CHAPTER TWO

2. METHODOLOGY, STUDY AREA AND TECHNIQUES TO

BE USED

2 . 1 Methodology

1. Literature Survey

First the literature survey was carried out. Local and international literature on

hospital waiting line studies, hospital management and simulation modeling

were found.

2. Study Area

National Hospital of Sri Lanka was selected as the study area. Since it is not

possible to study the whole hospital system in Sri Lanka, the National Hospital

of Sri Lanka (NHSL) was chosen for this research. NHSL is the largest

hospital in Sri Lanka and it provides number of specialty services. Treatment

^ procedures of all government hospitals are almost similar. Therefore NHSL is

considered as a representative hospital for this research.

3. Data Collection

Available, relevant information were collected in order to obtain a clear

picture of the current system. First the structure of the National Hospital was

studied. Details of main units and subunits of National Hospital: types of

services provided by each unit or subunit were considered. Then Outpatient

Department (OPD) and In-patient section were separately studied.

Out Patient Information

First the service Procedure at Out Patient Department (OPD) was studied.

Then the following data were collected.

(i). The average daily/monthly/annually input (attendance) of patients

(ii). Availability of facilities, resources - staff capacity, waiting area

(iii). Waiting line characteristics i.e. arrival pattern, service pattern

Chapter 2 - Methodology, Study area and Techniques to be Used Chapter 2 - Page 1

Inpatient Information

Service procedure at wards was studied. Then information such as,

(i). Average daily/monthly/annually input (admissions) of patients

(ii). Availability of facilities, resources like staff capacity, bed capacity

equipment and daily average floor patients

(iii). Information on length of stays, pre-operative stays and post-operative

stays were collected.

Allocation of Money

Annual budget allocation information for the National Hospital was

considered.

4. Methods of collecting relevant information

Data collection was done using hospital records, through observations and

through a questionnaire survey. Information like patients' attendance ward

admissions and availability of resources (staff capacity, bed capacity, etc.)

were obtained from hospital records. Waiting line characteristics such as

arrival time, service time, waiting time of patients were measured through

observations. A questionnaire survey was carried out at OPD of National

Hospital to obtain views of hospital staff and patients on hospital service and

hospital waiting lines. Under staff category only the medical staff (doctors)

and nursing staff were considered. In OPD there are 48 medical staff and 33

nursing staff. Questionnaires were distributed to these 81 staff members.

Fifty patients were chosen randomly and were interviewed to obtain their

views on hospital service. Questionnaires were distributed among selected

doctors at inpatient section also.

5. Data Analysis

Several statistical techniques such as, descriptive statistics,, queueing theory

techniques, Chi-square test, Ridit analysis and simulation techniques were

used in data analysis.


2.2 National Hospital of Sri Lanka (NHSL)

2.2.1 Background

The National Hospital of Sri Lanka is the main teaching hospital and the final referral

center of this country. This is the largest medical institute functioning under the

purview of the Ministry of Health. The Director of the National Hospital is

responsible to the Director General of Health Services for the smooth functioning of

the institution. At the end of the year 2001, the hospital consists of 2897 beds, which

represent 6% of the total beds in the public sector hospitals in Sri Lanka. A staff

employed is nearly 5800. The total number of consultants is 80 and the grade medical

officers including the intern house officers exceed 700. The Academic staff works as

honorary consultants in the four professorial units, clinical medicine, surgery,

gynaecology and psychiatry.

The hospital is situated in Colombo, the commercial capital city of Sri Lanka on a 30-

acre block of land. The building floor area excluding the area occupied by the

quarters and the Nurses Training School is nearly 75,000 square meters. The total

number of wards is 77. There are 21 operating theatres and 11 intensive care units.

The total number of intensive care beds is 78, out of which 34 are equipped with

ventilators and special monitoring equipment. The hospital has facilities to carry out

advanced medical investigation such as CT Scanning. Major operations such as

Coronary Artery Bypass Grafting (CABG) and kidney transplantation are performed

routinely.

