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UNIVERSITI TEKNIKAL MALAYSIA MELAKA
BORANG PENGESAHAN STATUS LAPORAN PROJEK SARJANA MUDA
TAJUK: An Assessment of Queuing System at Polyclinic community at Ayer Keroh
SESI PENGAJIAN: 20010/11 Semester 2 Saya CHAN KIEN HOW mengaku membenarkan Laporan PSM ini disimpan di Perpustakaan Universiti Teknikal Malaysia Melaka (UTeM) dengan syarat-syarat kegunaan seperti berikut:
1. Laporan PSM adalah hak milik Universiti Teknikal Malaysia Melaka dan penulis. 2. Perpustakaan Universiti Teknikal Malaysia Melaka dibenarkan membuat salinan
untuk tujuan pengajian sahaja dengan izin penulis. 3. Perpustakaan dibenarkan membuat salinan laporan PSM ini sebagai bahan
pertukaran antara institusi pengajian tinggi.
4. **Sila tandakan (√)
SULIT
TERHAD
TIDAK TERHAD
(Mengandungi maklumat yang berdarjah keselamatan atau kepentingan Malaysia yang termaktub di dalam
AKTA RAHSIA RASMI 1972)
(Mengandungi maklumat TERHAD yang telah ditentukan
oleh organisasi/badan di mana penyelidikan dijalankan)
Alamat Tetap:
1913 JALAN SK 13/5
43300 SERI KEMBANGAN
SELANGOR DARUL EHSAN
Tarikh: _________________________
Disahkan oleh:
PENYELIA PSM
Tarikh: _______________________
** Jika Laporan PSM ini SULIT atau TERHAD, sila lampirkan surat daripada pihak berkuasa/organisasi berkenaan dengan menyatakan sekali sebab dan tempoh laporan PSM ini perlu dikelaskan sebagai
SULIT atau TERHAD.
18 Mei 2011
UNIVERSITI TEKNIKAL MALAYSIA MELAKA
AN ASSESMENT OF QUEUING SYSTEM AT POLYCLINIC
COMMUNITY AYER KEROH
This report submitted in accordance with requirement of the Universiti Teknikal
Malaysia Melaka (UTeM) for the Bachelor Degree of Manufacturing Engineering
(Manufacturing Management)
by
CHAN KIEN HOW
B050710178
FACULTY OF MANUFACTURING ENGINEERING
2011
i
DECLARATION
I hereby declare that this report entitled “An Assessment of Queue System at
Polyclinic Community Ayer Keroh” is the result of my own research except as cited
in the references.
Signature :
Author’s Name : CHAN KIEN HOW
Date : 14d APRIL 2011
ii
APPROVAL
This report is submitted to the Faculty of Manufacturing Engineering of UTeM as a
partial fulfillment of the requirements for the degree of Bachelor of Manufacturing
Engineering (Manufacturing Management). The members of the supervisory
committee are as follow:
………………………………………
iii
ABSTRACT
Queuing is daily practiced in our life. There is a lot of knowledge is inherent in the
process of constructing a queue manner which capable to meet the incoming
customer and yet without losing the server competiveness in the system. In this final
year project, a queue system in Polyclinic is chosen as the assessment place to
identify current service level system is it capable to meet the increasing patient’s
capacity. The aim of this study is to adapt the Queue model and simulation method
on the Polyclinic Ayer Keroh system flow to study the current service time provided
by polyclinic is it meets the current arrival rate of the patient to the system. The data
of the arrival rate and service time is collected will be analyzed and further translated
into histogram and poses Goodness of Fit-Test by using Minitab Statistical Software
for family distribution identification. With the analyzed result family distribution, it
will be translated in the queuing theory and simulation. The relation of the system
like time-average number in system (L), average time spent in system per customer
(w), and server utilization (ρ) could be revealed. From the generated results and
discussion of the system’s relation is compared with the result of the survey which is
reflecting and indicating the patient desired service level provision by the polyclinic.
Verification and validation of the model is needed to be done prior the model is
compared with the standard. This can be concluded that the flow in system is stable
and upgradeable. The implementation of the queue model and simulation is justified
in this assessment. The potential improvement options are also suggested in order to
further improve the quality of the service provided to the patient.
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ABSTRAK
Beratur merupakan satu fenomena selalu berlaku dalam kehidupan seharian manusia.
