative officing strategies by surveying 4,004 IFMA member organizations (including
352 Canadian members). The study classified the new workplace strategies into two

basic categories, on-site premise strategies and off-site premise strategies.

On-site strategies involve modifying, reconfiguring or redesigning the workplace
to accommodate changes in processing, staffing or organizational structure. Off-site
strategies take advantage of technological advances in communications to offer peOple
more freedom and flexibility to do business from virtually anywhere. The study reported
the proportions of alternative officing strategies used among the member organizations
surveyed as follows: flexible work schedules (53%), modified office standards (46%),
shared space (41%), telecommuting (33%), activity setting (32%), virtual officing (13%),
hoteling (7%), and free address (7%)(See Index). The survey showed that many
organizations did not adopt a single strategy, but implemented a mixture of strategies
specifically tailored to support varied requirements.

Off-site strategies, including telecommuting, virtual officing, and some on-site
strategies, such as shared space, hoteling, free address and activity setting, out facility
costs by reducing the amount of office space per employee. The “Alternative Officing
Research and Workplace Strategies Study” (IFMA & Haworth Inc., 1995) reported cost
reductions of 48% for rent/lease property, 34% of furnishings, and 28% of utilities by
using alternative officing strategies.

Even though the 1995 IFMA-Haworth Inc. study observed that on-site strategies
are more commonly used today, the trend in usage is steadily shifting towards off-site
strategies. In the same year, WI_RE_12 magazine reported that 9.2 million Americans
would be telecommuters by the end of 1995. Moreover, M’s editors anticipate that
the number of telecommuters will triple in the next 15 years to encompass 20% of the
workforce. Nonetheless, physical space continues to play an important role in alternative
workplace strategies. Becker (1995) predicted that a company without a traditional

central headquarters would still occupy some physical real estate, and even the virtual

corporation of the future would maintain multi-use hubs combining meeting and
communication centers. On the other hand, Newhouse (1995) argues that at least half of
such a company’s personnel would remain at a main office due to widely varied human
personalities and job skill types. In general, the provision of office space is a significant
expenditure for most organizations. Thus, organizations are under continuous pressure to
develop and adopt strategies that provide for its needs while minimizing capital
investment. One widely used strategy is the shared space environment, which is
increasingly used in both on-site and off-site office space strategies. Stone and Luchetti
(1994) introduced a strategy called “behavior setting”, which focuses more on “what
people do in certain settings than what people do in certain roles”. In other words, this
approach emphasizes providing shared places designated to support particular behaviors.
Brand (1995) noted that benefits of this kind of environment include space efficiency,
construction cost savings and maximizing space and equipment utilization by increasing
the number of multiple users. Thus, the organizations were able to reduce their
investment in the increasingly expensive real estate market while shifting their interest
into new technology and communication tools.

In order to adjust themselves to today’s business climate, many organizations try
to implement a new agenda while using out-dated facilities. Such facilities are not
designed for the free-flow of communication between employees, new work patterns,
changing departmental organizations or customers’ requirements. These facilities are
generally neither structurally nor mechanically flexible enough to support current
upgrades in technology or accormnodate future growth. Several problems arise in space
management for current use and the prediction of space requirements for future planning.

However, the extent to which an organization changes its workplace is largely dependent

on its working capital. Other important factors, which influence the implementation of
new workplace planning are the resource requirements which depend on policies of the
organization. This crucial factor must be considered when making economically efficient
decisions. In general, estimation and prediction of physical space planning can be
calculated using some type of economic evaluation methodology, such as life-cycle cost,
net benefits or net savings. Sanquist (1996) proposes that such databases should include
cost per square foot, organization units, ownership, number of employees and types of
employees.

Traditionally, in the process of strategic planning and selecting the best alternative
for the new workplace, the organization based its decision on a series of on-site
workshops involving company executives, consultants, interior designers, architects, and
feedback fiom employees. Similar decision making processes are mentioned in other
recent documents published by IFMA & Haworth Inc. (1995), Werts (1996), Froggatt
(1997), Health & Thom-Silverton (1997), Sanquist (1996) and Mosby (1996).

Several methods have been used in order to test and predict resource requirements
for shared space strategies. Some organizations, in order to assure that the new
alternative will work out as they plan, agree to spend their capital investment on a real
life mock—up. Health & Thom-Silverton (1997) also reported a pilot study using a “beta-
site” in the main office when implementing alternative workplace strategies such as in the
case of Citicorp restructuring. Sanquist (1996) noted that the “Scenario Concept” had
become another tool, and was widely used for envisioning a future workplace. The
scenario process incorporates flexibility in design anticipating potential future needs.

This allows facility professionals to test their strategies against different factors in the

business environment. According to Herman Miller Research (1997)', a large
telecommunications corporation in conjunction with Herman Miller Research developed
people-to-work ratios (see: Index) for the corporation’s shared offices used by its
telecommuter employees. However, the report did not discuss how the method was
derived though the authors claimed the calculation was based on a simple statistical
formula. Furthermore, the report stated that “the experience base for evaluating this type
of data is still in its infancy, and there is no single formula that will fit every
organization Thus, these attempts address the fact that organizations have focused
their primary interest on space utilization due to expectations of evolving changes in the
workplace process.

As discussed earlier, several methods have been used to manage limited
resources, such as shared space strategies, yet few forecasting methods for space sharing
strategies have been published.

One of the most effective analytical tools that can be applied to this issue is
borrowed from management science, a computer simulation model for capacity planning.
This method includes trend analysis of differential usage and resource utilization ratios.
It is considered an effective method based on accepted statistical techniques. This model
can be operated as a computer generated queuing model to calculate the distributions of
the waiting time and resource utilization ratio. With the use of trend analysis combined
with computer simulation modeling, this technique can potentially ease the taSk of

constructing a complicated queuing model, and greatly reduce analysis time. Another

 

l Henna Miller Research Report (1997): httpl/www.Hennaamillerxonlmurchlnpornlonsitelfaqihuul

major advantage of this technique is that analyses can be obtained for almost any
specified array of parameters. Given the potentially overwhelming advantages of
specialized computer simulations for capacity planning, organizations can hardly afford
to ignore development of this tool.

This study will focus on a specialized computer-aided capacity planning model
applied to shared space forecasting for facility management. The proposed technique is a
combination of both the scenario concept and statistical modeling. This method will then
be tested for suitability and accuracy. The shared space setting selected as a study site to
test this model, was located in a large educational facility.

In an educational setting which has a large number of occupants such as a
university, the shared space approach has been primarily used as a solution to permitting
maximum student access to expensive or low usage equipment. These facilities may
include computer centers, copy centers. or intramural sports facilities. This strategy
provides similar benefits to the university’s facility administration system as it would to a
business organization. Moreover, it also increases the students’ accessibility to some
specific resources. However, since the university generally cannot provide enough
equipment to meet expanding demand, and space available within most buildings is quite
limited, shared resources allow the users to move to a designated place for a specific job
which is easier than moving spaces and equipment to people in set locations.

Pre-design programming in this type of setting is critical. Brand (1995)
emphasized that “this approach will not work if people do not have access to the right
space at the right time”. In order to make the setting yield the maximum benefit to users
and organizations, some important factors have to be taken into consideration during the

planning phase. These factors include ratios and distributions of users per unit of

equipment and space (resource utilization ratio), accessibility of users to a specified
resource (waiting time), trends in the growth of the number of users in that institution,
and also patterns of user behavior. Careful analysis of the results of these elements may
enable the facility to accommodate an acceptable number of users, which may be
expected to increase in the foreseeable future. This process is referred to as “Capacity
Planning”. Browning (1995) has defined the capacity planning approach as the process
of forecasting the current and future system behaviors regarding resource management
policies.

In practice, capacity planning usually consists of several steps including data
collection, trend analysis, modeling, forecasting and validation of results. The data
collection method includes the collection of service time of the users per station or
resource unit, accumulation of the waiting queue (inter-arrival time), and behavioral
patterns of limited resource users. As suggested by Sisal (1990), the methods for
collection of users’ behavior patterns should include interviews, focus groups, activity
logs and different kinds of observations of physical traces. These techniques are well
documented and have been widely used in many organizations. As mentioned above,
trend analysis is usually based on subjective interpretations of facility managers or
consultants dependening upon experience as the basis for their interpretations. The
results in this step, which are trends in the users inter-arrival rate and service time will be
used as components to predict the anticipated system behaviors. The outcome of the
analysis can be used as an input to the trends forecasting model of resources utilization.
Then the validated forecasting results may in turn be put into an original economic

assumptions analysis to achieve an integral implementation of policies (Browning, 1995).

Two important factors that cannot be over looked in the decision making process
are the waiting time and resources utilization ratio. The distribution of the waiting time
indicates the degree of accessibility to a particular resource. At the same time, the
resources utilization ratio shows the degree of utilization in relation to total resource
capacity. The optimization of these two factors is a function of relative expense of user
waiting time to resource cost. The waiting time and resources utilization ratio can be
derived from the queuing model constructed from the distributions of the inter-arrival
times and the service times.

The pre-design programming phase for shared space in a university deals with
planning for a limited resource, a broad scope of activities, implementation policies and
various external factors. The direct physical testing of optional policies or the
construction of a “beta site” is almost prohibitive because of the considerable amount of
capital investment required, in addition to being a time consuming procedure. Therefore,
a computer-aided capacity planning model incorporated with other programming
methods will be a usefiIl part of the pre-design process. A trend analysis model would
help assess potential outcomes of strategic decisions derived from the resource
estimation. This cost—effective approach can be replicated in many different
environments. The results from this model would illustrate future changes in system
behaviors regarding the anticipated policies with minimal risks and costs compared to
physical site testing. According to the proposed methodology, this conceptualization of
trend analysis and computer-aided capacity planning model is not specific to the
environment in this study, but should also be adaptable in the pre-design programming

phase of various types of resource-constrained environments.

This study examines an application of computer-aided capacity planning used in
space planning facility management. The methodology in this study, which has been
widely used in the area of resource management, can also be applied to the sphere of
facility management. A statistical methodology comprised of a trend analysis model and
computer simulation model for capacity planning is expected to be a valuable device
when used in conjunction with other techniques in the decision making process.

The objectives of the study are as follows:

1. To demonstrate that the computer-aided capacity planning model is applicable

to space and resource management for facility management.

2. To examine the suitability of the proposed procedure for future space

prediction by using the computer-aided capacity planning model.

3. To examine the precision and/or error of the simulation results and use this

information as a correction to modify the model for firrther investigation.

4. To study workload characteristics of the space sharing facility to use as

reference for simulation modeling.

5. To create a flexible and logic-based tool to help envision space planning

solutions for the facilities manager and end user.

The proposed study is divided into two stages. The first stage investigates the
pattern of the users’ behavior and trend analysis for capacity planning. In the second
stage, the simulation modeling technique will be examined. An accurate waiting time for
users and the resource utilization ratio are the expected results to be derived from this
model. In addressing these points, the results discussion is divided into three sections.
The first section describes the new perspective emerging from the observation of users’

behavior and workload characteristics from the field during the observation period. It

provides a basis for understanding the influence of different extraneous variables on user
behavior over time. This insight is crucial to constructing the simulation model. Second,
the accuracy of the results (dependent variables including waiting time and resource
utilization ratio) generated by the simulation model are examined by comparison to the
raw data collected from observation. The paper concludes with suggestions for further

investigation of the computer-aided capacity planning model.

10

CHAPTER 1

DESCRIPTION OF RESEARCH DESIGN

In testing an application of this computer-aided capacity planning model, it is
necessary to understand the principles and characteristics of a queuing system. This
chapter discusses the definition of simulation modeling including the functions and
relationship of system components, queuing discipline, and the characteristics of the
facility in this study.

This research involves the study of the relationship of four variables in a shared
space enviromnent. These variables include 1) users’ interarrival time, 2) service time of
each equipment or computer station being used, 3) users’ waiting time, and 4) the
resource utilization ratio over the whole cycle of a facility’s operation time. The
relationship and classification of these variables are illustrated in detail in the next
section. This computer section is considered a shared space environment or a system,
which is composed of various components. The shared space strategy is chiefly
implemented to increase resource utilization by having multiple users per resource unit or
station. Resource availability is generally on the basis of “first come, first served” (or
first in first out: FIFO), though resources can be reserved by scheduling in advance.
However, this study focuses on the first in first out queuing discipline, which is the only

queuing discipline used in this facility.