The National Hospital of Sri Lanka is mainly responsible for delivering a

comprehensive range of secondary and tertiary specialist care and medical

rehabilitation in certain identified fields of medicine. The General OPD section of the

Out Patients' Department mainly functions as a primary care unit. In 2001 there was a

total of 192,241 inpatient discharges and 1,064,238 attendances at the specialist

outpatient clinics. The General OPD visits amounted to 550,189 and there were

104,342 OPD visits in Accident Service. All services are provided free of charge.

However, patients who get admitted to the paying wards have to pay for their

services. A total of 48 paying beds are available in the hospital. This hospital is the


training center for the undergraduates following the MBBS degree of the Faculty of

Medicine, University of Colombo and also the main training center for the

postgraduate trainees attached to the Postgraduate Institute of Medicine. This hospital

also trains the intern medical officers. Practical training is also provided to the

students attached to the Nurses Training School Colombo, the Post Basic School of

Nursing, the School of Radiography, the School of Pharmacy and the School of

Physiotherapy and Occupational Therapy.

The hospital operates with funds generated under a recurrent budget of Rs. 750

million per annum. The Ministry of Health funds the entire amount.

2.2.2 Mission and Corporate Vision of National Hospital of Sri Lanka

Mission Statement

It is the policy of the government to promote the health of the community. Towards

this goal government provides preventive, curative and rehabilitative services free of

charge. Accordingly the mission of the National Hospital of Sri Lanka is "To provide

a customer or patient focused efficient health care service of the highest standards

in order to build a healthy nation ".

The objectives of National Hospital are,

(a) To meet the needs of the indoor and outdoor patients who seek treatment at

the National Hospital and to improve the hospital environment for their

benefit.

(b) To project the community at large an image of care, efficiency, dedication and

a sense of accountability.

(c) To encourage public participation in the activities of the hospital for provision

of health care.

(d) To provide a rewarding, fair and a challenging environment of work for its

staff, in order to attract and motivate well trained and qualified staff to work

in the hospital.

(e) To advise the government on the need for financial and material resources to

provide adequate secondary and tertiary health care to the community.


(f) To collaborate with other agencies and bodies both within and outside the

health care field, locally and overseas, to benefit the community.

(g) To train the medical undergraduates and the postgraduates and the nursing and

para-medical personnel.

(h) To promote research in various fields of medicine.

Corporate Vision

The National Hospital of Sri Lanka has established in its plan for the coming years,

the following corporate vision:

The National Hospital of Sri Lanka with the assistance of the Ministry of Health will

improve further its image and continue to maintain its status as the leading secondary

and tertiary health care provider in Sri Lanka, by developing centers of excellence in

all disciplines of Medicine.

2.2.3 Services Provided by National Hospital

1 . Main Services

1. General Medicine 2. General Surgery

3. Orthopaedic Surgery 4. Dermatology

5. Neurology 6. Cardiology

7. Neurosurgery 8. Oto-Rhino-Laryngology (ENT)

9. Cardiothoracic surgery 10. Psychiatry

11. Genito Urinary Surgery (Urology) 12. Gynaecology

13. Anaesthesia and Intensive Care 14. Plastic and Reconstructive Surgery

15. Burns Unit 16. Rheumatology and Rehabilitation

17. Pathology 18. Radiology

19. Accident Service 20. Paying Wards

21. Out Patients' Department

22. Special Services of the University Clinical Units (Professorial Units)


2. Other Services

Medical Examinations and Medical Boards

Every year nearly 4,000 medical examinations are carried out at the National

Hospital, to determine the fitness for employment and 1,500 patients are annually

examined by the Medical Boards to determine the fitness of employees for service

and to assess the disability caused by disease and trauma. In addition more

than 800 ill patients are assesseD each year, with a view to recommending

financial assistance form the President's Fund.

3. Special Programmes

Coronary Artery Bypass Grafting (CABG)

This is the surgical treatment for ischaemic heart disease. This operation is

routinely carried out in most of the developed countries. However in Sri Lanka

the operation was not routinely performed in government hospitals until recently.

It is now being carried out at the National Hospital of Sri Lanka free of charge.