Dalam process penjanaan satu antrian bukan sahaja yang mampu menambung
bilangan pesakit yang kian meningkat tetapi daya saing pelayan di system juga perlu
dikekalkan dan diasahkan. Dalam Projeck ini, sistem antrian di Poliklinik dipilih
sebagai tempat penilaian untuk mengenalpasti sistem perkhidmatan sekarang. Tujuan
kajian ini adalah untuk menyesuaikan model Antrian dan kaedah simulasi pada aliran
sistem Poliklinik Ayer Keroh untuk mengenalpasti masa perkhidmatan kini
disediakan oleh poliklinik mampu memenuhi tahap kedatangan pesakit masuk sistem.
Masa kedatangan dan perkhidmatan yang dikumpul akan dianalisis selanjutnya dan
diterjemahkan ke dalam histogram dan menjalani Goodness of Fit-Test dengan
menggunakan software statistik Minitab untuk pengenalan keluarga pengedaran.
Dengan hasil analisis pengedaran keluarga, ia akan diterjemahkan dalam teori antrian
dan simulasi. Hubungan sistem seperti jumlah rata-rata waktu dalam sistem (L),
rata-rata waktu yang dihabiskan pada sistem pada pelanggan (w), dan penggunaan
pelayan (ρ) dapat diungkapkan dalam perbincangan. Dari hasil perbincangan,
hubungan sistem akan berbanding dengan hasil tinjauan yang mencerminkan dan
menunjukkan tahap perkhidmatan yang diingini oleh pesakit terhadap poliklinik.
Pengesahan dan validasi model perlu dilakukan sebelum model ini berbanding
dengan piawai. Oleh itu, aliran dalam sistem boleh disimpulkan bahawa yang stabil.
Penerapan model antrian dan simulasi dalam penilaian ini adalah dibenarkan. Cara
dalam pembaikan sistem juga disarankan untuk meningkatkan kualiti perkhidmatan.
v
ACKNOWLEDGEMENTS
I would like to extend my sincere thanks to my supervisor, Profesor Madya Dr Adi
Saptari for his invaluable guidance and assistance throughout this project. I
appreciate the knowledge and advise that was gained from my supervisor. He had
given me valuable cooperation, assistance, support and suggestion during my project
activities.
I deeply appreciate the Polyclinic Community Ayer Keroh for providing the
opportunity to perform my research study in their treatment room area. I would like
to express my gratitude to all of the patients in the polyclinic for giving full support
when I was carried out the survey. Special thanks to Miss Gan, Senior of UTeM
Thanks for her kindness and sincerity to help me and also their willingness to share
their ideas and opinions in model developing.
Last but not least, I would like to thank my family and friends, who have supported
me and motivated me to lead me from beginning of this project to the end of report
submission.
vi
TABLE OF CONTENT
Declaration i
Approval ii
Abstract iii
Abstrak iv
Acknowledgement v
Table of Content vi
List of Figures x
List of Table xi
List of Abbreviations, Symbols, Nomenclatures xii
CHAPTER 1.INTRODUCTION 1
1.1 Background 1
1.2 Simulation 2
1.3 Polyclinic Community Ayer Keroh 3
1.4 Problem Statement 4
1.5 Objectives 4
1.6 Scope 4
1.7 Organization of Report 5
CHAPTER 2 LITERATURE REWIEW 7
2.1 Introduction 7
2.2 History of Queuing Theory 9
2.3 Queue Problem 10
2.3.1 Reneging 10
vii
2.3.2 Variable Arrival Rate 11
2.3.3 Blocking 12
2.3.4 System Design 13
2.3.5 Bottleneck 13
2.4 Characteristic of Queuing System 13
2.5 Queuing Notation 16
2.6 Steady State Behavior of Infinite-Population Markovian Model 17
2.6.1 Single-Server Queues with Poison Arrivals & unlimited Capacity 18
2.6.2 Multi Server Queue 19
2.7 Simulation 20
2.7.1 The Power of Simulation 21
2.7.2 System 22
2.7.3 Model 23
2.7.4 Development of Simulation Software 25
2.8 Publication Queuing System in Service Industry 27
CHAPTER 3 METHODOLOGY 30
3.1 Introduction 30
3.2 Methodology Overview 32
3.2.1 Design Survey 32
3.2.2 Analysis of Distribution 32
3.2.3 Model Conceptualization 35
3.2.4 Model Translation 37
3.2.5 Verification and Validation 38
3.3 Results and Discussion 39
3.4 Conclusion and Recommendation of Future Work 39
viii
CHAPTER 4: DATA COLLECTION AND MODEL DEVELOPMENT 40
4.1 Data Collection 40
4.1.1 Data Collection from Design Survey 40
4.1.2 Patient Arrival Time, Service Time Begin and End 42
4.2 Analysis of Distribution 43
4.2.1 Selecting Distribution Family 45
4.2.2 Morning Session 46
4.2.3 Afternoon Session 48
4.3 Model Conceptualization 49
4.3.1 Experiments Factors and Responses 49