Simulation Model and System Component

The simulation model used in the study is a discrete-event system simulation.
Banks & Carson II (1984) describe this discrete-event system simulation as the modeling
of the system in which the stated variable changes only at a discrete set of points in time.
The simulation models are analyzed by numerical methods rather than by analytical
methods. Numerical methods employ computational procedures to solve mathematical
models rather than using the deductive reasoning of mathematics to solve the model.
Banks & Carson II (1984) conclude that “the output measured fi'om the discrete-event
system simulation model) is an artificial history of the system which is generated based
on the model assumptions, and observations are collected to be analyzed and to estimate
the true system performance measures. ”

The system being studied is defined as a group of objects that are joined together
in some regular interaction or interdependence with the accomplishment of some
purpose. The system component can be defined as an entity, an attribute, an activity, a
state, and an event. An entity is an object of interest in the system. An attribute is a
property of an entity. An activity represents a time period of a specified length. The state
of a system is defined to be that collection of variables necessary to describe the system
at any time, relative to the objectives of the study. The event is defined as an
instantaneous occurrence that may change the state of the system.

Figure 1 comprises the definitions and concepts describing system components as
defined by Banks & Carson II (1984). They are used as a conceptual framework for
constructing the simulation of the queuing system for capacity planning for the computer

section examined in this study.

12

 

 

system

Model

System state
Entity
Attributes

Set

Event

Activity

Delay

A collection of entities (i. e. people and servers) that interact over time to
accomplish one or more goals

An abstract representation of a system, usually containing logical and/or
mathematical relationships which describe a system in terms of state, entities and
their attributes, sets, events, activities, and delays

A collection of variables that contain all the information necessary to describe
the system at anytime

Any object or component in the system which requires explicit representation in
the model (i. e., a servers, a users, a machine)

The properties of a given entity (i. e. the priority of the waiting users, routing of a
service)

A collection of (permanently or temporary) associated entities, order in some
logical fashion (such as all customers in waiting line, ordered by first comes,
first served or by priority)

An instantaneous occurrence that changes the state of a system (such as arrival
of a new user)

A time duration of specified length (i. e. service time or interarrival time), whose
length is known at onset (although it may be defined in terms of a statistical
distribution)

A time duration of unspecified length, whose length is not known until it ends (i. e.
a user '3 delay in a last in, first out waiting line, which when it begins, depends on
future arrivals)’

 

Figure 1: Source: Banks & Carson “(1994)

In the study of the computer section, the users and the computer stations in the

section are the entities. The utilization ratio of the computer is the attribute of the

system. The tasks that the users do on the computer station, i.e. checking e-mail, creating

a document are the activities. The number of occupied computer stations, the number of

users waiting in line or being served and the users’ arrival times are the System State.

To describe the event in more detail, the term “endogenous" refers to dependent

events and activities occurring within a system, while the term “exogenous” refers to

independent events and activities in environment that effect the system. Again, in this

study the arrival of users is an exogenous event while the time completion of the task on

the computer station (service time) is an endogenous event.

 

' Modified from Banks 82 Carson II (1984).

13

 

System Capacity

In the computer lab, the number of the computer stations limits the capacity of the
system. However, there are no limits on the number of the users allowed to wait in the
queue. Hence, an arriving user who finds the system fully occupied must either wait in
line or return to the calling population. In the queuing system of this study, the calling
population refers to as a population of potential users that may be defined as finite or

infinite.

Queuing System and Simulation Model Implementation

This section gives an overview of basic principles of the queuing model that apply
to this research. The terminology used in the queuing model and simulation model are
identified in conjunction with the computer lab (system). The latter sections of this
chapter discuss the characteristics, meaning and relationship of the variables in the

queuing model which are used as a component of the simulation model.

Queuing Models and Simulation of Queuing Systems

In this work, the system being investigated is referred to as a queuing system. The
key elements of a queuing system are composed of customers and servers. The customers
refer to any entity that arrives at the facility and require service. The server refers to any
person or machine providing the requested service. Thus, in the computer section, the

users are the customers and the computer stations are servers. (See Figure 2)

l4

 

System customers Servers

 

Computer Section Users Computer Stations

 

 

 

 

 

Figure 2: The queuing system of the Union Building computer section.

Banks & Carson II (1984) state that a queuing system is described by its calling
population, the nature of the arrival and the services, the system capacity and the queuing
model in discipline. In this study the calling population is treated as an infinite
population (approximately 40,000-student population). Users may be considered to be
from an infinite calling population, since the number of the customers being served or
waiting in the queue for service at any given time is always a negligible proportion of a
potential calling population. Thus, the arrival process of the infinite population is
unaffected by the number of users who have left the calling population and join the
queuing system. As a result, when the arrival rate over time from the infinite population
is homogeneous and usually assumed to be constant, the waiting time depends on the
number of users being served and waiting in the queue (SEE Figure 3).

A queuing model can be solved mathematically or analyzed through simulation
modeling. The queuing model is considered a powerful tool for designing, analyzing and
evaluating the system performance. Moreover, a computer driven simulation reduces the
complications and time consumed while enhancing flexibility in the computation process.
The computer generated queuing model allows the computation of many different

scenarios within a short time.

15

 

    
 

Calling Population

 

 

GOO

Waiting Time Server

 

Figure 3: Simple Queuing Model (Source: Banks & Carson II, 1984)

Queuing Notation
In 1953, Kendall proposed a widely adopted notational system for parallel server
systems. These letters represent the following variables for system characteristics:
A represent the interarrival time distribution.
B represents the service time distribution.
[Common symbol for A and B include M (exponential), D (Constant or
deterministic), ER (Erlang of order k), and G (arbitrary or general).]
c represents the number of parallel servers.

N represents the system capacity.
K represents the size of the population.2

The queuing model used in this study is based on the same format which can be
composed as M/M/x/oo/oo model. The M/M/x/oo/oo model describes a system that has x
servers, unlimited queuing capacity, and an infinite population of potential arrivals, and
the interarrival time and service time are exponentially distributed. When N and K are
infinite, they may be dropped from the notation. Hence these M/M/x/oo/oo is shortened to

M/M/x.

 

1 Banks & Carson II (1984).

16

Additional Banks & Carson II (1984) notation applied to this study are described
in figure 4. These notations are based on the parallel server systems that use the FIFO

queuing discipline.

 

A Interarrival-time distribution

A, Interarrival-time between user n-1 and n

it Arrival rate

Sn Service time of the nth arriving customer

p Server or resource utilization

W, Total time spent in the system by the nth arriving customer
n W 0 Total time spent in the waiting line by customer n

Note: (W,' = WQ, + S“)

 

 

 

Figure 4: Modified from Banks & Carson II (1984).

Even though this study focuses on the computer simulation, the principal and the
component of the computer section system are similar to the basic queuing model system
mentioned earlier. The variables in the study include interarrival time, service time,
waiting time, and resource utilization ratio. These variables influence the pattern of the
users’ behavior, users’ satisfaction, and the system performance. The users’ interarrival
time (exogenous event) and service time (endogenous event) are assumed to be
independent variables. The interarrival time and service time influence waiting time
(user satisfaction in terms of line length and delay of the waiting queue) and the resource
utilization ratio (percentage of time the computer station being used). Hence these two
dependent variables can be derived by using the users’ interarrival time and the service
time collected from the observations as input variables for the computer generated

queuing model. The waiting time and resource utilization ratio generated by the

17

simulation model are the output measures of the system. The characteristics of these

variables and system limitations are described in the following section.

Queue Behavior and Discipline

Queuing behavior refers to users’ actions while in a queue waiting to enter the
system. In the case of the computer section in the university, the incoming users may
wait in the queue for the service to begin, “balk”(leave when they see the line is too
long), or “renege”(leave after being in the line when they see the line is moving too
slowly). Normally when multiple queues are available in a congested system, the users
form a new line and then “jockey ” (move from one line to another when they think they
have chosen a slow line) (Banks &Carson II, 1984). The latter behavior does not occur in
this computer section system.

Queue discipline refers to the logical ordering of users in the queue and
determines which users will be chosen for the service when the server becomes free. The
common queue discipline used in this computer section is called first in, first out (FIFO).
This FIFO implies that the utilization of service commences in the same order as arrival,
but the users may leave the system in a different order because of irregular individual

service times (Banks &Carson II, 1984).

The Arrival Process and Interarrival Time (A)

The interarrival time is the elapsed time between the arrival of consecutive users.
The distribution of interarrival times determines the frequency and sequence of the users’
entry. The interarrival time, which is an exogenous event, affects waiting time and the

resource utilization ratio. In the arrival process, users may arrive individually or in

18

batches. Batch arrivals may be regular or random. For instance, the computer lab users

arrive in random size batches. Arrival of the computer lab users occurs at random times
described by a Poisson arrival process3. Banks & Carson II (1984) define the Poisson

arrival process as in the following:

“IfA,, represents the interarrival time between customer n-1 and customer n (A, is
the actual arrival time of the first customer), then for a Poisson arrival process, A,,
is exponentially distributed with mean [/1 time units. The arrival rate is ’1
customers per time unit. The number of arrivals in a time interval of length t, say
N (t), has the Poisson distribution with mean 11 customers. "

The Poisson arrival process has proven accurate in predicting arrival for many
service facilities including restaurants and drive-in banks, and other facilities that provide
service by the same process (See: Also Chapter 3: description of the computer section’s

arrival time and distribution).

Service Mechanism and Service Time (S)

Service time is the length of time that each user spends on the service station. The
service time of successive arrivals are denoted by S], 82, S3, etc. They may be of constant
or random duration. The service times of the users in the computer section are of random
duration since there is no rule regarding time limitations in this particular facility. In this
case, the service process is commonly characterized as a sequence of independent and
identically distributed random variables. In addition, service time in this facility
influences the length of waiting times. Considering this public computer lab as the

facility the university provided for all students, the service time also depends on time of

 

3 Banks & Carson Il (1984), Ross (1993).

I9

the day, day of the week and time of the semester. (See: Also Chapter 3: description of

the computer section’s service time and distribution)

Resource Utilization (0)

Server or resource utilization is defined as the proportion of time that a server (or
service station) is busy. Observed resource utilization, denoted by p, is defined over a
specified time interval (0,7). Resource utilization ratio is the percentage of time that the
service station is being used. Resource utilization ratio is the factor that indicates the
utilization of the facility and resources. The administrator of the facility tends to increase
the resource utilization concerning the return of investment and maximum performance

of a system.

Waiting Time (”7

Waiting time is the length of time that each user spends waiting in the queue.
Waiting time is the factor that indicates the user’s satisfaction in terms of line length and
delay spent in the waiting queue. Not surprisingly, waiting time and dissatisfaction are

directly proportional.

Relationship of Resource Utilization (p) and Waiting Time (”9

In order to achieve optimum facility operation performance, there are trade-offs
between resource utilization and user’s waiting time that the facility managers must
consider. The relationship of resource utilization and waiting time (the interest of the

users) are often in conflict. For instance, the shorter the waiting time, the greater the

20

user’s satisfaction. In order to reduce the waiting time, the number of servers have to be
increased which results in reduction of the resource utilization ratio. Different scenarios

of the relationship between resource utilization and waiting time are illustrated in figure

5.
1
. High waiting time. . High waiting time.
1 low mom“ utilization. , b high mourcee utilization.
a l
-i i
i
l
I
" l
E Beat caee. for real world:
Hedium Waiting time.
E medium theourcee utilization.
c l
1:, : .
.3 """"""""""""""" i“; """"""""""""""
9‘ i
n E
D l
I
I
‘ l
I
I
I
I
.4 I
l
E
g . Low waiting time. ; . Ideal caee: Low waiting time,
(1 low resourcee utilization. . 9 high resourcea utilization.

 

 

U I I I F I 1 I I 1

Resources Utilization

Figure 5: The Relationship between the Users’ Waiting Time (w) And the Resources Utilization Ratio (p).

Point a) Poor management: high waiting time, low resources utilization.
Point b) Low users satisfaction: high waiting time, high resources utilization.
Point c) Best case in real world: medium waiting time, medium resources utilization.

Point (1) Poor resources allocation estimation: low waiting time, low resources utilization.

Point e) Ideal case: low waiting time, high resources utilization.

21

From the diagram of the relationship between the user’s waiting time and the
resource utilization ratio, “point C” is the best case scenario for the system operation for
space sharing facility without implementing any scheduling system. The user’s waiting
time and resource utilization depends on the service time and interarrival time. For
instance, “point e” seems to be the most preferable case for any facility, it is less likely to
happen in the space sharing facility that open to the public without pre-designated space.

In summary, queuing models have been found to be very useful in analysis of
facilities where congestion for scarce resources may occur. The administrator of the
facility can use the queuing model, based on data collected from the field, to generate one
or more artificial histories of the system, such as for this computer lab. This simulation-
generated data in turn can be used to estimate desired performance measures.

The users’ interanival time and service time are independent variables that
influence the latter two variables, users’ waiting time and resource utilization ratio.
Operation cycle and time factor influences workload characteristics which are examined
and used as guidelines for construction of the simulation model due to the unique
characteristics of the facility being investigated.

The computer-aided capacity planning model is expected to be a useful space-
planning tool in forecasting use of the shared space environment, consistency and
reliability of the results before use in predictions of what-if scenarios have to be verified.
This rationale leads to the main purpose of this research, which is to test the validity of
this method by comparing the computer generated results to the field observations. The
tested factors include waiting time and resource utilization ratio which are computer
generated by using the input parameter (interarrival time and service time). Then they

are compared to the raw (existing) waiting time and resource utilization ratio from the

22

same observation session. Their independent variables are used as an input to the
simulation model.

