Simulation

Waiting Line

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Introduction

Definition (informal) A model is a simplified description of an

entity (an object, a system of objects) such that it preserves some defining components of the entity the relations between these components

that are of current interest.

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Introduction

Definition (more formal) A model is a construct invented as an aid to understand the system under study.

A model is a formal statement of: assumptions conceptualizations experimental design

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The purpose of a model

to help understand, describe, or predict

how things work in the real world by exploring a simplified

representation of a particular entity or phenomenon.

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Examples of models

a city map, a house floor plan, a photo of a house, an equation, a square, etc.

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Types of models

Static - a snapshot of the object/system at a particular time

Dynamic - model of changes in the object/system Continuous Discrete - changes occur at some time intervals

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Computational models

Simulate a set of processes observed in the natural world

in order to gain an understanding of these processes and to predict the outcome of natural processes

given a specific set of input parameters.

Conceptual and theoretical modeling constructs are expressed as sets of algorithms and implemented as software packages.

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Simulation

An experiment performed on a model Experiment: observing and studying the

behavior of a system Reasons for using simulation as a problem-

solving tool. The physical system is not available. The experiment may be dangerous. The cost of experimentation is too high.

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Discrete simulation

Components Entities: objects that interact Attributes: properties of entities Activities: processes that change the

system Events: occurrence of activities Statistics: measures of the performance of

the system

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Approaches

Time driven Event driven

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Time driven discrete simulation

Initialize time initialTimeWhile time < stopTime

• Execute all events to be done at this time

• Increment time Output measures

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Event driven discrete simulation

Initialize time initialTimeWhile more events to be done

• Advance time to the time of the earliest event

• Execute the earliest eventOutput measures

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Waiting line simulation

Objects

Waiting Line Waiting Line Service providers (Cashiers)Service providers (Cashiers) ClockClock

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Waiting LineWaiting Line Attributes: Input

probability of arrival line capacity processing time

Output average waiting time number of transactions maximum length of the waiting line unprocessed requests due to exceeding the

line capacity

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Waiting LineWaiting Line Events: Arrival:

record time in queue increment line length

Exit line: record waiting time: now – arrival increment transactions decrement line length

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Cashiers (service providers)

Attributes: Input

Number of cashiers Output

Status of each cashier Idle Busy, remaining processing time

Total idle time per cashier

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Cashiers (service providers)

Events: Get a customer to be served

Assign an available cashier to a customer Update cashier status

If idle, increment idle time If busy, decrement processing time

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Clock

Records the time in increments of 1Returns time

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Simulator

Initialize Simulation time S Processing time PT Probability of arrival P Line capacity L Number of cashiers C

Attributes: Current time elapsed, init 0 CT Available cashier

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Algorithm

While CT (current time elapsed) is less than S (simulation time) Record arrival with probability P If available cashier and line not empty

exit line assign cashier to do the service

Update cashiers’ status Increment CT

Prepare report

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Reports

average waiting time number of transactions maximum length of line average idle time maximum idle time