Renal Transplantation

A renal transplantation service is provided by a collaborative project of the

University Surgical and Medical Unit of the Hospital. The first renal transplant

operation at this hospital was done on 5 t h June 1987.

The National Poisons Information Centre

The center provides rapid and accurate information on poisons and

poisoning to physicians and para-medical personnel 24 hours a day, throughout

the year. It collects useful information on pesticides, drugs, and household

requisites. In addition data on venomous snakes and other harmful animal

species and poisonous plants are also available. The center also stores and

supplies antidotes and other drugs required to treat victims of poisoning, during

normal working hours.


2.3 Techniques to be used

2.3.1 Descriptive Methods

Tables and simple graphs were used to summarise the data to identify basic

patterns of data.

Chi-Square Test

Chi-square test is used to assess the independence of two variables

(Everitt, 1977).

Table 2.1 Two Dimensional Contingency Table

Columns (Variable 2) 1 2 j c Total

1 nn n12 nic n,. 2 n2i n2.

Rows . . . . . . (Variable 1 ) / « ,y

r nri nr.

Total rij n,2 ru n^. n. = N

Hypothesis

Ho: There is no association between two variables

Hp There is association between two variables

Chi-square Test Statistic

Where Ey's are the expected frequencies of the contingency table. n , x n,

E.. =— -N

Degrees of the freedom for test statistic is, d.f= (r-)x(c-l)=n where r is the number of rows and c is the number of columns of the table.

i • Then X1 ~ Xn-

If X2 > x _, a

m e n Ho is rejected, and it can be said that two variables are

associated at a % significance level.


2.3.2 Ridit Analysis

When data are available from two or more samples with the objects from each

sample distributed across a number of ordered categories ridit analysis can be

used to compare two samples. The only assumption made in ridit analysis is

that the discrete categories represent intervals of an underlying but

unobservable continuous distribution. No assumption is made about normality

or any other form for the distribution. Let k denote the number of categories

and n i and n2 be the sample sizes. Then this initial arithmetic is illustrated in

Table 2.2.

Table 2.2 An Illustration of the Calculation of Ridits

Outcome category

(1) (2) (3) (4) (5)=ridit Product

1 f . a , = f , / 2 b , = 0 C| = a i + b i ri=ci/ni

r , * f i

2 f 2 a 2 = f 2 / 2 b 2 = f i c 2= a 2 + b 2 r 2 = c\l n 2

r 2 * f 2

b 3 = f , + f 2

k f k a k = f k / 2 b k = a k - i + f k - i C k = a k + b k r k = c k/ n k r 2 * f 2

Total Sum

1. Column I contains the distribution over the various categories for the

reference group.

2. The entries in column 2 are simply the half of the entries in column 1.

3. The entries in column 3 are the accumulated entries in column 1, but

displaced one category downward.

4. Column 4 gives the sum of entries in column 2 and 3.

5. Divide entries in column 4 by sample size ni to get the ridit value.

• , , j , - SUM The mean ndit is calculated by n =

Similarly ridits and mean ridit for comparison group can be calculated.

Standard error for ridit difference is, s.e.{ri - n ) 2A/3«,« 2


The significance of the difference between n and n may be tested by

referring the value of z = = =—. s.e.(r2 -ri)

If z > Za (value of normal distribution at a significance level), the difference is

significant at the a % significance level.

2.3.3 Queueing Theory Techniques

2.3.3.1 Introduction to Queues

Queueing theory involves the mathematical study of queues, or waiting lines.

Queueing systems are prevalent throughout society. The adequacy of these systems

can have an important effect on the quality of life and productivity. Queueing theory

studies the queueing systems by formulating mathematical models of their operation

and then using these models to derive measures of performance (Hiller, Liberman,

1995). In designing queueing systems it should be aimed for a balance between

service to customers (short queues implying many servers) and economic

considerations (not too many servers).

Queue is the flow of customers requiring service and it is characterized by a

maximum permissible number of customers that it can contain. Queues can be finite

or infinite.