The selected facility for this investigation is a university students Union Building
“public” computer lab in Michigan State University. The section provides computer
stations for students and is accessible to all students on campus. The workload
characteristics of the users cycle over the course of each semester. The workload
characteristics include the distribution of service time, interarrival time, and the
proportion of the different type of users who use the computer station (i.e. number of
IBM compatible users versus number of Macintosh users). These factors influence the
operation of any facility. The extensive understanding of workload characteristics leads
to a better facility planning and implementation of a policy that support the majority of
users’ demands.

The computer section possesses a simple characteristic of a shared space
environment. The operation of this computer section is based on the FIFO and neither
has any reservation system, nor the restriction of time used on the computer station. It is
suitable for the primary study of the workload characteristic and the variable produced by
these factors (waiting time and resource utilization ratio) and compared with the
simulation’s results.

The proposed study is divided into two stages. The first stage investigates the
pattern of the users’ behavior and workload characteristic for capacity planning. The
process includes data collection of users’ interarrival time, service time. Then the data
will be analyzed and calculated the statistical distribution for each parameter to be used

as input for the simulation model.

23

In the second stage, the simulation modeling technique will be examined. A
customized computer simulation model (in JAVA) for capacity planning is used as a tool
to generate scenarios based on parameters and the model derived from the first stage.
Results of the computer generated waiting time for users and the resource utilization ratio

are compared to the raw data collected from the field.

Figure 6 illustrates an application of the computer-aided capacity planning model based on

the principal of queuing system modeling discussed in this chapter.

Start
-_.- M _____s _ . .- -_i_ .*.R
_-_._.___1__-___. .____t______
. COIIOCI
Collect lnterarnval . .
time a Servrce “Imagig &
"m Ratio
‘ .
i
_ _..5————!—_I .__.. —— —-«
___..__ .-__ _L_ ___._. ;
1 Input parameters into is-
‘5 computer software ,5
—— —-91 Data Analysis , -
No i I
i v i
.__.__ Goodness-ot-F'it- >. Verify result from the 5
Tests real data g“
Yea T T— ‘V~ _ __‘
L, _
r—— <— —el, Predict Trend
i
L. _____ _- -9
N° ;
‘ Y
i
5 5A a Verify Trends
,_ __1'__ ._ _
End

24

CHAPTER 2
DATA COLLECTION

This chapter discusses the data collection process, including the design of
observation periods and sampling methods. The environment of the study site, workload
characteristics and operation cycle are investigated to determine the factors and
constraints influencing the system being studied. The devices used in data collection
including customized Visual basic software, observers’ tasks and JAVA simulation

program are presented for further understanding of the data collecting process.

Environment of the Data Collection

The data are derived from the real life events of the every day activities over eight
weeks of field observation. The setting of this computer section is an open environment.
In order to obtain a precise information and evaluation of the variables being

investigated, any action that might introduce an artifact into the data was avoided.

Study Location

The studied site is a computer lab in the student Union Building of Michigan State
University (MSU), East Lansing, Michigan. This section is a computer facility open to
all MSU students seven days a week. This computer facility provides a total of 82
computer stations, pooled dot-matrix printers, and a laser printing service. There are two

different kinds of computers. These include 32 IBM compatible computers and 50

25

Macintosh computers. The rationale for selecting this computer section for the study of
space sharing was based on the service mechanism of this particular computer section.
Similar to the typical shared space system, this computer lab is considered an unassigned
workspace. The “service” provided in this computer lab is based on a FIFO (first in, first
out) queuing discipline. This is a result of a policy that aims at increasing multiple users
per resource (computer station) and yields the maximum convenience (accessibility) for

users.

Workload Characteristics (Types and characteristics and behavior of users)

The majority of the users of this public computer section are Michigan State
University students. However, the policy of this computer section allows some guest
users to utilize the computer service for tasks not requiring a student ID; such as for word
processing or database programs. The tasks that users perform in this computer section
are as follows:

0 Class registration

0 Checking e-mail

0 Using the intemet

o Homework and report preparation

0 Others

CLASS REGISTRA TION
Students may register for courses for the current semester at the beginning of

semesters, and at the end of the semesters for upcoming semesters. During this period,

26

the computer section is very crowded and is expected to have a short interarrival time and
short service time.
CHECKING E-MAIL

Checking e-mail results in irregular service times on each computer station. The
service time when users only check their e-mail is shorter than when they reply to mail.
This task induces a high turn over rate of the users of this computer facility. In the
beginning of the semester, the new users such as freshman students need to set up their e-
mail accounts, which increases a total service time of the facility.
USING THE INTERNET

This task time may vary depending on the preference of each user. Normally
when users come to use the Internet, they may check their e-mail and play computer
games to pass their time. (See: the result from the observation.)
HOME WORK AND REPORT

Students use the computer stations to do home work and reports throughout the
semester. However, when collecting data for the study, it is expected that the number of
users will increase before the semester break (i.e. before the midterm examination) and
before final examinations at the end of the semester. These behaviors result in the
fluctuation of interarrival time and service time of that period mentioned above. In
addition, sometimes when the students have to do a group report, multiple Students may
be working in groups on one or two computer stations
OTHERS

This public computer section at the Student Union Building also provides some
typing tutorial software and other software with similar functions. The utilization of

these programs leads to the longer service time on the computer station as well. In

27

addition, there are some software games such as solitaire and jig saw puzzle on some
computer stations. However, it is not possible from current observations to record or
determine how the utilization of these programs contributes to the distribution of service

time in the computer section.

The Operation Cycle

Understanding the operation cycle is critical to the data collection process and
simulation of the performance of the facility. The whole data collection process should
cover the facility’s operation cycle, which contains the critical value of the users’
interarrival time and waiting time. This information (maximum and minimum users’
interarrival and waiting times) is essential to a thorough evaluation of the performance of
the system.

In this computer facility, the operation cycle corresponds to the semester year and
university calendar. The operation cycle begins before the university is opened because
the computer section has to allow some time for the students to enroll and set up their e-
mail accounts. However, the university accepts new students in fall, spring, and summer
semester, which leads to a fluctuation in the number of users in the computer section at
the beginning of each semester. Normally, fall semester represents the major arrival time
for incoming students, resulting in a greater user interarrival time distribution in the
computer section than at any other time of the year. The computer section has different
working hours during the semester break and summer semester in accordance with the

smaller number of students on campus at this period of time.

28

Devices

This section describes the method and devices used in the collection of the
variables critical to this study. The data collecting process focuses mainly on the
recording of users’ interarrival time and service time throughout one semester. The data
regarding users’ waiting time is collected in order to verify the result generated by the
computer simulation model. The data collection plan and schedule are described in the
next section.

This study focuses on recording and evaluating of the numerical data (interarrival
time and service time), which then is interpreted into the characteristic of the distribution
of each variable throughout the whole study period. The customized software and

devices including the observers in the data collection process are described below.

Customized Visual Basic programs

Two customized Visual Basic programs software were written specifically for this
data collection process. Each program was used to collect the interarrival time, and
service time of each station. These programs are designed to count time, number of
users, and then file the report in the form of a data log. These two customized data
collecting programs are for the documentation of: l) interanival time and service time, 2)

waiting time in the queue. (See: Figure 7-Figure)

29

I. Service

[Hark --> click "Start“l

 

 

 

 

 

 

 

 

 

 

 

 

 

[P12] [P13] [P14] [P15] -a
P21 F22 1323 , . _P24 P25 P26
P31 P32 P33 P34 P35 P36
P41 T42 P43 P44 P45 '31:] P47
P51 P52 P53 P54 P55 P56 P57

 

 

 

 

 

M11 ] M12 ] M13 1
M21 1 M22 [M23

 

 

 

M31 ] M32 ] M33
M41 ] M42 ] M43

 

 

 

M51 ] M52 ] M53
M61] M62 ] M63

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

M71 ] M72 ] i473 ] M74 M75 M76] M771 M77
M61 J M62 [ M63 ] M64 M65 M66 ] M67 ] M66
M31 ] M32 ] M33 ] M34 M35 M36 ] M37 M36"
M01 ] M02 ] M03 ] M04 M05 M06 ] M07 M03

 

 

 

 

Figure 7: GUI of Interarrival time and service time recording program on Visual Basic

 

Enter number of students in the queue E

 

 

 

 

" OK I tamer"

__._M 1 “PA A . -_» .1. A. _ .A -z‘.‘_-._._. “_‘.-.‘ .‘u “AAA #4. n. e_;

 

Figure 8: CU] of Queuing recording program on Visual Basic

—I

1 2 3 4 5 6 7'6 310 1112131415] 16[17]16]13]20
“w " f . ‘ :‘ .. " I :“I.‘;I .l I .:

‘l-S ' ‘ ‘ I Z-Anive I l Dune! I

.._ - 4 _ s... mt..- _. .......__

 

 

 

 

 

 

 

 

 

 

 

 

i

 

 

l

Figure 9: GUI of queuing recording program on Visual Basic

30

Data were collected by three observers using these programs. One observer was
responsible for recording the data including user’s interarrival time and service time
aided by the other two observers who were responsible for monitoring arrival times and

also observing the users’ behavior in the computer section.

Customized JA VA program for simulation

The customized JAVA program for Simulation of the distribution of waiting time
and utilization ratio is used to simulate the pattern of the users’ behavior based on the
given parameters (mean interarrival time and mean service time) derived from the
previous statistical analysis of the data collected. The simulation model in JAVA
generates the users’ waiting time and resource utilization ratio within the time period
specified. The results of the waiting time and the utilization ratio were then compared to
the sampling data collected from the field.

Similar simulation software is commonly used for predicting the outcomes on
service lines in manufacturing systems. However, this software is quite expensive, thus
this study used the customized JAVA program, which is able to perform the same
functions, and can be viewed on the Internet with a standard web browser.

This customized JAVA program contains the following basic features:

1) Input boxes for:

0 Mean of users’ interarrival time (seconds)

0 Mean of service time (seconds)

0 Simulation time (second)

0 Unit of service stations or computer stations

(See: Figure lO-Figure 12 below.)

3]

 

 

sumo-7*

:311

ml
- 10 e'

5‘22“. .

 

 

Figure 10: GUI of simulation Results

1:“ Simulator 5 Netscape

_,'~& 5‘ 155.59 m 11*

Swain-(seer) [amon—

 

 

 

Figure 11: Input Measures Menu

 

Utrltutlen : Mll' 61.17 1 our-61.17 S

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Isle. The : Inn-0.0m eel-onsec

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 12: Graphic display of Users' waiting time and Resource Utilization Ratio

2) Output report. The output report displays several forms including the time log, and
real time graphical distribution of the variables of interest. The time log includes user’s
arrival time, service time, waiting time in the queue line log and trace of the utilization of
the computer stations. The utilization ratio can be displayed in real time as a percentage
of the facility’s utilization as well. The length of the waiting queue is displayed as a
symbol in the same manner as the real event when a user enters the facility. The color of
the user’s symbol changes corresponding to the time the user spends waiting in the queue

line.

Observers
Observers are trained to use the data collection programs mentioned above. In

each data collecting session, one of the observers is administering and recording the data

33

using the data collecting program (customized Visual Basic program) on one of the
computer section’s IBM compatible stations. At the same time, one or two of the other
observers are monitoring the arrivals, length of service time and departures of the

computer section users and inform the observer who is responsible for recording the data.

Data Collection Schedule

The data collection periods were separated into subcategories based on the
academic calendar, which is described as follow:
a) Beginning of the semester (four weeks)

b) Midterm examination (four weeks)
c) After midterm examination (four weeks)
d) Final week (four weeks)

Data collected from period “a. to b.” was analyzed and used in constructing the
trend analysis of the users’ interarrival time and service time. Then this trend was
projected and customized to predict the future trend (period “c. to d.”) based on the data
in period “c.” In the same period of time (“6. to d.”) the waiting time and the resource
utilization were collected in order to verify the result from the computer simulation
model. The data collected in period “c. to d.” were used in verifying the result from the

trend analysis. ( See Figure 1: Study Plan Flow Chart).

Period of Observation

We assumed that the distribution of interarrival times and the service time of the

users might vary from day to day and even from hour to hour. As the operation cycle of

34

the university’s facility depends on the semester and class schedule as well as the
students’ activities during the weekdays and weekend. From the 16-week duration of
observation, data collection schedules were designed to cover a representative cross
section of the data. However, the data collected from every observation session were
examined the different and of their distribution in order to test the assumption we formed
before the beginning of this investigation. The result of this test is presented in the next

chapter.