4.3.2 Model Scope 50
4.3.3 Model Level of Detail 51
4.3.4 Assumption 51
4.3.5 Simplification 51
4.4 Model Translation 51
4.4.1 Queue Model (Queuing Theory) 51
4.4.1 Morning Session 52
4.4.2 Afternoon Session 52
4.4.2 Simulation model 53
4.5 Verification and Validation 55
4.5.1 Verification 55
4.5.2 Validation 56
CHAPTER 5: REULTS AND DISCUSSION 60
5.1 Results 60
5.1.1 Results of the collected data 61
5.1.2 Results of the Queuing Model 61
ix
5.1.3 Results of the Simulated Model 62
5.2 Discussion 62
5.2.1 Discussion on the Collected Data 62
5.2.2 Discussion on the Queue Model 63
5.2.3 Discussion on the Simulation Model 63
5.2.4 Discussion of the Patient Satisfactory Level 63
5.2.5 Ways of Improvement in Polyclinic Performance 64
CHAPTER 6: CONCLUSION AND RECOMMENDATION 65
References 67
Appendix-1 FYP 1 Gantt Chart
Appendix-2 FYP 2 Gantt Chart
Appendix-3 Questionnaire
Appendix-4 Collected Data Record
x
LIST OF FIGURES
1.1 The Basic Queuing Process 2
2.1 Simple Queuing model 8
2.2 Sever center 2, with c = 3 parallel servers 16
2.3 Multiserver Queuing System 20
3.1 Flow Chart of the Project Plan 31
3.2 Methodology flow chart of steps, method and expected results gain in
this research 34
3.3 Sample negative Exponential Distribution 33
3.4 Sample Poison Distribution 33
3.5 Framework for Conceptual Modelling 35
3.6 Activity Cycle for Single Server Queue 36
3.7 Process Flow Diagram for Single Server Queue 38
4.1 Process Flow diagram of the patient in polyclinic 41
4.2 Logic Flow Diagram for a single queue server in Polyclinic 42
4.3 Histogram of Inter-arrival at Emergency Room 47
4.4 Histogram of Service Time at Emergency Room 47
4.5 Goodness of Fit-Test Service Time at Emergency Room 48
4.5 Polyclinic Outpatient Department Simulation model 54
4.6 Simulation Model for Morning Session 54
4.7 Simulation model for Afternoon session 55
4.8 Validated data for morning session 57
4.9 Invalidated data for Afternoon session 57
4.10 Power curve for morning session 58
4.11 Power curve for evening session 59
xi
LIST OF TABLE
2.1 Queuing Notation for Parallel Server Systems 17
2.2 Steady-State Parameter of M/G/1 Queue 18
2.3 Steady-State Parameter of M/M/1 Queue 19
2.4 Steady-State Parameter of M/M/∞ Queue 20
2.5 Development of the Simulation Software 26
2.6 Summary of the Publication of Queuing Theory 27
3.1 Sample of the table for data collection 33
3.2 Component List 36
4.1 Sample data collected for Treatment Room A 43
4.2 Surveyed Result of 𝜆 , μ , WQ, Wn in morning session 44
4.3 Surveyed Result of 𝜆 , μ , Wn in Afternoon session 44
4.4 Surveyed Result of Mean Time of 𝜆 , μ , wQ, WQ, Wn for both session 44
4.5 Distribution for Inter-arrival & Service Time in Morning Session 46
4.6 Distribution for Inter-arrival & Service Time in Afternoon Session 48
4.7 Model Scope 49
4.8 Model Level of Detail 50
4.9 Analysis of M/M/1 in morning session 52
4.10 Analysis of M/M/1 in Afternoon session 52
4.11 Summary Process Input 53
4.12 Total Time spent in the system of 10 replications 56
4.13 Total Time Spent in the System from the collected data 57
5.1 Result of Survey of Patients Satisfactory Level 61
5.2 Results of μ, wQ, Wn from collected data 61
5.3 Results of wQ, and LQ from Queuing Model 61
5.4 Results of wQ, LQ, μ and Wn from Queuing Model 62
xii
LIST OF ABBREVIATIONS, SYMBOLS,
NOMENCLATURES
A/B/c/N/K - Notational system for parallel server systems
A - Represents inter-arrival time distribution
An - Inter-arrival time between customer n-1 and n
B - Represents the service-time distribution
c - Represents the number of parallel servers
D - Constant or deterministic
DES - Discrete Event Simulation
Ek - Erlang of order k
FIFO - First-in-First-Out
FYP - Final Year Project
G - Arbitrary or general
GI - General independent
H - Hyperexponential
K - Represents the size of the calling population
LIFO - Last-In-Last-Out
M - Exponential or Markov
N - Represents the system capability
OPD - Outpatient Department
PH - phase-type
Pn - Steady-state probability of having n customers in system
Pn(t) - Probability of n customers in system at time t
PR - Priority
PSM - Projek Saujana Muda
xiii
QA - Queuing Analytic Theory
R&D - Research and Development
SIRO - Service-In-Random-Order
SPT - Shortest Processing Time