Queuing systems occur at many situations like,

1. At banks, super markets, hospitals, schools and some other public and private

places (waiting for service)

2. Queues occur at computers waiting for a response

3. At failure situations (waiting for a failure to occur)


Queue Characteristics

Any queuing situation can be broken into 6 main elements.

1 . Input Source (Calling Population)

The population from which arrivals come is referred to as the calling

population. One characteristic of the input source is its size. The size is

the total number of customers that might require service from time to time.

The size can be finite or infinite.

2. Arrival process

The arrival process contains four parts

1. Pattern - Whether it is controlled or not

2. Grouping - The way customers occur

For example customers arrive singly as well as in groups.

3. Time between arrival statistics - Mean, variability and distribution of

successive arrivals.

4. Degree of impatience - Whether customers leave before being served.

3. Physical Characteristics of Queue

This means number of queues (one or more) and the length of the queue

(limited or unlimited capacity).

4. Queue discipline

This means the method by which a customer is selected for service out of

all those awaiting service. Some commonly used queuing disciplines are

described as follows.

1. FIFO - First-In-First-Out

2. LIFO - Last-In-Last-Out

3. JSQ - Join the Shortest Queue •

4. SIRO - Service-In-Random-Order ')"•

5. Favorite server specified (in barber shops)


6. Priority queues

In priority discipline queueing models, the queue discipline is based on a

priority system. Thus the order in which members of the queue are

selected for service is based on their assigned priorities,

(i). Non-preemptive priorities - Once a server has begun serving a

customer, the service should be completed without any interruptions,

(ii). Preemptive resume priorities - The lowest customers being served

are interrupted whenever a higher priority customer enters the system.

7. Other

5. Service mechanism

a. Single server, single line

A r r i v a l s Q u e u e

• O O o S e r v e


• o o o

b. Multiple servers, single line

o

o o

S e r v e r 1

S e r v e r 2

S e r v e r 3

c. Sequential servers, single line


• o o o S e r v e r 1 o S e r v e r 2 o S e r v e r 3

d. Multiple servers, multiple lines

A r r i v a l s _ _ Q u e u e

• o o o A r r i v a l s Q u e u e _

* o o o A r r i v a l s

S e r v e r 1

S e r v e r 2

• * o o o S e r v e r 3

Figure 2.1 Common Queueing Systems


This is defined by the server's characteristics as follows.

1. Number of servers

a. One - no choice, single server and single line

b. Multiple - choice of servers, multiple server and single line

c. Serial - sequential servers, single line

d. Parallel - multiple server, multiple line

2. Service time/server statistics - Mean, variability and service

distribution

The Basic Queueing Process

Thus the basic queueing process assumed by most queueing models is as follows.

1. An input source or calling population generates customers requiring service

over time. These customers enter the queuing system and join a queue

2. At certain times a member of the queue is selected for service by some rule

known as queue discipline.

3. The required service is then performed for the customer by the service

mechanism.

4. Customers exist or return to the queue.

Most of queueing models assume that all interarrival times are independent and

identically distributed and that all service times are independent and identically

distributed. Such models are labeled as follows.

6. Exit

Customer leaves the system or probability of returning to the system.

Population

Figure 2 .2 Basic Queuing Process


A/B/C/D/E (1)

Where, A - The probability distribution for the arrival process

B - The probability distribution for the service process

C - Number of channels (servers)

D - The maximum number of customers allowed in the queueing system

(either being served or waiting for service)

E - The maximum number of customers in total

Some common options for A and B are,

M - Poisson arrival distribution (exponential interarrival distribution) or a

exponential service time distribution

D - Deterministic or constant value

G - General distribution (but with a known mean and variance)

Ek - Erlang distribution (shape parameter = k)

If D and E in (1) are not specified then it is assumed that they are infinite.

For example the M/M/l queueing system, the simplest queueing system, has

Poisson arrival distribution, an exponential service time distribution and a singl

channel (one server). In this system it is always assumed that there is just a singl

queue (waiting line) and customers move from this single queue to the servers.

2.3.3.2 Queuing Notation and Terminology

The following standard terminology and notation will be used.