Data collection for statistical analysis
As described in the plan for data collection, this process utilized customized
Visual basic programs and observers to collect the users’ interarrival time and service
time from the beginning of the semester until the week after the midterm examination.
The collecting time was distributed into 14 groups, which are described as following:
-Beginning of the semester (First quarter of the observation session)
-Midterm examination (Second quarter of the observation session)
In each week the collecting time will be distributed into:
-Weekdays
-Weekend
During weekdays, the time will be distributed into:
-Before 10:00 am.
~10:00 a.m. - 2:00 pm.
-2:00 pm. - 6:00 pm.
-After 6:00 pm.

During weekend, the time will be distributed into:

35

-12:00 am. - 2:00 pm.
-2:00 pm. - 6:00 pm.

-After 6:00 pm.

These 14 groups cover the duration of the first 8 weeks of Spring semester, which
consists of approximately 182 periods. To obtain the data, 3 periods for each grouping
were randomly selected for 2-hour observation sessions. This schedule produces 42 total
observation sessions. The plan for data collection was designed to investigate the
variability of the distribution of the interanival time and waiting time corresponding to

the computer lab hours. (See: Table l-Table 2)

Sampling Method

The sampling method used to collect the users’ interarrival time and service time
is designed to cover the cross section of the entire 8 weeks of spring semester. From the
total 182 observation sessions derived by the criteria stated above, we decided to examine
thirty percent of the total time period which produces 42 observation sessions.

The criteria used to select the observation sessions were based on the stratified
random sampling method in which the data population is divided into a number of
mutually exclusive subpopulations (or subgroups). Each stratum that we assumed to
have a homogenous data distribution is selected to be observed by a simple random
sampling method. The selection was done by randomly drawing the number assigned for
each period in the duration of the study from each grouping (or stratum). The planning
strata sample size of this study is based on the allocation of the total sample size of the

total sample size to the individual strata. (Tables 1 & 2).

36

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Begiiiningfiof the semester Week days Before 10:00 am.
(The First Quarter Ofthe 10:00 am. - 2:00 pm.
Semester) T 2:00 p.m. - 6:00 p.m.
. After 6:00 pm.
Weekend 10:00 am. - 2:00 pm.
2:00 pm. - 6:00 pm.
After 6:00 pm.
Midterm examination _ Week days Before 10:00 a.m.
‘ (The Second Quarter ofthe 10:00 am. - 2:00 pm.
Semester) if 2:00 pm. - 6:00 pm.
After 6:00 pm.
" Weekend 10:00 am. - 2:00 pm.

 

2:00 pm. - 6:00 pm.

 

 

After 6:00 pm.

 

Table I: Data Collection Periods

37

 

 

 

Week day : The First Quarter
13 14 15 16 17
20 21 22 23 24

January

 

27 28 29 30 31

 

 

total = 15 gays ,

Week dav : The Second Quarter
3 4 5 6 7
1011 121314
17 1819 20 21

February

 

24 25 26 27 28

 

 

total = 2 3
Week dav : The Third Quarter
March 10 ll 12 13 14
17 18 19 20 21
24 25 26 27 28

 

 

 

 

total = 15 days ,

Week dav : The Forth Quarter
April 31 1 2 3 4
7 8 9 10 11
14 1516 17 18

 

21 22 23 24 25

 

total = 20 days

Total of 98 days observation.

Break.)

38

 

 

Weekend : The First Quarter
January 18 19
25 26
1 2

 

 

total = 6 davs

 

 

Weekend : The Second Quarter
February 8 9
15 16
22 23
l 2

 

total = 8 days

 

 

Weekend : The Third Quarter
March 8 9
15 16
22 23

 

 

togl = 6 d_avs

 

 

Week : The Forth Quarter
April 29 30
5 6
12 13
19 20

 

 

total = 8 davs

Table 2: Periods in Springs Semester based on MSU academic calendar. (Not including Spring

CHAPTER 3
DATA ANALYSIS: METHODOLOGY

This chapter describes the data analysis and methodology used in order to obtain
the parameters of interarrival distribution and waiting time used to construct the
simulation model. Then the parameters from each group of the data, including users’
interarrival time and service time are used as inputs for the simulation model to generate
the waiting time and resource utilization ratio. Finally, the simulation results are
compared to the raw data (real waiting time and resources utilization ratio) from the
sample and examined as to the accuracy of the model. This chapter is divided into two
sections including; 1) Data analysis for constructing the simulation model and 2) the
comparison of the results generated by the simulation model and the data collected from

the field.

Data analysis for constructing the simulation model

Data from each of the 42 observation sessions was analyzed to determine the
appropriate distributions as described in the following:
6) Collect data of interarrival time of users, and service time of users per computer
from a selected public computer section.
b) Group the data and identify the distribution by constructing a histogram. Then
make the distribution assumptions of the data on the basis of the histogram shape. .

0) Estimate the distribution of parameters.

39

d) According to Poisson distribution the distribution of interarrival time and service
time are assumed to be exponentially distributed.

e) Test the hypotheses with a Goodness-of-Fit test (Kolmogorov-Smimov test) to
verify whether the interarrival time and service time are exponentially distributed.

f) If the distribution of interarrival time and service time are exponential, use the
average of each group of data as the estimator.

g) Use the estimator from each data group to construct the computer simulation
model Discrete-Event System Simulation.

h) Compare the results of waiting time and resource utilization ratio generated by the

simulation model with data collected by observation.

Estimation of the Data Distribution (interarrival time and service time) Based on
Principal of Poisson Process

The estimation of the data distribution is very important in determining the input
parameters used in the simulation model. According to Banks & Carson II (1984), ”the
arrival time and service time may be described as a counting function N (t) define for all
t 2 0. This counting function will represent the number of event that occurred in [0,t].
Time zero is the point at which the observation began, whether or not an arrival occurred
at that instant. For each interval [0,t], the value N (t) is an observation of a random
variable where only possible values that can be assumed by N (t) are the integers
0,1,2...”

The counting process, {N (t), t 2 0} is said to be a Poisson process with rate A if
the following assumptions are fulfilled:

l) Arrivals occur one at a time.

40

2) {N (t), t 2 0} has stationary increments: The distribution of the number of arrivals
between t and t + 3 depends only on length of the interval 5, and not on the starting
point t. Thus, arrivals are completely at random without rush or slack periods.

3) {N (t), t 2 0} has independent increments: The number of arrivals during
nonoverlapping time intervals are considered independent random variables. Thus, a
large or small number of arrivals in one time interval had no effect on the number of
arrivals in subsequent time intervals. Future arrivals occur completely at random,
independent of the number of arrivals in past time intervals. 1

If arrivals are in accordance with a Poisson process, then the process meets the
three assumptions above. In the Poisson process, it is proved that all the interarrival
times (A1, A2,. . .), are exponentially distributed and independent with mean l/A. As an
alternative definition of a Poisson process, it can be shown that if interarrival times are

distributed exponentially and independently, then the number of arrivals by time t, say N

(t) is a Poisson process.2

According to the property of Poisson process, if the distribution of interarrival
process in this computer facility meets the three assumptions as mentioned above, the
distribution of the interarrival time is assumed to be exponentially distributed. Similarly,
the distribution of the service time in this computer facility can be performed with the
same process.

Hence the distribution of the interarrival time and service time are assumed to be

exponentially distributed, which is required to test the hypothesis (distribution

assumption) before using the estimator of the data as the input to the simulation model.

 

' Banks & Carson II, 1984.

1 Ross, 1981.

41

Kolmogorov-Smirnov Test for Goodness of F it for Exponential Distribution

The Kolmogorov-Smimov (K-S) test is a test of uniformity and used in
verification of a new generator. The test measures the degree of agreement between the
distribution of a sample of generated random numbers and the theoretical uniform
distribution. It is also based on the null hypothesis of no significant difference between
the sample distribution and the theoretical distribution.

The K-S test is particularly useful when the sample sizes are small. If the size of
the data set from each observation session is varied, it is appropriate to use the
Kolmogorov-Smirnov test in this study. In order to use the K-S test to examine the
distribution of interarrival process, the null hypothesis and its alternate are formed as
follows:

Ho .' the interarrival times are exponentially distributed
H1 : the interarrival time are not exponentially distributed

According to Banks & Carson II (1984), when the data are collected over the
interval 0 to T, it is proved that if the underlying distribution of inter arrival time (T),
T 2....) is exponential, the arrival times are uniformly distributed on the interval (0,7). The
arrival times (Tl, T1+T2, T1+T2+T3,....,T1+.....+T.,) are obtained by adding interarrival
times. The arrival times are then normalized to a (0,1) interval so that the Kolmogorov-
Smimov test can be applied.

The K-S test utilizes a statistic that is based on the differences between the
cumulative sample function and the cumulative probability function for the population.
The K-S Test does not depend on the specific form of the cumulative probability function
of the population. The K-S test procedure can be applied to the hypothesis testing of the

service time distribution, thus it can be used to test whether the cumulative probability

42

function has a specific form. Since the estimator for exponential distribution is an
average, the averages of interarrival time and service time are valid to use as the input
estimators in the model. After the interarrival time and service time distribution are
proven to be exponential, the estimators (mean of interarrival time and mean of service
time) from each group of data are used to generate the waiting time and resources

utilization ratio of that session.

Data Interpretation
7 Users’ interarrival time and service time of each data collecting session are
converted into numerical data by the same customized Visual Basic program that was
used in the data collecting process. Data from each observation session are composed of
two sub group: 1) data for the 50 Macintosh Computer Stations and 2) data for the 32 PC
(IBM Compatible) computer stations. The users’ interarrival time and service time of
each sub groups are recorded and analyzed independently.
The following section discusses briefly the conceptualization of each variable and

the method used to derive their estimators.

INTERARRI VAL TIME

Interarrival Time is the elapsed time between two consecutive user arrivals. The
unit of interarrival time is in “seconds.” The estimator used to represent each data set is
the average (u). Though in the analysis of interarrival time, A (Up) is used as an
estimator for the distribution of interarrival rate. Since interarrival rate is equal to
l/interarrival time, [I is an appropriate estimator used for the distribution of interarrival

time when assuming that it is exponentially distributed. In collecting the data of the

43

arrival process, we are able to identify whether the users come to use the PC (IBM
compatible) stations or Mac stations. The procedures used to estimate the average
interarrival time of the users of each type of the computer station are as follows:
N = Total number of users arrival
n pc = number of PC (IBM compatible) users
It MAC = number of Macintosh users

Avg. interarrival time (Avg. (N)} = Avg. interarrival time of each data set (PC+MAC)

 

Average Interarrival time of IBM Compatible Section= Avg.(N)x [PIC (Seconds)

n

 

Average interarrival time of MAC stations = Avg.(N)x (Seconds)

n
SERVICE TIME

Service time is a length of time that each user spends at the service station. The
unit used in measuring service time is in “seconds.” In addition, the distribution of
service time does not depend on the arrival of users to the facility. In opposition to the
data collection of the interarrival time, we are able to identify the service time that each
user spends on the station and type of computer station that is being used. In this
situation, we do not have to estimate the average usage of the PC station and MAC
station by using the total service time. The calculation for average of service time of

each data group is shown as the followings:

n pc = number of PC (IBM compatible) users

n MAC = number of MAC users

Average Service time of PC stations = TotalPCservrceTtme (Second)

nPC

 

TotalMA Cservice Time
nIlMC

 

Average Service time of MAC stations (Second)
RESOURCE U TILIZA TION RA TIo

Resource utilization ratio is the percentage of time that the service station is being
used. The resource utilization ratio indicates the percentage of the resource used at the
discreet point of time. The total resource utilization ratio can be the calculated in two
different ways. The first method is to calculate the resource utilization ratio for every
time interval (second, minute, and etc.), and then use the average of the summation of
total utilization ratio as the estimator for that observation period. The second method is
to calculate the resource utilization ratio whenever there is a change in number of users
(users’ arrival or leaving), then use the average of the summation of total resource
utilization ratio of that period as the estimator of that observation period.

N = numbers of the station being used
Ns = numbers of station available

Resource utilization = A]— x100 (Percent)

nS
WAITING TIME
Waiting time is a length of time that each user spends waiting in the queue. The
unit of waiting time used in this study is “seconds.” It can be derived directly from the
time that each user spends waiting in the queue line. The estimator for waiting time used
in comparison to the result generated by the simulation model and raw data is the average

([4) of the waiting time for each observation period.

45

Cluster Analysis

A total of 42 data collecting sessions for the period of data collection in Spring
semester are separated into two major periods: approximately one month from the
beginning of the semester (period a) and another month before the midterm examination.
Within each period, the data collections are separated into weekdays and weekend
assuming that the interarrival time and service time may have different characteristics
(distributions). And we the weekday data collection are separated into four periods,
weekend into three periods corresponding to the computer section hours and in order to
cover the cross sectional of the data distributed within the facility.

Though, the data collections are dissected into several different subgroups based
on the assumption that they may have different attributes, the cluster analysis is used to
test the dispersion of the data throughout the data collection process. The scatter plot
using the coordination of interarrival time and service time of each data collecting
session verifies whether or not the data set possesses a different distribution and is
divided into groups as per our prior assumptions. Two different scatter plots for the
MAC computer stations and IBM Compatible computer stations are created for this

cluster analysis.