λ - Arrival rate
λe - Effective arrival rate
μ - Service rate of one server
ρ - Server utilization
Sn - service time of the nth arriving customer
Wn - Total time spent in the system by the nth arriving customer
WQn - Total time spent waiting in queue by customer n
L(t) - The number of customers in system at time t
LQ(t)- The number of customers in queue at time t
L - Long-run time-average number of customers in system
LQ - Long-run time-average number of customers in queue
W - Long-run average time spent in system per customer
wQ - Long-run average time spent in queue per customer
𝒙 - Mean
𝜎 - Standard deviation
1
CHAPTER 1 INTRODUCTION
1.1 Background
Queuing is a daily practices in human life. Queue existence usually when peoples
wait to get services provided from the server. There are several characteristic or
types of queue, which is in virtual or physical form. Virtual queuing is usually
providing a waiting area or room with seat, whereby the person in queue is required
to remember his place in the queue system, or take a ticket with a number from a
machine. These types of queue typically are found at hospital, government
department and etc. A queue may long or short. A long waiting queue is a wastages
and non-value-added phenomenon. Therefore, many researches are interested in
queue behavior study to overcome or minimize this unpleasant circumstance. One of
the ways to understand the queue behavior is via queue model.
A simple queuing model consist 3 main related fields which are population of
potential customer, waiting line customer and server. The waiting line of customers
where are came from a calling potential population of potential customers being
entertained or served by server. In a simple expression, customers from time to time
and join in a queue, are eventually served and finally leave the system. The term of
customers refers to any type of entity that can be viewed as requesting service from a
system. Therefore, many service facilities, production system, repair and
maintenance facilities, communication and computer systems and transport and
material-handling system can be view as queuing systems. In the queuing system it
may congested with the buffer of material or waiting customer in restaurant at the
bottleneck area or at the counters.
2
There are several approaches to solve or ease queuing system which is in terms of
mathematically or simulation model. In illustrating the queuing system behavior by
using queuing model, there is several criteria need to take consideration before
implement it. The consisting criteria are input sources, type of queue, queue
discipline practice in the system, service mechanism, service time, system capacity
and the queuing terminology & notation. Once these criteria are obtained, long run
measure performance of queuing systems could be carried out by using the formulae.
The relation of the system like time-average number in system (L), average time
spent in system per customer (w), and server utilization (ρ) could be revealed. Figure
1.1 shows the illustration of basic queuing process.
Figure 1.1The Basic Queuing Process
1.2 Simulation
Simulation is a powerful and useful tool for designing and evaluating the
performance of queuing systems. Typical measurement of system performance
including server utilization (% of time of a server is busy), length of waiting line,
client in the waiting lines, and delays of the customer. There are two aspects of
consideration when attempting to improve a simulation which is analyst trading offs
between server utilization and customer satisfaction in terms of line lengths and
delay. In a high competency era, most of the sector is facing the challenge of quickly
designing and implementing complex production and service system that are capable
of meeting the growing demands for quality, delivery, affordability and service. With
recent advances in computing and software technology, simulation is a powerful
Queue Service Mechanism
Input Source
Customers Served
Customers
Queuing System
3
tools and technology for systems study and improvement. Simulation is an animation
of the system study by imitating actual system characteristic that exhibit event which
takes place over time.
