Contemporary methods of discrete event simulation

Mike Pidd

Department of Management Science

Lancaster University Management School

UK

M.Pidd@lancaster.ac.uk

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Some simulation application areas

Manufacturing - plant layout & sizing, plant

'optimisation', process design

Health care - clinic planning, blood transfusion

services, AIDS transmission, renal dialysis services

Business process improvement

Air travel - airport operations, air traffic control

Road transport - traffic simulations, on-line traffic

control

Emergency planning - evacuation modelling

Military - battle plans, scenario analysis

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Why simulate?

Mathematical models

may be too simplified

often intractable

Real experimentation

expensive

slow (or too fast!)

dangerous

may be illegal

often can‟t be replicated

Surely

there‟s a

better way?

To support the careful analysis of decisions and

plans before any implementation

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Computer simulation: basics

Dynamic

model(s)

Inputs (policies) Outputs (responses)

Interaction

Experimentation on a dynamic system model

Activities in computer simulation5

Modelling

ComputingExperimenting

Abstracting and

representing the main

features of the system

of interest

Producing a

model than can

be run on a PC

or other

computer

Using the

model to

explore

options or gain

understanding

It often becomes difficult to separate these

Discrete event simulation Stochastic behaviour

Next event time handling

Focus on individual entities (e.g. machines, people, vehicles)

Software: Micro Saint, Simul8, Witness etc

System dynamics Deterministic behaviour

Time slicing

Focus on rates of change of populations (e.g. birth rates, sales rates)

Software: Vensim, Powersim, IThink

Multi-agent based Focus on large number of (semi) autonomous agents

Time slicing

Rules govern agent interactions and behaviour

Software: Swarm, Repast etc

Simulation approaches in management science

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Discrete event simulation models

Discrete entities: e.g. people, machines, vehicles, jobs, orders, patients Change state as the simulation proceeds

State changes individually tracked during the simulation

Discrete events: times at which the entities change state.

E.g. 2:00 pm lecture stats, 3:00 pm patient discharged Some may be exogenous (externally generated)

e.g. injecting new customers into a simulation

Some will be endogenous (internally generated by the interaction of entities)

e.g. repairman starts work on damaged machine

System is simulated by managing the state changes of the entities

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DES time-handling options

Fixed time increment - time slicing

Move time along in pre-determined chunks

Analogy – time-lapse photography

PROBLEM : need to know time slice in advance, but system's activity may vary.

Variable time increment - next event technique

Keep track of when events are due

Move from event to event, ignoring in-between

System activity drives the simulation

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Time slicing

Time

x

Time-sliced approximation

Data series

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Simple job-shop

Machine

A

Machine

B

Orders Finished jobs

Time = 1 + (batch size)/50 Time = 3 + (batch size)/100

Order number Batch size Day expected

1 200 1

2 400 8

3 100 14

4 200 18

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Job-shop: time slicing

Job # Due TimeA TimeB

1 1 5 5

2 8 9 7

3 14 3 4

4 18 5 5

Day QA QB OnA OnB

1

2

3

4

5

6

7

8

9

10

- 1- -

- - -1

- - -

1

- - -

1- - -1

- - - 1

- - - 1

- -

1

2

- -

1

2

- - 12

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Next event simulation

Job

# Arrival day

Machine A Machine B

Start day End day Start day End day

1

2

3

4

13

Time slicing simulation, 32 events

Day Jobs queuing Jobs in progress Day Jobs queuing Jobs in progress

for m/c A for m/c B m/c A m/c B for m/c A for m/c B m/c A m/c B

1 - - 1 - 17 - - 3 2

2 - - 1 - 18 4 - 3 2

3 - - 1 - 19 4 - 3 2

4 - - 1 - 20 - 3 4 2

5 - - 1 - 21 - 3 4 2

6 - - - 1 22 - 3 4 2

7 - - - 1 23 - 3 4 2

8 - - 2 1 24 - - 4 3

9 - - 2 1 25 - 4 4 3

10 - - 2 1 26 - 4 - 3

11 - - 2 - 27 - 4 - 3

12 - - 2 - 28 - - - 4

13 - - 2 - 29 - - - 4

14 3 - 2 - 30 - - - 4

15 3 - 2 - 31 - - - 4

16 3 - 2 - 32 - - - 4

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DES modelling: next event time handling

Variable time increment -next event technique

Keep track of when events are due

Move from event to event, ignoring in-between

System activity drives the simulation

Start, time, t=0

Do all events due

at time t

Simulation

over?