Comparison of the Results

This section gives the general idea of the method and principles in comparison of
the simulation results to the data collected from the field observation. The overview of
the simulation events generated by the computer described in the following section will

give a better picture of how it works. Characteristics of the system being studied and

46

criteria in using the simulation results as the estimator to verify this model are also

described.

Data collection for verification of the computer simulation results
The waiting time and the resource utilization ratio was collected from the
beginning of the semester to the week before midterm examination periods. Data were

then compared to the simulation result at that specific time to test the simulation model.

The Computer Simulation for Queuing Model

The model used in predicting the waiting time and resource utilization ratio in
this study is the MM] queuing model, which is a discrete event simulation. As
mentioned in a prior chapter, this basic queuing model generates the output measures for
a discrete point in time, which permits the evaluator to test the capacity of the resource
available in different scenarios. These input measures influence the utilization of the
facility including number of stations available, interarrival time and service time. As
opposed to a more complicated model, it is not able to generate continuous output
measures throughout the operation cycle (semester year). However, the results from
discrete-event simulation can be put together “manually” and used in predicting the
capacity of the facility throughout the operation cycle as well.

In order to simulate usage of this computer lab at the MSU Union Building, the
simulation is separated into two models including the IBM compatible stations and the
MAC stations. Upon arrival, users of different types of computers wait in a different
queue. Normally, there is only a waiting queue for PC stations, which have a smaller
number of resources available. When MAC users arrive, they will go directly to the

available MAC stations without spending time in a waiting queue. The two types of

47

computer stations have different user interfaces. It is common that the users will use, and
wait in the queue line if it is not available, for the type that they are familiar with.
Though, the MAC stations and PC stations are in the same computer section, they are
located in different sections and groupings, which allows the user to determine the
availability of the type of stations that they prefer to use. The observations reveal that
some of the MAC users tend to stay longer, over two hours (observation session), and
sometimes use more than one computer station at a time (the station that they use and the
adjacent one). According to the different characteristics of the users and the computers
themselves, it is appropriate to evaluate the two types of computers in a different model

for clarity of the output measures extraction.

48

The M/M/l queuing model principal is described as follows:
ENTER- Arrival Time (t)

_ Random next user arrival (t+At)

#— Put event “ENTER (t+At)” into Event Queue

 

L Check if there is any computer station available
If available, enter the computer station and use
If not available, wait in the Waiting Queue
USE- Service Time (5)
Random service time (1+ AS)
Put event “EXIT (ti-AS)” into Event Queue
EXIT
First user in the Waiting Queue enters the computer station

Exit

The simulation model is programmed to be operated continuously following the
event from the discipline described above within the time given by the evaluator.
However, in the beginning of the computer simulation process, the number of users in the
system starts from zero as when the facility opens in the morning. In contrast, the
number of users in a normal computer operation hour that we want to test does not begin
with zero since there are some users already in the lab. To obtain the precise waiting

time and resource utilization ratio of those periods, we have to run the simulation more

49

than the two hours (simulation time) to let the program pass the transient state, and then
the waiting time and resource utilization ratio climbs up to the steady state.

From Monday through Friday, the computer section is considered a non-
terminating system since it is operated 24 hours continuously. The non-terminating
system differs from the terminating system in that the non-terminating system study is
focused on the characteristics or the behaviors in the steady state or the long-run
properties. The steady state of this system refers to the typical running operation whereas
the transient stage refers to the running operation that starts from the empty or idle stage.
During the transient stage, “within a replication, there will be a higher than the typical
probability of the system being uncontested for time close to 0” (Banks & Carson II,
1984). As a result, the estimators derived from the simulation will be biased low, and this
bias can lead to misleading results.

Considering the characteristics of a non-terminating system, it is important not to
be influenced by the initial condition of a model at time 0 in the study. Hence, when
simulating the system, we have to monitor the variables produced by the model. When
the value of the variable stops rising and remains in the steady range, this value will be a
valid estimator for the analysis. From the experience in simulating the model in this
study, the typical transient stage requires approximately two-simulation hours. The
value of waiting time and resource utilization ratio obtained after the first two-simulation
hours are considered reliable as a replicate of a system behavior and in turn used as the

output measures for the analysis.

50

Output Analysis (Paired t test)

The examination of output analysis for each type of output is determined by the
result from the steady state to obtain a reliable output report. The test used in comparison
of the simulation results and the historical inputs is a “paired t test” based on the Central
Limit Theorem. In the paired t test, the historical out put is paired with the model output
since each was produced by the same input data set.

The Central Limit Theorem is defined as follows: “The distribution fitnction of
arithmetic of a large number of independent, identically distributed random variables is
approximately equal to standard normal distribution function (approximately
adjusted)....” (Larson, 1969). This theorem is applied when analyzing the simulation
output. Harrel et a1. (1996) describes that “a performance response produced from a
single replication of a stochastic... (or process composed of randomly occurring events)
simulation can be considered a single sample from the distribution of all possible
responses. Each independent model replication made thereafter produces another

sample from the response distribution.”

5]

Banks & Carson II (1984) and Harrel et al. suggest the formula for computation

of t statistic by

to = Sample mean different
,ud = True mean different
S4 = Deviation from mean

K = number of input data sets

 

_ E-fld

nss/JE

to

 

 

 

Similarly, in this study we do not know the probability distribution which
represents all the possible outcomes. However, we know that the collection of the K sets
of input data are separated in time, it is reasonable to assume that the K differences
(between the historical outputs and model output) are statistically independent. Thus, the
pairs of differences of the historical outputs and model outputs constitute a random
sample and are approximately normally distributed with some mean [14 and variance old.
With this information, we can use a standard normal probability density function to
define confidence intervals for the point estimate of pd.

Then the t test of the null hypothesis of no mean difference are used as follow:

Ho : 1.14 = 0
Versus the alternative of significant difference:

H1 Zpd¢0

52

The test of no mean difference is done by computing the to statistic using the
paired t test mention earlier, and comparing the value obtained with the critical value
to/2,K-l from the Table of Percentage Points of the Students t Distribution with u Degrees
of Freedom. (See: Appendix D). The criteria for the test is if I tol S ta/2J(-|, do not reject
Ho of no mean difference and conclude that test provides no evidence of model
inadequacy. If | tel > Ia/zx-“ reject the reject Ho of no mean difference and conclude that

the model is inadequate (Banks & Carson II, 1984).

53

CHAPTER 4

RESULTS & DISCUSSION

This study focuses on testing the applicability and suitability of the Computer-
Aided Capacity Planning Model for Facilities Management. The suitability of the data
collection procedure including the methods of data collection and observation session,
especially the data collection schedule and planning, are examined and discussed in
detail. This chapter concludes by comparing the simulation results to the data derived
from the field observation to validate the model. The accuracy of the waiting time and
resource utilization ratio which are the main purpose of the simulation including the
results from the IBM compatible section and Macintosh section are presented and

compared.

Field Observation and Workload Characteristic

In the data collection planning process, the workload characteristic is taken into
consideration when grouping data into strata for observation. As mentioned in the early
chapters, we assume that the independent variables influence the capacity planning of the
computer section including interarrival time and service time and should depend on the
cycle of operation (university schedule). On the other hand, the variation of workload

characteristics is a result from the users’ activities; which cycle over the semester.

54

These activities include class registration, coursework, checking e—mail, using the
Internet, etc. The major activities assumed to have most influence on the interarrival time
and service time are class registration and coursework during midterm and final exams.
Class registration may contribute to interarrival rate (or high arrival rate: large numbers
of users arrive continuously) and the service time is assumed to be in the intermediate to
long duration. Coursework during examination periods may contribute to a low
interarrival time (high arrival rate) and very high service time.

Similarly, we assmne that weekday interarrival and service times differ from the
weekends. Weekdays may have low interarrival time (high arrival rate) because of the
high number of the students on campus who would come and use the computers in this
Union building computer lab. On the contrary, weekends are assumed to have high
interarrival time (low arrival rate) and high service time because fewer students remain
on campus and they may come and use Internet, check e-mail or even do their homework.
However, the weekend users do not have much time constraints on use as compared to
weekday users since there are less or none users waiting outside in the queue line.

The Union Building computer lab is composed of two different kinds of computer
stations. Observations revealed different workload characteristics of the IBM compatible
users and the Macintosh users. IBM compatible users tend to have a longer period of
service time, and normally spend some time waiting in the queue during peak weekday
hours before entering the section. This is the result of the smaller number of computer
stations available (32 computer stations), and one or two stations usually out of service,
further reducing available the number of available workstations. Because of the relative
scarcity of IBM compatible machines, users tend to be more possessive towards a station

once occupied. When the queue grows long, users waiting at the end tend to abandon

55

their place when the waiting time exceeds ten minutes. This may reduce user satisfaction
toward operation of this computer lab.

Unlike IBM compatible users, Macintosh users tend to move around, select and
change computer stations until they are satisfied. Some users occupy multiple stations.
The same group of users may use a computer longer than a couple hours at one time.
These users may leave their belongings at the station that they use and leave the section
and then return to resume using that computer. This occurrence may happen more than
one or two times per session for the Macintosh users. The Macintosh section is less
crowded than the IBM compatible section. The users do not have to form the queue in
order to enter the section. When the Macintosh users arrive and find the waiting line for
IBM compatible computer stations, they will go directly into the Macintosh section to
avoid waiting in the line. These assumptions for variations in interarrival time and

service time are tested by using cluster analysis.

Cluster Analysis

Cluster analysis is used to determine the grouping of data. We performed
separate tests for the IBM compatible section and the Macintosh computer section since
their operation and users are independent. The cluster analysis used the coordination of
the plotted average of interarrival time and service times from the same observation.
These are used to test the assumption of the variation of the workload characteristics
correlated with the stratified random sampling method. (See: Appendix A: IBM
compatible computer section and Macintosh computer section’s Interarrival Time and
Service Time). In these scatter plots, the interarrival time and the service time of each

data set represent its unique characteristic. If the assumptions that the data have 14

56

different characteristics as we expected prior to the data collection is true, then the data

sets from each stratum should be clustered in the same group and vice versa.

PC Section (IBM Compatible)

The PC section is composed of 32 IBM compatible computer stations. Normally,
at least one to two computers are out of service, reducing the true count to 30-31
computer stations available for the users. Figure 13 illustrates the scatter plot of the IBM
compatible section using the coordinate of interarrival time and service time of each
observation period. We can see that the average interarrival time for the IBM
compatible section clusters around 300 seconds (5 minutes), and service times vary from
900 seconds (15 minutes) toSOOO (approximately 1 hour 33minutes). The only outlier
data set is “1251739” which is from Saturday, January the 25 at 17:39 hours. This data

set is also an outlier data in the cluster analysis for Macintosh section.

Clumr Arr-lyi- for PC Section

2500 MM.-. _. .. ,. -....,..-. .._.-.~ . _-_-.. W __._ - ._.....-~.,.__ ,. .__...,_._ ...-._.h.... _ _.._. -___. ....-._._.__ v...

Q 4— Outlier E
mo a,__._-, “a _ W, L_, -. .7 .7 . A, ., . _.____.._.._.__ __ ,_. ._-____ ._. ,'

 

. x 'x
’2' + in" ‘- oa- '

 

 

o 1000 2000 3000 4000 5000 0000 ‘
Senlce Tune (Second)

Figure 13: Cluster Analysis for PC Section (Full Scale)

57

Figure 14 shows the close up grouping of the clustering data in the range of 0 to
300 seconds (5 minutes) of interarrival time. We can see that the greater number of data
sets (Cluster A) cluster around interarrival time of 60 to 180 seconds (1to 3 minutes)
and the service time around 1200 to 3000 seconds (20 minutes to 50 minutes). In Cluster
B, the data sets group around interanival time of 120 to 180 seconds (2 to 3 minutes) and
service time around 3600 to 5000 seconds (60 to approximately 80 minutes).

From the grouping of the data set in the scatter plot shown in Figure 14, it is
obvious that period of time in the day does not influence the interanival time and service
time of the users of the IBM compatible computer section as we assumed before
collecting the data. 78.69% of the data collected are cumulated in cluster A, which
contains the data set from weekdays in different time periods of the day.

Most of the data sets (13.04%) in cluster B are comprised of the data from the
weekend which have high interarrival time (low interarrival rate: small number of users
enter the section) and high service time. A few fragments of the data sets from cluster B
are from the weekday in the week of midterm examination. The high service time and
low interarrival time in this analysis is consistent with to the assumption we proposed
before collecting the data.

For the outliers, the data sets are from the first period quarter of the semester in
the afternoon period. The proportion of the data is only 8.27%, which is insignificant
when comparing the grouping of the entire data set. In the close up figure (Figure 14),
there are two outliers including two data sets from weekend. These data are from the
verge of the first and second quarter of the semester. We are not surprised to see the data

sets from the weekend of the third and forth week of the semester that have high

58

interarrival time (range of 250 to 260 seconds) and medium service time (2300 to 3000

seconds).