Application of simulation is very vast. Simulation is being used to study systems in
the design stage, before such systems are built. Simulation modeling consist two
main usage which act as an analysis tool for predicting the effect of changes to
existing systems and as a design tool to predict the performance of new systems
under varying sets of circumstances. In some Instances, a model can be developed
which is simple enough to be “tackle” by mathematical methods or other mathematic
techniques. The solution usually consist one or more numerical parameters which are
called measures of performance of the system. It is because of Simulation is capable
predict the performance accurately so it is being widely applied in manufacturing
industries, wafer fabrication, construction engineering & project management,
business processing, military, logistics, hospital or health system, transportation &
distribution, and etc.
1.3 Polyclinic Community Ayer Keroh
This project will study about polyclinic service at Malacca. There are two policlinics
community services in Malacca which are policlinic community Peringgit and
polyclinic community Ayer Keroh. The area of the study is at polyclinic community
Ayer Keroh, Melaka. Polyclinic community Ayer Keroh was launch on 8th of July
2003 by the Chief Ministry of Malacca, YB Datuk Wira Mohd Ali bin Mohd Rustam.
The Director of the polyclinic is Dr Hj. Jamal bin Ali Johari. This policlinic is
supervision by Dr Ismail Saleh who is health officer of Daerah Melaka Tengah Bukit
Baru. Currently, the patient numbers at polyclinic has increased. The ratio of the
patient to the doctor is typically high. Each of the doctors needs to serve approximate
50 patients each day. It decreases the efficiency of the service which causes patient
wait too long for getting service.
4
1.4 Problem Statement
In recent year the demand for health care services all over the world has risen. This
phenomenon occurred due to ageing population has increase, this kind of situation is
expected continue into the future. This phenomenon also happened in Malacca area.
Meanwhile, the number of resources such as nurse, doctor, dentist, bed, space and etc
is very limited to be fulfilled the need of current market. Therefore, this situation
increase server workload so that bottleneck situation might occur. There is a need to
analyse the level of service in polyclinic so as to find mechanisms by which
improvements in service efficiency and cost effectiveness, without reducing patient
care. This is suit with government’s effort to upgrade the healthcare industry in
encouraging us to do research and development (R&D).
1.5 Objectives
1. To identify the customer service level at Polyclinic Community Ayer Keroh.
2. Model and simulate the Queues System in Polyclinic Community Ayer
Keroh.
3. Propose improvement of queue system based on the ideal time of patient
willing to experience in waiting for service provided in Polyclinic
Community Ayer Keroh.
1.6 Scope
Since the service provided in the polyclinic is very wide. In this study will explore
the outpatient department. Each of the department is provided with the waiting area
and space for the patient. The study will concern the patient who desired to get the
consultancy service in the outpatient department (OPD). A set of interviews to the
patients in determining the customer services level at polyclinic will be done in this
research. Moreover, the ideal time for the patient wait in the system will be
determined.
5
1.7 Organization of Report
Basically this report consists of 5 chapters which included Introduction, Literature
Review, Methodology, Results and Discussion, Last chapter is Conclusion which
adds on with suggestion or recommendation for future study. The summary of each
chapter contents is briefed as below:
Chapter 1: Introduction
This Chapter briefly explained about the background of the study, background
information of the hospital in concern, problem statement of the study, objective of
this project, scope which is covered in this report and the structure of organization
report.
Chapter 2: Literature Review
All the theory applied in this research will be covered in this chapter. Such as
Queuing theory and Simulation theory will be discuss further in this chapter.
Moreover, the journal or article of current application of Queuing Theory and
Simulation Theory in service industry will be discussed in this chapter as well.
Chapter 3: Methodology
This Chapter is concerned about the methods and techniques which will be carried
out in this project for the process of conducting the study. The methods and
technique used are explained in this chapter.
Chapter 4: Model Development and Data Collection
In this chapter, the conceptual model will be developed. Assumptions regarding in
this simulation project also presented in this chapter. The steps to develop queuing
model via calculation and simulation model via WITHNESS software are shown in
this chapter. Moreover, the Fitness-Test for the data collected will be illustrated in
this chapter via manual calculation and MiniTab software.
6
Chapter 5: Results and Discussion
All the quantitative and qualitative findings of the study in this project are recorded
in this chapter. The data from results parts, finding obtained from the results are
evaluated in this part. Discussion also includes the performances of the current and
proposed improved model.
