Faculty of Engineering

Gadjah Mada University

System Modeling and SimulationPart 2: System Simulation

1 – An Introduction

Andi SudiarsoMechanical & Industrial Engineering

Materials• Concepts and definitions: system, state, and model

• Activity Cycle Diagram (ACD)

• Input distributions and random generators

• Empirical Simulations

• Discrete Event Simulation (DES)

• Monte Carlo Simulation

• Software and Visualisation

• Verification and Validation

• System improvement using simulation

Askin, R.G., Standridge, C.R., 1993, Modeling and Analysisof Manufacturing Systems, John Wiley & Sons Inc.

Banks, J., Carson, J.S., Nelson, B.L., Nicol, D.M., 2000,Discrete-Event System Simulation, 2nd Ed., Prentice-HallInc., New Jersey

Bateman, R.E., Bowden, G., Gogg, J., Harrel, C.R., Mott,R.A., 1997, System Improvement using Simulation, 5th Ed.,Promodel Corp.

Law, A.M., Kelton, W.D., 2000, Simulation Modeling andAnalysis, 3rd Ed., McGraw-Hill, New York

Other related books.

References

Quizzes and assignments (10%)

Simulation project (10%)

Final exam (30%)

Total (Part 2): 50%

Markings

Simulation Project (1)

• group project (same as the laboratory groups)

• the simulation project is related to a chosen topic

(the topics have been given)

• data and models are based on a real system, please

include the information in relation to when the data

are collected (the precise date and time) and where

they come from (name of institution or company)

• deadline for (revised) submission is a day before the

final examination, presentation will be arranged at the

end of lectures (the 6th and 7th week).

Simulation Project (2)

Follow the format below:

• cover page (title, logo, student names, dept/university)

• list of contents

• Chapter 1: Introduction (at least consists of

background, aim and objectives, assumptions)

• Chapter 2: The company or institution (a brief

description, ACD, the date and time of observation)

• Chapter 3: Simulation Design (selecting distributions,

goodness of fit, random generator, models, outputs)

Simulation Project (3)

• Chapter 4: Results and Discussion (example of screen

views during simulation and animation if any, real

system results, add experiments with models or system,

analysis and discussion)

• Chapter 5: Conclusions and Further Work

• References

• Appendices (the raw data, flowchart and listing

program if any, softcopy on CD, etc.)

Register or login at elisa.ugm.ac.id

e-Lisa (1)

Register at ‘komunitas’ System Modeling and Simulation

e-Lisa (2)

System

Experiment with

the actual system

Experiment with

a model of

the system

Physical

model

Mathematical

model

Analytical

SolutionSimulation

(Law and Kelton, 2000)

System is defined as a collection of entities that act andinteract together toward the accomplishment of somelogical ends (Schmidt and Taylor, 1970).

Definitions (1)

Model is a form of mathematical or logical relationships,based on a set of assumptions, to try to gain someunderstanding of how the corresponding system behaves.

Analytic is an exact information on questions of interest,for example if we know the the distance (d) to be travelledand the velocity (v, it is assumed constant), then we canwork with the model to get the travelling time: t = d / v.

Simulation is a technique for using computer to imitate theoperations of various kinds of real-world processes orfacilities. Simulation is used for evaluating a modelnumerically and to estimate the desired truecharacteristics of the model based on the data obtained.

States of a system are collection of variables necessary todescribe a system at a particular time, relative to theobjectives of a study (Fishman, 1978), for example thenumber of busy machines, arrival time of customers,position and velocity of a car.

Definitions (2)

A continuous system is a system for which the statevariables change continuously with respect to time. Forexample, a moving car on a road is a continuous entitysince the position and velocity can change continuouslywith respect to time.

A discrete system is one for which the state variableschange instantaneously at separated points in time, suchas a bank system. The number of customers in a bankchanges only when a customer arrives or finishes beingserved and then departs.

System classifications (1)

Continuous versus discrete system

A static system is a system in which time plays no role, forexample Monte Carlo simulation.

A dynamic system is a system that evolves over time, suchas material handling system in a shop floor.