 

 

 

L..- -‘.__ #flc-_._v 2.- -7 ._.-._. --_... - _ .. -.__.____.AL_ __ 2. .2 7 -,, -7. ._.._. __ _, , _ , ,i

Figure 14: Cluster Analysis for PC Section (Close up)

Macintosh Section

50 Macintosh computer stations are provided in the Macintosh section of the
Union Building computer section. Similar to IBM compatible section, 3 to 4 the
Macintosh computers are normally out of service at the time leaving only 46 to 47
computer stations remaining available for the users.

From the full-scale cluster analysis (Figure 15) for Macintosh section, we found
the same outlier data set which also appeared on the IBM compatible section. This data
set was from Saturday, January the 25"1 which was the beginning of the semester.

Regardless the outlier, the major group of data cluster around the service time of 600 to

59

3800 seconds (10 to 63.34 minutes) and the interarrival time around 60 to 270 seconds (1

to 4.5 minutes)

Gun! Anon-la for new Baden

 

 

 

1m .. - ,.,...-....~._-...._.,...,.....,...-WM..._-_...-.._...,_...M_. Wt.,_-ww-.~~...~_W_ ,,-,_ ,,-,_,-fi,..,,_- ,,-_,, __,i ,7
‘— Outlier 7
“mp _ ,. -,C .Ai,,. -. ,. __.. -7 ._..__..-__- , ._7 __ 7 , miii , ,, V, c - , ,
‘amb 7_ --_ii ‘g-._.__2C—_V____.-fi._*_v_____rw_.-fl‘#__i
i
.5..-~_--_¢ ,w_,, .. -2c—fl.._,___c_
| f
f “r ~ A v-—-—‘ a 7 — A — k ~ 7 i i - —— —— i H ~7
2 m T T“ — "fl“! "T‘V‘TMTTHTH "fix—"'— "T"
. . .l+ : x I .
00 an um 1m an) an am an an can I
“MMM)

Figure 15: Cluster Analysis for Macintosh Section

A characteristic that complicates collection of Macintosh users’ data is that users
tend to change computer stations quite often. This results from a fair amount of the
computers in the Macintosh section being out of service. Moreover, there are some users
who occupy more than one computer over a few hours, and may leave the station
unattended from time to time and eventually return to that computer again. These
particular characteristics contribute to the low overall service time of the Macintosh
section. Obviously, it is a pitfall from using the software which is not designed to trace
subjects continuously moving from station to station. The program counts discrete
service time from the time user begins using the computer until he finishes using that

station.

60

From the observation, fewer users enter the Macintosh section than the IBM
compatible section, and occasionally more than one user uses a single computer station at
one time. With a greater number of the computer stations provided in the Macintosh

section and a lower average service time, there is not a waiting line for the Macintosh

 

users at all.
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Figure 16: Cluster Analysis for Macintosh Section (Closed up)

When taking a close look at the grouping of the data set, we find that the data set
divided into two clusters (see Figure 16). 84.78% of the over all data sets have the service
time in the range of 1200 to 1800 seconds (20 to 30 minutes) and the interarrival time in
the range of 80 to 300 seconds (1.34 to 5 minutes). Within this cluster, the data groups
heavily around service time of 1500 to 1800 seconds (25 to 60 minutes) and the

interarrival time around 80 to 150 seconds (1.34 to 2.5 minutes).

61

In the smaller cluster, 14.21% of the total data sets group around the service time
of 2200 to 2800 seconds (36.67 to 46.67 minutes) and the interarrival time of 90 to 200
seconds (3 to 3.34 minutes). These data sets are from both weekdays and weekends in
the different periods of time. The data set in the range of high service time usually
derived from a week closer to the examination period and the period of time in the day
does not produce a significant contribution to the high service time.

When analyzing the proportion of the stratum of data collection within each
cluster, we found that different quarters of the semester and weekday and weekend period
contribute to the different workload characteristics of the computer lab users. However,
the different quarters of the semester do not have significant influence on the distribution
of the workload characteristic as much as the difference on the weekday and weekend.
The outlier data does not have any characteristics in common with one another. There is
no trend in the distribution of the outliers. In conclusion, the strata designed for data
collection planning are not correlated with the characteristic (interarrival time and service
time) of the data sets.

For a further examination of the distribution of the data from each stratum, we
calculate the percentage of the distribution of the data set from different strata within
each cluster to identify for a stronger conclusion (support of the conclusion). The
following tables and pie charts show the calculation of the distribution of the data-
collecting stratum per cluster and per overall data set. The tables and pie charts show that
the data from different strata scatter in both clusters and the outliers which means that the
characteristics of the data set within each stratum are not associated with the planning of

data collection as we assumed.

62

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65

Cluster 1-PC Section (n=36)

  
  
 

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'°”°" “we . 19%
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Pencd—dVlbekday
14%
Period-2 Vlbekday
26% ‘
Mod-3mm ?
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Figure 18: Distribution of Different Periods of Day in the Week within Cluster 1 of PC Section

Cluster 2-PC (n=5)

é Period-1 Weekday

1. 0%

‘ Period-l Weekend
20%

   
   

Period-4 Weekday
40% ‘

Period-2 Weekend Period-1 Weekend
40% 0%

Figure 19: Distribution of Different Periods of Day in the Week within Cluster 2 of PC Section

66

Cluster 1-MAC (n=30)
Period-1 Weekend
Period-2 Weekend 0%
20% Period-l Weekday

Period-l Weekend 2 3 “/-

Period-4 Weekday
. _

   
 

Pernod-2 Weekday i

Period-3 Weekday 23% 1

3l%

1

Figure 20: Distribution of Different Periods of Day in the Week within Cluster 1 of Macintosh

Section

Cluster 2-MAC (n=5)

Period-I Weekday
0%

Period~l Weekend
20% ’

   
   

Period-2 W eekend

09'.

Period-l Weekend Period-2 Weekday
0% 40%

Periodd Weekday Period-3 Weekday
/- 0%

Figure 21: Distribution of Different Periods of Day in the Week within Cluster 2 of Macintosh

Section

67

To this end, we can conclude that the stratum that we have planned prior to the
data collection is too fine, and the period of observation of each session may be too short.
The data sets from different time of the day do not have significant differences in their
characteristics. The cluster analysis reveals that the variation of data groupings depends
on the cycle of operation (users’ time line and work due to the university schedule) and
the different users’ pattern of behavior on weekday and weekend.

Though the service times of the Macintosh Section users should be viewed with
caution, due to their attributes in computer use and the instrument designed for data
collection, the service times derived from the same group of users are reliable. On the
contrary, the data collected from the IBM compatible stations is quite reliable due to the
rigid characteristics and constraints upon the relatively small number of computers in this
section. The service time and interarrival time derived from this group of users are more
reliable than that of the Macintosh users.

In conclusion, the design for data collection can be improved for the further
investigation by reducing the stratum of data collection period and focus on the different
workload characteristics of: 1) weekday versus weekend and 2) cycle of the semester.
The observation session in the facility that has 24-hour operation like this must have an
intensive preliminary study to cover the users that use the resource for longer than 2
hours to obtain a precise service time distribution. Instead of spending a small fraction of
the observation session to investigate the different users’ patterns of behavior in the
different times of the day, we should focus more on the longer observation session based
on the stratum suggested above. Moreover, the instrument used in recording data must
be able to trace the users who move around and change computers or occupy more than

one computer at a time.

68

Trend Analysis

Trend analysis is normally used to describe and predicting the underlying process
of the operation of the system of interest. In the 8-week duration of an intensive study of
the computer section, cyclical components of a time series are suitable to use in
predicting change or variation for the future trend due to its ability to capture the factor’ 5
influence on the pattern or cycle of the operation. In this study we hope to use the
cyclical component analysis to evaluate the short-term outlook of the pattern of the users
in the Union Building computer section and forecast the pattern of the users’ behavior in
the next 8 weeks in the third and forth quarters of the semester.

When proposing the study for Computer-Aided Capacity Planning for Facilities
Management, we also planned to use the same set of data in predicting the cyclical
component of the variable in this study as well. In the beginning of data collection for
sample of interarrival time and service time of the computer section, we assumed that the
data collected for the simulation should be pertinent to the trend analysis for the cyclical
component as well. Thus we spent 42 sessions of observation which produced 84 hours
of observation time. However, when the service times and interarrival times were
plotted, they did not lend themselves to fitting the periodic function. The plotting lines
have erratic movement of an irregular component and did not allow us to predict the
alternating pattern of expansion or contraction of the cycle. (See Figures 19-21 below).

Figure 19-21 illustrate the result of the interarrival time and service time over the
observation period of 8 weeks plotted versus time. Evidently, they cannot be used to
predict trends of the interested variables. However, we can see the fluctuation of the
(high) interarrival time in the beginning of the semester in the period after class

registration was over. (Please note that the higher interarrival time the longer the next

69

user arrival after the prior one). For the rest of the semester the interarrival time in this
time series plot does not lend itself to fit any assumptions we had prior to the data

collection.

 

2m

PClnterarrivalTlme
d N N w

 

 

 

 

 

77 105 133 161 189 217

Figure 22: Time Series Plot of PC Interarrival Time

 

 

 

 

 

 

 

77 105 133 161 189 217
Period

Figure 23: Time Series Plot of PC Service Time

70

In summary, data collection using a stratified sample mixed with simple random
sampling techniques is not appropriate to apply to the cyclical component trend analysis
in this experiment as designed. The reading of the data for trend analysis should be made
at equally time intervals, and it should be fine enough to be able to smooth the fluctuation
in a time series. To obtain a reliable and readable result for trend analysis, we should
collect the data for a longer period of time which would cover at least a whole cycle of

operation of the facility.

7l

Simulation results

In this section, simulation results and the field data are compared and analyzed to
complete the test of the Computer-Aided Capacity Planning Model for Facilities
Management in this study. However, the main purpose of this research is to test the
assumptions of applicability and suitability of this model when implemented in a real
setting used a shared space strategy. The advantages and pitfalls of the procedure and the
instruments designed for collecting the data in this study are determined when the
simulation results are correlated with the raw data.

The variables of interest in verification of simulation results are overall waiting
time and the resource utilization ratio. As described in the early chapters, the waiting
times are collected by using the customized Visual Basic program (Figure 8: GUI of
Queuing recording program on Visual Basic.) to collect the queue line and the length of
waiting time of the users in the line. These waiting times are from the IBM compatible
section alone since, from the observation, the users of the Macintosh section do not have

to wait in a queue line at all.

The comparison of resource utilization ratio for both IBM compatible section and the
Macintosh section.

Raw data for resource utilization ratio from each observation session is calculated
individually by using the formula described in chapter 4. Then the raw utilization ratio
from each session (historical outputs) is compared to the results from the simulation
(model outputs). In the following section, we will examine the simulation results (or the

model output) by the category variable of interest.

72

The tables showing the comparison of the historical outputs and the model outputs
of both resource utilization ratio (IBM Compatible section & Macintosh section) and the

waiting time (IBM Compatible section) are in the Appendix B. (See Table 7.)

Resource Utilization: Model Outputs

On the two systems studied, IBM compatible and Macintosh sections, each
system is independent and has different workload characteristics. The model designed
for this study tends to match with the characteristics of the IBM compatible section rather
than the Macintosh section.

The following charts show the difference of the historical outputs (resource
utilization ratio) and the model outputs from each observation session. From the chart,
we can see that the model outputs of resource utilization for the IBM compatible section
is more precise than those of the Macintosh section. The results of the paired t test of no
mean difference support the assumptions that we have based on the experience from the

field observation.

73

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75

The results of the t test at 99 percent Confidence Interval of null hypothesis of no
mean difference for both IBM Compatible and Macintosh’s utilization ratio are shown
below.

to = Sample mean difference
,ud = True mean difference
54 = Deviation from mean

K = number of input data sets

 

Ho zud=0

H1 zud¢0

 

 

 

THE IBM COMPATIBLE SECTION: RESOURCE UTILIZATION RATIO
At 99 percent Confidence Interval: toos, 40 = 2.70

3: 1.040688

yd = True mean difference (assume = 0)

 

Sd=2.496101
K =41

t _ d-ud _ 1.40688

0 Ssh/K 2.496101 /J4—1
to=2.669625

76

Since I tol = 2.669625 < tan,“ = 2.70, the null hypothesis of Ho of no mean
difference can not be rejected and conclude that no inconsistency is detected between
system response and model prediction in terms of mean production level. This means

that the model for predicting IBM Compatible section resource utilization works reliably.

THE MACINTOSH SECTION: RESOURCE UTILIZATION RATIO
At 99 percent Confidence Interval: tacos, 40 = 2.70

d = 22.79002
,ud = True mean difference (assume = 0)
S; = 26.82225

K=41

_ 217—pd = 22.79002
5. NE 26.82225 NET

 

to

to = 5.440533

Since I tol = 5.440533> ta/2,K-l= 2.70, then we reject Ho of no mean difference and
conclude test is that the model is inadequate. Unlike the IBM model, the model for
predicting the Macintosh section’s resource utilization ratio does not work reliably.