State of system = number of customers in queueing system.

Queue length = number of customers waiting for service

= state of system minus number of customers being served.

N(t) = number of customers in queueing system at time t (t> 0).

P„(t) - probability of exactly n customers in queuing system at time /, given

number at time 0.

s = number of servers (parallel service channels) in queueing system.

k„ = mean arrival rate (expected number of arrivals per unit time) of neew

customers when n customers are in system.

/j„ = mean service rate for overall system (expected number of customers

completing service per unit time) when n customers are in system.


Note : /jn represents combined rate at which all busy servers (those

serving customers) achieve service completion.

When Xn is a constant for all n, this constant is denoted by X. When the mean service

rate per busy server is constant for all n > 1, this constant is denoted by //.

(p„ = S/J when n > s, that is, when all s servers are busy.) Under these circumstances,

l/X and l/ju are the expected interarrival time and the expected service time

respectively.

Utilization Factor p

p = X l{sp) is defined as the utilization factor for the service facility.That is, the

expected fraction of thime the individual servers are busy, because X l(sp) represents

he fraction of the system's service capacity (sp) that is being utilized on the average

by arriving customers (X).

Steady-state Condition

When a queueing system has recently begun operation, the state of the system

(number of customers in the system) will be greatly affected by the initial state. Then

the system is said to be in a transient condition. However after sufficient time has

passed, the state of the system becomes essentially independent of the initial state and

the passed time (except under unusual circumstances that p > 1, in which case the

stateof the system tends to grow continually larger as time goes on). Now the system

has essentially reached the steady-state condition, where the probability distribution

of the state of the system remains the same over time. The following notation

assumes that the system is in a steady-state condition.

Pn = probability of exactly n customers in the queueing system.

L = expected number of customers in queueing system.

Lq - expected queue length (excludes customers being served).

W = waiting time in system (includes service time) for each individual customer.

W=E(W )

W q = waiting time in queue (excludes service time) for each individual customer.

Wq = E(Wq)

Chapter 2 - Methodology, Study area and Techniques to be Used Chapter 2- Page 14

Assume that Xn is a constant X for all n. It has been proved that in a steady-state

queueing process,

L = XW (2)

Lq = XWa. (3)

If the X„ are not equal then A can be replaced in these equations by X , the average

arrival rate over the long run. Now assume that the mean service time is a constant,

for all n > 1. It then follows that,

W=W0+l_ (4)

2.3.3.3 Decision Making

Designing a queueing system involves making one or a combination of the decisions;

number of servers at service facility, efficiency of the servers and number of service

facilities. When such problems are formulated in terms of a queueing model, the

corresponding decision variables usually are s (number of servers at each facility), /j

(mean service rate per busy server) and X (mean arrival rate at each facility).

All those decisions involve the general question of the appropriate level of service to

provide in a queuing system. As mentioned in the Chapter 1, decisions regarding the

amount of service capacity to provide are based primarily on two considerations: the

cost incurred by providing the service as shown in Figure 2.2 and the amount of

waiting for that service as in Figure 2.3. The objective of reducing service costs

recommends a minimal level of service. On the other hand, long waiting times are

undesirable, which recommends a high level of service. Therefore it is necessary to

have some type of compromise. Thus Figure 2.2 and Figure 2.3 are combined as

shown in Figure 2.4. The solution point in the curve gives the best balance between

the average delay in being serviced and the cost of providing that service.

In situations where service is provided on a nonprofit basis to customers external to

the organization such as social service systems, the cost of waiting usually is a social

cost of some kind. Thus it is necessary to evaluate the consequences of the waiting

for the individuals involved and/or for society as a whole and try to impute a


monetary value to avoiding these consequences. This kind of cost is quite difficult to

estimate, and it may be necessary to revert to other criteria.

