Lecture 5Simulation

Simulation is a very general technique for estimating statistical measures of complex systems.

A system is modeled as if the random variables were known.

Definition

The approach taken is to model the behaviour of individual elements within the system, often using random sampling to generate realistic variability.

Systems, Models, and Simulation (cont’d.)

Types of systems Discrete

State variables change instantaneously at separated points in time

Bank model: State changes occur only when a customer arrives or departs

Continuous State variables change continuously as a function of

time Airplane flight: State variables like position, velocity

change continuously Many systems are partly discrete, partly continuous

Studying a System

SystemsManufacturing facilityBank or other

personal-service operation

Transportation/logistics/distribution operation

Hospital facilities (emergency room, operating room, admissions)

Computer network Freeway system Business process

(insurance office) Chemical plant Fast-food restaurant Supermarket Theme park Emergency-response

system

kinds of systems1. continuous systems - state varies

continuously in time, chemical applications

2. discrete systems - observed only at some fixed regular time points. An example of a discrete system is an inventory model in which we inspect the stock only once a week.

3. discrete-event systems - the system is completely determined by a sequence of random event times t1, t2, . . ., and by the changes in the state of the system which take place at these moments.

Simulation Process

The simulation process consists of problem definition, conceptual modelling, data collection, model coding, model verification and validation, experimentation and analysis of results, and solution implementation.

Application Areas

logistics and supply chain, service operations management, business process improvement, health and social care information system, environment and many more.

What is Simulation? A Simulation of a system is the operation

of a model, which is a representation of that system.

The model is amenable to manipulation which would be impossible, too expensive, or too impractical to perform on the system which it portrays.

The operation of the model can be studied, and, from this, properties concerning the behavior of the actual system can be inferred.

Different Kinds of Simulation

Static vs. DynamicContinuous-change vs.

Discrete-changeDeterministic vs.

Stochastic

Computer Simulation

refers to methods for studying a wide variety of models of systemsNumerically evaluate on a computerUse software to imitate the system’s operations and characteristics, often over time

Using Computers to Simulate

General-purpose languages (FORTRAN)

Support packages Spreadsheets

Usually static models Financial scenarios, distribution

sampling, SQC Simulation languages

GPSS, SIMSCRIPT, SLAM, SIMAN

Evolution

Uses of simulation have evolved with hardware, software

The early years (1950s-1960s) Very expensive, specialized tool to use Required big computers, special

training Mostly in FORTRAN (or even Assembler) Processing cost as high as $1000/hour

for a sub-286 level machine

When Simulations are Used (cont’d.)

The formative years (1970s-early 1980s) Computers got faster, cheaper Often used to clean up “disasters” in

auto, aerospace industries The recent past (late 1980s-1990s)

Wider acceptance across more areas (Traditional manufacturing applications, Services, Health care, “Business processes”)

EXAMPLES OF SYSTEMS AND COMPONENTS

System Entities Attributes Activities Events StateVariables

Banking Customers Checkingaccountbalance

Makingdeposits

Arrival;Departure

# of busytellers; # ofcustomerswaiting

Note: State Variables may change continuously (continuous sys.)over time or they may change only at a discrete set of points (discrete sys.) in time.

Advantages of Simulation

Flexibility to model things as they are (even if messy and complicated)Allows uncertainty, non-stationarity in modelingUser friendly computer applications

Monte Carlo simulation

Monte Carlo simulation is a computerized mathematical technique that allows people to account for risk in quantitative analysis and decision making.

furnishes the decision-maker with a range of possible outcomes and the probabilities they will occur for any choice of action.. It shows the extreme possibilities