As explained in the cluster analysis section, the IBM compatible users have more
static work patterns which permit the observers to collect a reliable users’ service time on
the computer station. On the contrary, the Macintosh users tend to move around and
have irregular work patterns that do not conform with the devices designed for collecting

the service time. Therefore the Macintosh users’ service time derived from observation

77

has a tendency to be lower than their actual service time. This factor contributes to the
mean difference between the historical output (derived from the observation) and the
model output.

Another input variable studied is the interarrival time. The interarrival time
collected for both types of computers are reliable since the observers are able to monitor
and record all of the user arrivals of both sections with the provided data collecting
device.

With a reliable interarrival time and the unreliable service time of the Macintosh
section, we found that the model is not able to predict the valid utilization ratio for this
system. The historical outputs of each input data set that derived from the observation
are calculated based on the following method:

Ui = Utilization ratio at interval i
At,- = length of time interval i
T = Total observation time

n

Avg. Utilization Ratio Historical Outputs: 2| (U: x At.)
T

 

The interval i is determined by a change in the system when a user enters the
system and begins using a computer and/or user finishes using the computer. The total
observation time (T) is the summation of the length of time interval at each constant
utilization ratio of the system.

The model output of the Macintosh utilization ratio based on the given input

number of interarrival time and the service time of the same observation period of those

78

specific historical outputs (raw data of interarrival time and service time) used in
comparison.

Since the Macintosh users have the irregular work patterns such as: 1) an
individual occupied more than one computer, 2) an individual occupies the computer but
he may leave the lab and return to that computer again, 3) an individual moves from the
station to station, and 4) an individual occupies the computer longer than the observation
period. These factors contribute a higher resource utilization ratio of the actual system
than the model output using the same input data (service time and interarrival time).

The work patterns described above have induced a service time and resource
utilization ratio to be shorter than the actual value.

The effect of this work pattern can be seen on the different case in a simple
system of two computers and two different pattern of users’ behavior. First example, the
user enters the system and uses the first computer for 5 minutes, and then moves to the
second computer and spends another 5 minutes on another station. When using the data
collecting device designed for this research, the program will record that there are two of
5 minute-time interval during which the computers are occupied. Thus, the average of
service time for this system is equal to 5 minutes. In comparison, the same user enter the
system of two computer and uses only one computer for 10 minutes and leaves the
system when he finishes. Therefore the average service time of the system is equal to 10
minutes even though a total service time of the first case and the second case are the
same.

The similar problem affects the inaccuracy of the estimation of utilization ratio
model outputs. When we observed the waiting time fiom the system when the user

moved from one station to another station such as the example in the first case, the

79

average service time is shorter than the actual service time (total time user spends in the
system). Since the model output (result) is based on the given (unreliable) service time
and interarrival time, the result generated by the model should be different (shorter) than
the system utilization historical outputs. Figure 28 illustrates the different utilization
ratio of the actual system utilization ratio derived from the observation and the utilization

ratio model outputs.

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The actual system utilization The model outputs of system

utilization
Figure 26: The comparison of Actual Service time and the Service time used as inputs for the model

The gray areas in each figure indicates utilization ratio of the system at each
interval. These two systems have the same value of the average service time (5 minutes).
The average utilization ratio of the actual system is two times higher than the model
output because users move from one station to another. In the simulation model, we are
able to input the historical service time, but not the pattern of computer swapping.
Therefore the model randomly generates a user who uses the system with an average
service time of 5 minutes and then leaves the system when the user finishes using the first

station that he occupies.

80

To correct this deficiency, the data-collecting device should be able to trace the
user pattern of behavior and allow the researcher to identify the total service time of each
user instead of the fraction of the service time. Then we should be able to obtain the
correct service time and the resource utilization ratio to use as the historical outputs and

the valid input for the simulation model.

Waiting Time: Model Outputs

In the verification of waiting time, we are able to perform the paired t test only for
the historical output and the model outputs of the IBM Compatible section. For the
Macintosh section which has more computer stations available and less users arrival,
there is no waiting line for the Macintosh users at all.

In this study, we collect the waiting time of the users in the queue line in order to
represent the waiting time historical output to compare with the model outputs.
However, we do not focus in the study on the distribution of the waiting time historical
outputs. Thus, we have set up the criteria for leaving probability for the simulation
model based on the experience from the field observation. The criteria are as follow:

1. A user is not considered waiting if he enters a computer station within 30 seconds
after he arrives.

2. A user may leave immediately if there are at least 10 users ahead of him in the queue.
The probability of leaving is 80%

3. A user in the queue may leave if there are at least 5 users ahead of him in the waiting
line and he has waited for at least 15 minutes. The probability of leaving depends on

his position in the waiting line, but will not exceed 75%.

81

The following chart and paired t test results show the mean difference of waiting
time historical outputs and model outputs. The table of the mean difference of waiting

time historical outputs and model outputs are shown in the Appendix. (See: Appendix B).

82

 

 

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Waiting Time (IBM Compatible Section)

Comparison of Historical Outputs and Model Outputs:

Figure 27

The waiting time model outputs derived from using the interanival time and
service time inputs correlate with the leave criteria that we have set up. The paired t test

for mean difference of waiting time historical outputs and model out puts are as follow:

THE IBM COMPATIBLE SECTION: WAITING TIME
At 99 percent Confidence Interval: tags, 40 = 2.70

2: -3192939

pd = True mean difference (assume = 0)

 

Sd=50.78866
K=41

, =_d_—_tg_ _ -31.92939

0 SSA/E 50.78866 /~/4_1
to = -4.025462

Since I tol = 4.025462> tat/2,105 2.70, then we reject Ho of no mean difference and
conclude that the model is inadequate. This paired t-test shows that the model and
leaving criteria used for the IBM compatible section’s waiting time does not work.

The inadequacy of the waiting time model outputs may derive from several
factors. First, it may be due to insufficient study of the waiting queue. Sometimes a
group of users will wait in a queue line to use one computer, when it comes to their turn,
the whole group of users will leave a waiting line at the same time to the available

computer station. In this case, the record of the average waiting time from the

84

observation is higher than the actual waiting time that the users wait in the queue line.
Secondly, we do not know the actual distribution of users criteria, therefore the leaving
criteria used in the simulation model are merely the assumptions. The probability of the
leaving used in the simulation model may be higher or lower than the actual distribution
of the leaving pattern of the users in the waiting line.

Waiting time is the factor that has the most effect on the users’ satisfaction. To
achieve reliable waiting time model outputs, we have to perform an extensive study of
the waiting queue and behavior of the users in the line. The results from the study of the
distribution of leave behavior can be used as a valid leave criteria for the simulation
model. Another aspect from the user viewpoint is that the criteria to estimate users’
satisfaction should be the average waiting time of the users in the waiting line. Even
though it is common to use the overall waiting time (average waiting time of all users in
the system) to evaluate a system capacity and users satisfaction. The average waiting time
of the users in the waiting line may represent the fluctuation of the waiting time and the

users who may be effected by the congestion of the system.

Application

Collecting data for the Computer-Aided Capacity Planning Model reveals
different aspects of the problem of modeling the Union building computer lab study site.
Data collection also allows the evaluator to understand experience of the user within the
facility instead of looking at the facility operation from an ivory tower. However, the
goal of each facility is varied and depends on the policy of the organization. In the
university computer lab, the administrative staff may desire to focus on maximizing the

resource utilization ratio rather than minimizing the users’ waiting time. On the contrary,

85

the policy of the business organization, which the users’ satisfaction means maximizing
profits, the facility manager may have to maintain a balance of resource utilization and
users’ waiting time.

Data collected for constructing the Capacity Planning Model can be used to
determine system operation in terms of the relationship between resource utilization ratio
and users’ waiting time. When plotting the actual resource utilization ratio against the
users’ waiting time, the distribution of the data sets from the observation may give a clear
picture of the true characteristic of the system. A scatter plot chart using the coordination
of the actual resource utilization ratio and the users’ waiting time of each data set from
the IBM Compatible section are used to evaluate the overall state of the resource
utilization ratio and the users’ waiting time of this section.

Figure 28 shows the relationship of the resource utilization ratio and overall users’
waiting time of the data sets. The area of the scatter plot is divided into quarters based on
the theoretical model (see figure 5). The following table shows the distribution of the

data sets in each quarter.

 

. ' Resource‘utilization ratio Versus Overallaverage users’ waiting time

A...

 

 

 

 

 

 

 

Quarters Percentage
High waiting time, high resource utilization ratio 12.19%
High waiting time, low resource utilization ratio 0.0%
Low waiting time, low resource utilization ratio 19.51%
Low waiting time, high resource utilization ratio 68.29%

 

Table 5: Distribution of the data sets in the scatter plot using coordination of the actual system’s

resource utilization ratio and overall users’ waiting time.

86

 

 

 

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The analysis of the relationship of the actual resource utilization ratio and
overall users’ waiting time in the IBM Compatible section indicates that the majority of
the data sets (68.29%) fall in the “low waiting time, high resource utilization ratio”
quarter. None of the data set falls in the area of “high waiting time, low resource
utilization ratio”. A fair amount of data sets (19.51%) fall in the “low waiting time, low
resource utilization ratio” area. And the smallest number data sets (12.19%) fall in the
area of “high waiting time, high resource utilization ratio.”

The analysis of the actual system’s resource utilization ratio and waiting time is
very helpful when there is a need to determine the direction of system capacity
improvement. For instance, after reviewing the distribution of the data sets in the scatter
plot, the facility manager may want to increase the resource utilization ratio of the
system, and decide that the number of data sets falling into the area of high resource
utilization ratio, low waiting, time should be increased. The Computer-aided capacity-
planing model can be used to explore potential alternatives towards achieving this goal.
There are several ways to optimize the use of individual computer stations in the IBM
compatible section. These alternatives include; 1) increase the number of stations in the
section, 2) upgrade the computers, 3) limit computer usage time, etc.

In the following section, we use the validated model of the IBM Compatible
section to generate forecasts of resource utilization in different scenarios. The first
scenario is when we apply various numbers of computer stations in the IBM Compatible
section. In the second scenario we reduce service time assuming that there is a limitation
on computer usage time or the computer is upgraded and it works faster and the users can
accomplish their work in shorter time. The last scenario models the different interarrival

times versus the resource utilization ratio and users’ waiting time. This scenario can be

88

used when there is an increasing or reducing numbers of users who come to the use the
IBM Compatible computers at this computer lab.

Figure 29 shows the resource utilization ratio forecasts generated by applying the
different nmnbers of computers in the IBM Compatible section. The fixed values used in
this scenario are average of service time and average of interarrival time from a large
group of data sets (Cluster A) in the scatter plot. We assume that these values represent
normal or everyday situation of the IBM Compatible section in the computer lab.

Figure 30 shows resource utilization ratios resulting from forecast generated by
varying service times in the IBM Compatible section. The fixed values used in this
scenario are the number of computer stations (30 stations) the average interarrival time
(120 seconds) from the large group of data (Cluster A) in the cluster analysis for IBM
Compatible section.

Figure 31 shows resource utilization and users’ waiting time resulting from
forecast generated by varying average interarrival times in the IBM Compatible section.
The fixed values used in this scenario are number of the computer stations (30 stations)
and the average service time (2100 seconds) from the large group of data (Cluster A) in
the cluster analysis for IBM Compatible section.

The scenario testing above demonstrates the use of the Computer-Aided Capacity
Planing model to generate different resource utilization ratios in different scenarios.
However, to use the model to assist in decision making for capacity planing in a facility
would be complete when the model can generate an accurate waiting time so that the
facility manager can be able to balance the users’ demand and the organization goal.
Subsequent implementation of scatter plot, using model outputs’ resource utilization and

waiting times may be used to evaluate the effectiveness of the model.

89

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Summary

In conclusion, the paired t-test of no mean difference of the historical outputs and
model outputs reveals that the model for predicting the resource utilization ratio for the
IBM compatible section works and produce a reliable outputs. The model for predicting
the Macintosh section’ resource utilization ratio and the model for predicting the IBM
compatible waiting time do not work and generate inaccurate results. On the other hand,
the test proved that the model worked once and did not work twice. The causes for the
shortcoming of these models are from different factors including the planning of data
collection, inappropriate devices and misinterpretation of the data.

As Shannon (1975) notes that there is a constant interplay between the
construction of the model and the collection of the needed input data. Planning of data
collection is considered a crucial part of the simulation project in this study. The data
collection of this research begins together with the early stage of the model building. The
assumptions for the data collecting frequency are based on the facility cycle of operation.
The cluster analysis of the characteristic of the interarrival time and the service time
shows insignificant difference of the workload characteristic between different times of a
day. Hence, the frequency of the data collection should be reduced and observation
session should be expanded. Longer observation helps the modeler to obtain a precise
service time of any users who occupy the computer at a greater length of time.