Cost of service per arrival

Level of service

Expected waiting time

Level of service

Figure 2.3 Service cost as a function of service level

Figure 2.4 Expected waiting time as a function of service level

Expected cost

Sum of costs / / Cost of service E(SC)

Cost of waiting E(WC)

Solution Level of service

Figure 2.5 Conceptual solution procedures for many waiting-line problems

2.3.3.4 Statistical Analysis

Mean (Average) and Standard Deviation

Mean 3c

1. Let x be a random variable with values xi, X2, xj, xn then the sample

mean or average , x is defined as,


2. In a frequency table with class mid points x / , X2, x j , x„ and

corresponding frequencies fi,f2,f3, ,fn the mean , x is defined as,

x = V^^, where n = Yfi

Standard Deviation a

1. For a random variable x with values xh X2, xs, xn the sample

standard deviation is defined as,

n-l

2. In a frequency table with class mid points Xi, x ? , x j , x „ and

corresponding frequencies / / , / ? , / J , , ./̂ the sample standard

deviation is defined as,

1 5>? -E 1=1 1=1

n-\

/ n

Statistical Distributions

Statistical distribution of arrivals and services should be determined. First a

frequency table should be derived from the raw data and probabilities at different

frequency intervals should be calculated. The distribution determination can be

done roughly, visually by putting data into a bar chart format. More accurately,

statistical distribution can be verified by using the chi square goodness of fit test.

Probability Distribution Function, p(x)

Every statistical distribution can be expressed in a mathematical form, p(x) that can be

used to plot the distribution. The p(x) for a continuous distribution is called a

probability density function (pdf). For a discrete distribution, p(x) is called a

probability mass function (pmf).


1. Probability density function for a discrete random variable

Let x be a discrete random variable with values x/, JC?, xs, x „ . With each

possible outcome x,-, suppose p{xi) = Pr(x = x ) be the probability of Xj.

If (a) /?(*,-)> 0 V x,-

(b) !/>(*/) = 1 ,

p is called the discrete density function of x or the probability distribution of x .

2. Probability density function for a continuous random variable

Let x be a continuous random variable.

If (a)/7x;>0Vx,

(b) \ f ( x ) d x = \ ,

function/is called the probability distribution function of x

Functional Form of Statistical Distributions

1 . The Discrete Uniform Distribution

Let a and b constants with a < b. The uniform density on the interval (a, b) is the

density f defined by,

\l{b - a) a < x <b

0 elsewhere /(*)

2. Exponential Distribution

Suppose X represents either inter-arrival or service times. This random variable is

said to have an exponential distribution with parameter p . if it has density function,

f i x )

I M ^ X > 0

0, x < 0


3. The Poison Distribution

Suppose time between arrivals or services are exponentially distributed with

parameter [i (>0). Let X be the number of occurrences in a unit time interval. Then X

has a Poisson distribution with parameter [i and density function is defined as,

p(X = x) = JC = 0,1,2,.

x\ 0, elsewhere

4. Normal Distribution

This continuous distribution has a pdf of,

e-(x-fj)2/2a2

f ( x ) = = = — - OO < X < CO

crv I n

where e « 2.71828, n » 3.14159 and x represents the variable of interest with mean p

and standard deviation cr.

5. Erlang distribution

This is a general distribution in that it can be used to approximate many kinds of

distributions such as the exponential, Poisson, normal, and constant depending on the

value of parameter m. The general pdf is,

p ( x ) = m m x m - ' e m x / M , x > 0 , m = 1,2,3, /T(m-1)!

Where m is a shape parameter and a 2 = j f _ 4-5'" m


Graphical form of Statistical Distributions

The probability bar charts for some statistical distributions look as follows.

Eiiang distribution

Figure 2.6 Statistical Distributions

Chapter 2 - Methodology, Study area and Techniques to be Used Chapter 2 - Page 2 0

2.3.4 Simulation Techniques

2.3.4.1 Introduction to Simulation

Simulation is a widely used tool for estimating the performance of complex stochastic

systems. Simulation is inherently an imprecise technique. It provides only statistical

estimates rather than exact results and it compares alternatives rather than generating

an optimal one. Simulation provides a way of experimenting with proposed systems

or policies without actually implementing them. Sound statistical theory should be

used in designing these experiments. Long simulation runs often are needed to obtain

statistically significant results. However, variance-reducing techniques can be very

helpful in reducing the length of the runs needed.