Stop

No

Yes

Schedule

future events

on calendarFind time of

next event(s)

in calendar

Move t to time

of next event

Requires

•„Diary‟ for future

commitments (event calendar,

event list, event queue, …)

•Simulation executive

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DES modelling: stochastic behaviour

Deterministic

All durations of activities entirely predictable and

known. System runs like clockwork.

Stochastic

Durations of activities can only be known

probabilistically.

Hence need to simulate this variation by taking

samples from appropriate probability distributions.

The simulation is a sampling experiment which needs

to be replicated.

Dangers in stochastic simulations

Profit

Prob

Profit

Prob

A BA B

Large risk of

wrong inference

Random sampling leads to sampling variation and to

sampling errors. Need careful analysis.

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-1200

-1000

-800

-600

-400

-200

0

200

400

600

800

1000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

Cost Diff

Mean

UCL

LCL

The problem of inference…

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Notice we‟re still unable to be sure if

Z is +ve or –ve, after 50 replications

Simple example: 2 policies, (A & B) which produce most profit?

Suppose Z = Profit(A) – Profit(B)

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Problem of sampling variation

Confidence in results improves with number

of independent replicates (n)

But only with the square root of n

The sequence in which the replicates occur

can make a difference

Need to be very careful when analysing DES

output

nsreplicatiot independen n from meanx where

. CIn

sx α

GMP OCRSim

Time handling

Next event technique throughout

Each call handled individually

Each police response is individual

Stochastic sampling

Call volumes (vary by day & time of day)

Time to deal with each call

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No specialties

By specialty

DGHPSim: time handling & sampling20

Emergencies

to A&EA&E model Admit?

Discharged

Inpatient

waiting list

model

Inpatient

model

Emergency GP referrals

Outpatient

model

Diagnostics

Admit?GP elective

referrals

DGHPSim time handling

Time handling

Accident & emergency: next event technique, individual patients &

treatment

Outpatient model: daily arrivals and clinics (time slicing)

Inpatient model: next event technique, individual patients &

treatments from waiting list.

Stochastic sampling

Patient arrivals (vary by day & time of day)

Treatment times (inpatient & outpatient)

Type of patient (case mix)

Time spent on wards

Movement between wards

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Discrete event simulation software

Two main options

Write a

simulation

program

Use a visual

interactive

modelling system

(VIMS)

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Writing a simulation program

Can use almost any programming language

General purpose: e.g. C, C++, C#, Java, Pascal, VB

Simulation language: e.g. MODSIM, Simscript, Simula

Can develop a library for re-use

Allows bespoke application development

BUT

Requires good programming skills

Program development is slow

Rarely done outside defence & academe

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Features of VIMS

Graphical interface Pre-defined objects

Drag & drop

Property sheets

Some degree of programmability Own „language‟

Relatively self-contained Model building

Model execution

Experimental control & analysis

Hide the hard bits

Arena

Automod

Extend

GoldSim

Micro Saint

ProModel

SimProcess

Simul8

Taylor II

Witness

…etc…

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Micro Saint Sharp: a typical VIMS

Network diagram: sequence of tasks through which

entities flow

State changes (events) occur at task beginning or end, e.g.

Begin Inspect: Joe from Idle to Busy, Queue reduced by 1

End Inspect: Joe from Busy to Idle, Car leaves or waits for repair

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VIMS are great … but …

Often over-sold

“In just x minutes (x <10) you can build a fully

working model …”

Need programming skills for realistic modelling

Knowing Excel macros may not be enough

Built-in languages usually proprietary

Why do this when dot.net allows other approaches?

Can be useful to know how the engine works

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Some current research at Lancaster

Component-based modelling Users assemble only the components they need

Possible pay per use basis

Integration through Microsoft .net or similar

Distributed simulation For large problems on high performance computers

Policy modelling Health care – but not at clinic or specialty level

Use to check feasibility of options: e.g. waiting times for elective surgery

Conceptual modelling Developing representations that are independent of computer

software

Value of agent-based modelling