A lesson learned from the data collection planning is the preliminary data
collection should be implemented before outlining the actual data collection schedule.
The preliminary data collection will provide the information necessary to construct a data

collection framework. Since the data collection stage consumes a large portion of time, it

93

is important to invest this great length of time to collect sufficient data that represents
the true characteristic of the system.

The customized Visual Basic program, which is the data collecting device used in
this study, produces reliable information and is able to record the correct the data
collection of the IBM Compatible section. For the case of Macintosh section, the
program is not able to trace the total service time of the users who move around and the
users who occupy multiple computer stations. Hence the service time of the Macintosh
users which is derived fiom this method are neither reliable nor valid. The waiting time
collecting program also has the same deficiency as well. The design deficiencies of the
program along with human error of the observers contribute to the inaccuracy of the data
interpretation. Some other instrument such as a time lapse video or a computer based
users’ service log can be used as the alternative data-collecting tools.

At the early stage of data collection planning for simulation model, we hope to
use the same sets of data to generate a trend of the workload characteristic of this facility,
and use this trend to help predicting the anticipate system behavior. However, the data-
collecting schedule is designed to be randomly distributed to be able to cover different
workload characteristics from the different period of time within the cycle of operation.
The randomly distributed observation periods do not have equal space between each
other therefore the results of time series plot of the data are irregular and can not be
described by a periodic mathematical function.

Ideally, data collection for short-term trend forecasting requires a high frequency
and regular data collection at schedule. It is advisable to perform extensive study for
trend analysis of the workload characteristic to obtain a pertinent reading, and then used

to construct time series components.

94

When the model works, it can be used as a flexible tool in decision making to
forecast resource needs. From the example of the IBM compatible model, we are able to
adjust the number of computer stations provided for the users to forecast the resource
utilization ratio. The advantage of the simulation model is that it can be used again and
again, without spending time collecting the data all over again, whenever the
administrative staff of the facility wants to readjust the resource allocation to meet the

users’ demand or meet the criteria of the organization

95

CHAPTER 5
CONCLUSION

Research Contribution

Continuous competitive pressures drive most contemporary businesses to improve
performance. To meet this demand, facility management professionals continuously
devise and challenge methods to measure and improve facility performance. The shared
space facility is a common and potentially winning strategy. However, the complex
multi-factorial dynamics of shared space facilities complicate efforts to describe and
analyze these systems. Traditional opinion models used to evaluate and predict system
performance prove particularly inadequate in describing these systems. The major
weakness of this approach is that important decisions are based upon insufficient or
subjective observations. Decisions based on beliefs and biases have uncertain accuracy
and no precision. With the cost-driven high stakes decisions of today’s facility operation,
the potential analytical and predictive superiority of computer-aided simulation models
justifies their development. The objectively quantifiable nature of computer-aided
simulation models permits the potential to describe and forecast shared space facilities
with accuracy and precision.

The computer-aided capacity planning model for facility management can be
broken down into three phases. The first phase is the initial statement of the problem or
problem formulation. Often, the initial objective has to be reset and fine-tuned to

correspond with the nature of the system being studied. Preliminary observations help

96

. I:

 

recalibrate and clarify the orientation of the project. The second phase includes model
building, data collection, coding, and statistical analysis. This process resulted in the
selection of a discrete-event simulation model described as a statistical experiment by
Banks and Carson II (1984). The last phase is comprised of verification and validation of
the model using a statistical inference from the results of the simulation tested against the
observed data.

Study of the computer-aided capacity planning model reveals the benefits and
pitfalls using this method to describe and predict the dynamics of the space sharing
facility. The collection of data by field observations was an essential but exhaustingly
laborious component of this investigation. From the study log I calculated that data
collection and descriptive analysis consumed approximately 70% of the time spent on
this investigation. Planning data collection, fitting the model, and validation expended
the remaining 30% the total investigation time.

In perspective, this investigation of a computer-aided capacity planning model for
the shared space facility was applied to two separate systems(the IBM compatible section
and the Macintosh section). For the Macintosh section, the erroneous results and the
misinterpretation of the data arise from a discordance of the system behavior and the
instrumentation along with the design for data collection. By the same token, the problem
due to the instrmnentation occurs with the waiting time data collection for the IBM
compatible section.

Operating cycles of the facility is another important factor to consider in
implement a simulation model for capacity planing. It is advisable that the preliminary
data collection should be conducted in the early stage of the data collection planing to

determine the appropriate data collecting schedule, device and length of each observation

97

hi

 

period. The lesson learned from this study is that the device used in recording the data
should conform to the pattern of user’ behavior of the system. Otherwise it would lead to
the misinterpretation of the variables derived from the process. The preliminary study of
the workload characteristics will prepare the modeler for an appropriate course of action
required for the design of the simulation model. Then a sufficient data collection design
for the simulation project should cover a whole operation cycle to be able to use as the
inputs to generate a valid model projection. However, this great length of data collection
period can be laborious and costly.

In the real world, time and capital investment is at the core of the facility
operation, the decision to implement the simulation project to help forecast the capacity
planning should be taken into consideration. In a smaller scale facility or a small project,
the return of time and capital investment to conduct the data collection and perform the
data analysis may be unsatisfactory. The first alternative for this problem can be
overcome by using an electronic or digital data-collecting device that is able to trace the
interarrival time and the total service time of the user in the system. This method will
help reduce the cost associated with contracting the observer to collect the data for a long
duration of time. The second alternative is to construct the model based on a record
obtained from the facility that has a closed system operation and distribution of a
workload characteristic.

When initiating the simulation project, the collaboration of the modeler and the
in-house facility manager is very important. Some organizations may have significant
detail on some aspects of their operations, and yet have some sketchy information in

other areas. These sorts of information can be very useful for the modeler to achieve a

98

more accurate detail of data to create a simulation model that represents the true system
characteristic.

To assess the benefit from a simulation investment, the simulation impact can be
categorized as Manpower and Operation (Harrel, 1996). However, productivity and
quality improvement can be achieved through the implementation of the simulation. The
organization should evaluate the benefit and financial costs associated with the project
including: 1) model building or purchasing the software, 2) outside consulting, 3)
over/under capacity, 4) carrying cost and wait time, and 5) training.

9 In summary, the computer-aided capacity planing is an appropriate tool to use in
forecasting the resource requirement in shared space for facility management incorporate
with an opinion model. The successful implementation depends on how well the phases
in the simulation has been developed and performed. It is also contingent upon how
thoroughly the system analyst has involved the facility management profession of that
system during the entire project. The system analyst and the facility manager should
exchange the knowledge of the nature of the workload characteristic, the model-building
process and the interpretation of inputs and outputs data. Therefore the likelihood of a

vigorous implementation is enhanced.

Further Investigation

A further study of computer-aided capacity planning model would be more
accurate when being narrowed down to study a single type of system. The extensive
study of a single system would enable us to monitor the distribution and of the interested
variables in the system, thus it would lead to a fully developed model. Furthermore, the
preliminary data collection is recommended to perform in the early stage of model

99

 

development. As noted earlier, the preliminary data collection will help determines the
appropriate model for planing of data collection.

Further research is needed to study the underlying characteristic of the users in the
queue line. The understanding of characteristic of the users in waiting line including
leave characteristic will create a model that represent a system true characteristic.
Specifically, there is a need for studies aimed at determining the actual distribution of the
leave characteristic to be used as the leave criteria for the simulation model.

Although this study was performed on the computer lab of an educational setting,
the same application can be replicated and tested in different types of setting such as
shared office in a corporate facility or shared resource in the department store. The
replication of this method will help investigate the applicability of this method in diverse
environment.

Considering the purpose of the simulation used in this study, the two important
factors generated from the computer-aided capacity planning model are resource
utilization ratio and waiting time. In turn the administrative staff and facility manager
can use these two factors to evaluate the performance critique the policy of this facility.
Despite the resource utilization ratio, the user’s waiting time is used to indicate user’ 3
satisfaction, and is very subjective in nature. A further study using the combination of
qualitative methods such as observation of behavior trace using time lapse video to study
the behavior and the response of the users in different system condition should be taken
into consideration. Relative to the unobtrusive observation of the behavior trace, user’s
inputs from interview or questionnaire are the best indication of a users’ satisfaction

toward the system operation.

100

APPENDICES

APPENDIX A

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Observation IBM Compatible Difference
Session Utilization Ratio

Historical Outputs Model Outputs Di

(Second) (Second) (Second)
1211116 91.215 91.87 -0.655
1211739 82.534 75.18 0.14
1212116 90.728 90.87 -2.447
1240824 47.718 46.74 0.978
1251017 30.234 26.24 3.994
1251739 5.8472 6.1 0.2528
1261433 90.846 82.65 5.923
1270830 61.8 61.2 -2.59
1271555 29.716 25.23 4.486
1291517 81.183 78.65 2.533
1301307 87.207 84.89 2.317
1301437 90.356 88.12 2.236
1312139 39.9 35.54 0.67
2021040 40.493 34.87 4.623
2021415 83.445 72.75 2.695
2021529 85.974 76.57 3.404
2021832 87.355 79.54 -1 .185
2031307 88.353 84.85 -4.309
2041744 83.621 80.89 2.731
2051239 82.828 80.1 2.728
2051639 72.402 70.3 2.102
2052158 94.974 86.87 4.003
2070842 34.096 31.17 -0.975
2071628 77.928 72.6 ~0.672
2081549 53.431 50.17 3.261
2111311 98.666 90.35 0.316
2111432 87.518 84.86 2.658
2121529 75.577 73.97 1.607
2151548 69.345 66.39 2.955
2161110 46.184 42.16 -l.537
2172309 90.641 79.73 0.91 1
2181638 90.059 85.06 3.429
2191154 92.798 88.86 1.65
2200836 66.113 63.96 4.619
2210848 60.265 58.82 1.445
2242244 95.031 82.86 -0.829
2250916 70.518 68.51 2.008
2281348 56.36 53.21 -1.97
9241107 99.368 91.16 0208
9260927 35.858 33.95 .3337
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Table 6: Comparison of Historical Outputs and Model Outputs: Utilization Ratio (IBM compatible)

104

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Table 7: Comparison of Historical Outputs and Model Outputs: Resource utilization Ratio

(Macintosh)

105

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APPENDIX C

Appendix c

Comparison of system and Model outputs measures when using identical historical

 

 

outputs.
System Model Observed Squared Deviation
Input Data Output, Output. Drfi'erence, from Mean,
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107

APPENDIX D

Appendix D

PERCENTAGE POINTS OF THE STUDENTS I
DISTRIBUTION WITH 6 DEGREES Of FREEDOM

 

 

 

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1 63.66 31.82 12.71 6.31 3.08
2 9.92 6.92 4.30 2.92 1.89
3 5.84 4.54 3.18 2.35 1.64
4 4.60 3.75 2.78 2.13 1.53
5 4.03 3.36 2.57 2.02 1.48
6 3.71 3.14 2.45 1.94 1.44
7 3.50 3.00 2.36 I.” 1.42
8 3.36 2.90 2.31 1.86 1.40
9 3.25 2.82 2.26 1.83 1.38

10 3.17 2.76 2.23 1.81 1.37

11 3.11 2.72 2.20 1.80 1.36

12 3.06 2.68 2.18 1.78 1.36

13 3.01 2.65 2.16 1.77 1.35

14 2.98 2.62 2.14 1.76 1.34

15 2.95 2.60 2.13 1.75 1.34

16 2.92 2.58 2.12 1.75 1.34

17 2.90 2.57 2.1 l 1.74 1.33

18 2.88 2.55 2.10 1.73 1.33

19 2.86 2.54 2.09 1.73 1.33

20 2.84 2.53 2.09 1.72 1.32

21 2.83 2.52 2.08 1.72 1.32

22 2.82 2.51 2.07 1.72 1.32

23 2.81 2.50 2.07 1.71 1.32

24 2.80 2.49 2.06 1.71 1.32

25 2.79 248 2.06 1.71 1.32

26 2.78 2.48 2.“ 1.71 1.32

27 2.77 2.47 2.05 1.70 1.31

28 2.76 2.47 2.05 1 .70 1 .31

29 2.76 2.46 2.04 1 .70 1 .31

30 2.75 2.46 2.04 1.70 1.31

40 2.70 2.42 2.02 1.68 1.30

60 2.66 2.39 2.“) 1.67 1.30

120 2.62 2.36 1 .98 1.66 1.29

on 2.58 2.33 1.96 1.645 1 .28

 

 

 

Sauce: Robert E. Shannon. System sanitation: 770: Art and
Science, (1.”) 1975, p. 1175. Reprinted by permission of Prentice-Hail.
1nc.. Engicwood Gills. NJ.

Figure 36: Percentage of the Students t Distribution
With 0 Degree of Freedom
(Source: Bank & Carson II, 1984)

108

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