Several tactical problems arise when traditional statistical estimation procedures are

applied to simulated experiments. These problems include prescribing appropriate

stating conditions, determining when a steady-state condition has been reached and

dealing with statistically dependent observations. The regenerative method of

statistical analysis can be used to eliminate these problems.

Simulation is a slow and costly way to study a problem. It usually requires a large

amount of time and expense for analysis and programming and considerable computer

running time. Simulation yields only numerical data about the performance of the

system, so that it will not provide any additional insight to the cause-and-effect

relationships within the system.

2.3.4.2 Formulating and Implementing a Simulation Model

Constructing a Model

The first step in a simulation study is to develop a model representing the system to be

investigated. This requires a through familiarization with the operating realities of the

system and the objectives of the study. Then the real system should be reduced to a

logical flow diagram. The system is there by broken into set of components linked


together by a master flow diagram, where the components themselves may be broken

down into subcomponents and so on. Ultimately the system is decomposed into a set

of elements for which operating rules may be given. These operating rules predict the

events that will be generated by the corresponding elements, perhaps in terms of

probability distributions. After specifying these elements, rules and logical linkage,

the model needs to be thoroughly tested by piece by piece.

Preparing a Simulation Program

The basic purpose of most simulation studies is to compare alternatives. Therefore the

simulation program must be flexible enough to accommodate readily the alternatives

that will be considered. Most of the instructions in a simulation program are logical,

also some simple arithmetic work required. General simulation programming

languages can be used to simulate real world systems. For example, GPSS and

SIMSCRIPT are two such languages that are widely used. These languages are

designed especially to expedite the type of programming (and reprogramming) unique

to simulation.

Simulation programming languages have several specific purposes. One is to provide

a convenient means of describing the element that commonly appear in simulation

models. Another is to changing the design and operating policies of the system being

simulated, so that the large number of configurations can be considered easily. These

languages also are designed to obtain data and statistics on the behavior of the system

being simulated.

Validating the Model

The typical simulation model consists of a high number of elements, rules and logical

linkages. After the writing and debugging of the computer program, it is important to

test the validity of the model. When some form of the real system has already been in

operation, its performance data should be compared with the corresponding output

data from the model. Standard statistical tests can sometimes be used to determine

whether the difference in the means, variances and probability distributions

generating the two sets of data are statistically significant. The time dependent


behavior of the data might also be compared statistically. If the model may be used

again in the future, careful records of its prediction and of actual results should be

kept to continue the validation process.

2.3.4.3 GPSS/PC - General Purpose Simulation System (Minuteman Software)

In 1961 IBM introduced the first commercially successful simulation language,

* General Purpose Simulation System (GPSS). After IBM ceased maintaining their

fifth and final version of GPSS (GPSSV) in the mid 1970s, Wolverine Software

introduced in 1977 an upgraded mainframe version of GPSS called GPSS/H. In 1984,

Minuteman Software developed and successfully marketed GPSS/PC, a

microcomputer version of GPSS. This

language will run on any IBM compatible microcomputer that uses MS-DOS

operating system and has at least 320K of RAM. Obviously the faster the operating

speed of the microcomputer, the faster GPSS/PC will run. In 1988, Minuteman

developed an EMS version that can run on microcomputers with enhanced memory

* (LIM version 3.2 or 4.0) up to 32 megabytes. Hence, GPSS/PC can now be used to

simulate many systems that earlier could only be run using a mainframe GPSS

language.

Simulation Using GPSS/PC

Like any other simulation language, GPSS/PC basically requires block and control

statements, Transactions and Commands to write a simplified computer program.

Semantically meaningful Block statements are used to follow the logical flow of the

k system being modeled (e.g. GENERATE, QUEUE, DEPART, SEIZE, RELEASE). Control

statements are used to, provide blocks with information or to receive information

from blocks, control the flow of transactions through the model or to End a GPSS/PC

session (e.g. FUNCTION, VARIABLE, TABLE, START, END). Transactions are used to

represent the flow of units through the model (e.g. people, parts, information).