Chapter 6: Conclusion and Recommendation
This chapter is final part of the report. Summarizes of important findings of the study
will be stated in this section. Recommendations for future work in this area are also
included in this chapter.
7
CHAPTER 2 LITERATURE REVIEW
2.1 Introduction
Federick S.H and Gerald J.L, stated, “Queuing Theory is the study of waiting in all
these various guises. The queuing model is to represent the various types of queuing
systems that arise in practice. Formulas for each model indicate how the
corresponding queuing system should perform, including the average amount of
waiting that will occur, under a variety of circumstances.” From the analysis of Jerry
Banker et al “Queuing model, whether solved mathematically or analyzed through
simulation, provide the analyst with a powerful tool for designing and evaluating the
performance of queuing systems. Typical measures of system performance include
server utilization (percentage of time a server is busy), length of waiting lines, and
delays of customers. Quite often, when designing or attempting to improve a queuing
system, the analyst (or decision maker) is involved in tradeoffs between server
utilization and customer satisfaction in term of lines length and delays. Queuing
theory and simulation analysis are used to predict these measures of system
performance as a function of the input parameters. The input parameters include the
arrival rate of customers, the service demands of customers, the rate at which a
server works, and the number and arrangement of servers.” Figure 2.1 illustrate the
simple queuing model.
8
Figure 2.1 Simple queuing model
A considerable body of research has shown that queuing theory can be useful in
real- world healthcare situations, and some reviews of this work have appeared.
McClain (1976) reviews research on models for evaluating the impact of bed
assignment policies on utilization, waiting time, and the probability of turning
away patients. Nosek and Wilson (2001) review the use of queuing theory in
pharmacy applications with particular attention to improving customer satisfaction.
Customer satisfaction is improved by predicting and reducing waiting times and
adjusting staffing. Preater (2002) presents a brief history of the use of queuing
theory in healthcare and points to an extensive bibliography of the research that lists
many papers (however, it provides no description of the applications or results).
Green (2006a) presents the theory of queuing as applied in healthcare. She
discusses the relationship amongst delays, utilization and the number of servers;
the basic M/M/s model, its assumptions and extensions; and the applications of the
theory to determine the required number of servers.
Queuing models and simulation models each have their advantages. It is clear
that queuing models are simpler, require less data, and provide more generic
results than simulation However, discrete-event simulation permits modelling the
details of complex patient flows. Jacobson et al. (2006) present a list of steps that
must be done carefully to model each healthcare scenario successfully using
simulation and warn about the slim margins of tolerable error and the effects of
such errors in lost lives. Tucker et al. (1999) and Kao and Tung (1981) use
simulation to validate, refine or otherwise complement the results obtained by
queuing theory.
Calling population of potential customers
Waiting line of Customer Server
9
2.2 History of Queuing Theory
From the research of Encyclopedia of American Industries, below is the summary of
the history queuing theory: “The first to develop a viable queuing theory was the
French mathematician S.D. Poisson (1781-1840). Poisson created a distribution
function to describe the probability of a prescribed outcome after repeated iterations
of independent trials. Because Poisson used a statistical approach, the distributions
he used could be applied to any situation where excessive demands are made on a
limited resource.
The most important application of queuing theory occurred during the late 1800s,
when telephone companies were faced with the problem of how many operators to
place on duty at a given time. At the time, all calls were switched manually by an
operator who physically connected a wire to a switchboard. Each customer required
the operator only for the few seconds it took to relay directions and have the plug
inserted and the time recorded. After the call was set up, the operator was free to
accept another call. The problem for an early telephone traffic engineer was how
many switchboards should be set up in an area.
Beyond that, supervisors were faced with the problem of how many operators to
keep on the boards. Too many, and most operators would remain idle for minutes at a
time. Too few, and operators would be overwhelmed by service requests, perhaps
never catching up until additional help was added.
Often, callers who were unable to gain an operator's attention simply hung up in
frustration and, suspecting it was a busy time for the operators, would wait several
minutes before trying again. Others stayed on the line, waiting their turn to talk to the
operator. Yet others would call repeatedly, hoping the operator would be sufficiently
annoyed by repeated calls to serve them next.
These behavioral discrepancies caused problems for traffic engineers because they
affected the level of demand for service from an operator. A call turned away was
lost, not to come back until much later, and was effectively out of the system. Callers