System classifications (2)

Static versus dynamic system

A deterministic system does not contain any probabilistic(i.e. random) component, for example simple chemicalreaction system that the output is determined once a setof input quantities and relationships have been specified.

A stochastic system has at least one random component,such as most queueing and inventory systems are modeledstochastically.

System classifications (3)

Deterministic versus stochastic system

Simulation

Simulation is one of the most widely used operation

research and management science

techniques (Law & Kelton, 2000).

Some limitations of simulation:

• To study large scale systems tends to be very

complex use an advanced software

• A large amount of time is required with complex

system simulation faster, multi-processors

computer, parallel and distributed simulation,

internet

Steps in Simulation (1)(adapted from Law and Kelton, 2000)

BEGIN

Conceptual

model valid?

Collect data and

define a modelWrite a computer

program and verify

Y

Formulate problem

and plan the study

B

N Make

pilot runs

A

1

2

3

4

5

Steps in Simulation (2)(adapted from Law and Kelton, 2000)

Analyse

output dataY

Design

experiments

END

Programmed

model valid?

A

Results,

Graphs Make production

runs

B

N6

7

8

9

10

Determining Events and Variables (1)

Event is defined as an instantaneous occurrence that

may change the state of the system.

System state is the collection of state variables

necessary to describe the system at a particular

time.

(Simulation) clock is a variable in a simulation that

gives the current value of simulated time.

- next-event time advance (skips over inactivity

periods, preferred)

- fixed-increment time advance (does not skip)

• Each event is represented by a node.

• Events are connected by directed arrows depicting

how events may be scheduled from other events and

from themselves.

• Smooth arrow indicates that an event at the end of

the arrow may be scheduled from the event at the

beginning of the arrow in a (possibly) non-zero

amount of time.

• Jagged arrow indicates that the event at its end is

scheduled initially.

Determining Events and Variables (2)

1. Event-graph method (Schruben, 1983)

Example of Event-Graph (1)

Event graph of a queueing model

Arrival Departure

Example of Event-Graph (2)

Event graph of a queueing model with

separate enter-service event

DepartureEnter

serviceArrival

• ACD describes the cycles of entities and their

interactions with other entities.

Determining Events and Variables (3)

2. Activity Cycle Diagram (ACD)

• An entity is a man or an object which moves or

changes place that may change the state of the

system, for example customer, patient, workpiece

and machine permanent and temporary entities.

• An attribute of entity is a unique characteristic from

each class of entity which represents a defined

value that related to an entity, for example machine

status, workpiece size, patient or customer type.

• Each entity from a class of entity shares the same

attribute but the value may be different.

Determining Events and Variables (4)

Continued …

• A resource is an object or a unit of simulation

which has no characteristic but create a constraint

for the activity of entity, for example the number of

machine.

• Capacity of a resource is defined as the number of

similar resource in the system.

ACD Symbols

Symbols used in ACD

: queue

: activity

: direction or sequence of

activity

Other books add:

: creation or removal of

an entity

Example of ACD (1)

Example: An A&E of hospital

A patient arrives at an A&E of hospital. The patient

needs to wait a short period before he or she could be

allocated a bed to stay. There are available 10 beds in

the A&E department.

Purpose: to calculate the bed utilisation.

Example of ACD (2)

An ACD of hospital stay

WAIT OUTSIDE

ARRIVAL

STAY

IDLE: patient

: bed

Exercise #1

Maintenance of a machine

There is a machine used for machining workpieces

in a workshop. If there is a problem occurred with a

part of machine, a mechanic will repair or replace

the broken part with a new one.

1. List the entity and its activity!

2. Draw the ACD of the system!

Purpose: to know the lifespan of the part.

Assignment #1A restaurant with food trays

There is a restaurant with 3 staff serving food to

customers. The staff uses food trays to serve menus

ordered by the customers. The trays need to be

washed after use.

1. List the entity and its activity!

2. Draw the ACD of the system!

Purpose: to know the required number of food trays.

To be submitted before the next course starts.