Commands are used to help, write, and interact with the program (e.g. EDIT, SAVE,

DISPLAY, RENUMBER, REPORT).


Basic GPSS/PC Simulation Blocks and Control Statements

Blocks and control statements can be grouped into categories (permanent entities);

facilities, storages, queues, functions, tables, variables, save-values, matrices and

logicswitches.

1. Facilities - Entities that can handle only one transaction at a time, such as a

bank teller, telephone operator or surgeon.

2. Storages - These entities can be engaged by one or more transactions at a

time such as a warehouse, a group of indistinguishable safe-

deposit booths or an airplane.

3. Queues - Queues form and are kept track of in a simulation model

whether the QUEUE block is used or not.

4. Functions - These are used to input discrete or continuous frequency

distribution data, statistical or otherwise into the model.

5. Tables - Tables allow the models to show results in a frequency-

distribution format.

6. Variables - Mathematical and logical expressions can be evaluated using

variables.

6. Save-values-These are like transaction parameters in that numerical

attributes can be stored for future references. But unlike

parameters this information is available at all times and at all

points in the model.

Block/Control Statement Format

Every GPSS/PC block and control statement has the following format. l : / '

Line number Label Block or Control N a m e Operands (A, B, . . . ) ; C o m m a n d s

"Line number" orders the model statements. The "Label" optionally used with some

blocks, allows for a block or control statement to be referenced elsewhere in the

simulation model. The "Operands" or information fields (one to six) provide data

necessary for the proper operation o f the block or control statement. "Comments"

(descriptive verbiage preceded by a semicolon) can follow all the block and control

Chapter 2 - Methodology, Study area and Techniques to be Used Chapter 2 - Page 2 4

statements. Full line comment statement can be written by putting an asterisk (*) in

the first position of the "Label" field.

Some Commonly Used Block and Control Statements

GENERATE

This block creates original transactions (customers) for future entry to the simulation

model.

Label (opt ional) G E N E R A T E A, B, C, D, E

QUEUE

This block updates queue entity statistics to reflect an increase in content (customers

enter the queue). Label (opt ional) Q U E U E A, B

DEPART

This block registers statistics that indicate a reduction in the content o f a queue entity.

This departs the queue. In order for queue statistics in the output report t o have any

meaning, The QUEUE'S companion block, DEPART must be placed in the simulation

model so that the time transactions spend traversing from the QUEUE block t o its

DEPART block constitutes actual queue o r waiting time.

Label (opt ional) D E P A R T A, B

SEIZE

When the active transaction attempts t o enter a SEIZE block, it waits for o r acquires

ownership o f a facility. This represents a facility that can serve only one customer

(transaction) at a time.

Label (opt ional) SEIZE A

ADVANCE

This block delays the progress o f a transaction for a specified amount o f simulated

time (i.e. serves the customer).

Label (opt ional) A D V A N C E A, B


RELEASE

This block releases ownership of a facility or removes a preempted transaction from

contention for a facility. Every SEIZE block needs to be paired with a RELEASE

block in order for facility statistics in the output report to be meaningful. The

RELEASE block defines the end of a particular transaction's ownership of a facility.

Label (optional) RELEASE A

TABLE

The TABLE statement initializes a frequency distribution table.

Label TABLE A, B, C, D

QTABLE

This statement initializes a queue time frequency distribution able.

Label QTABLE A, B, C, D

TRANSFER

This block causes the active transaction to jump to a new location.

Label (optional) TRANSFER A, B, C, D

STORAGE

The STORAGE control statement defines a storage entity and its maximum capacity

in the current model.

Label STORAGE A

TERMINATE

The TERMINATE block removes the active transaction from the simulation and

optionally reduces the termination count. Since transactions take up memory space,

all transactions that are no longer needed in the model should be terminated. At least

one TERMINATE block in the model.

Label (optional) TERMINATE A


CHAPTER TWO - dl.lib.uom.lk

Documents

Transcript of CHAPTER TWO - dl.lib.uom.lk