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General Simulation Principles

Refer to Chapter 3 Very Important Chapter Section 3.1

Memorize all basic definitions & be able to discuss thoroughly

Also includes additional material not in book

Discrete Event Systems

Discrete systems – focus of course Framework for modeling systems General Terminology General Purpose Languages vs.

Simulation Packages Dynamic (over time) Stochastic (randomness)

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*Terminology (pg. 89)

System Model System State Entity Attributes List

Event Event notice Event list (FEL) Activity Delay Clock

Terminology

System

Collection of one or more entities interacting together over time to accomplish some goal or goals School Airport Gas Station Human Body

ModelAbstract representation of

a system, in form other than the system itself Includes relationships

that describe system (state, entities, activities, events, processes, delays, etc.)

Mathematical, physical, computer program, etc.

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Terminology

System StateCollection of variables

necessary to fully describe the system at a point in time Number-in-queue Number-of-servers Status-of-servers

EntityObject or component of

system that requires representation in the model; an object of interest Customer Server Queue

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Terminology

AttributesProperties of an entity

that describe it

1. Length (of queue)

2. Capacity (of queue)

3. Status (of server)

4. Speed (of server)

5. Type (of customer

Attribute ValuesActual values assigned to

an attribute at a particular point in time1. 0 to Capacity

2. 1, 2, 3, …

3. Busy, Idle, On-Break

4. Num. Services/Time

5. Business, Personal

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Terminology

ListCollection of associated

entities, ordered in some manner FIFO queue of

customers Priority queue of

customers Available servers

EventInstantaneous occurrence

that changes the state of system Arrival of customer Completion of service Breakdown of

machine

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Terminology

Event NoticeRecord of event to

occur at current or future time + data necessary to execute it; event type & time Arrival, 10 End-service, 30

Event List (FEL) Future Event List List of Event Notices

ordered by time Typically a linked list Is the “driver” for a

simulation program

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Terminology: ACTIVITY Duration of time of specified length known

when begins; scheduled & desired; Unconditional wait

Duration determination Deterministic: always 10 minutes Statistical: Uniform (1,10) Functional: based on attribute (age, capacity)

Begins & Ends with an Event Service time: Begin Service, End Service

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Terminology: DELAY

Duration of time of unspecified, indefinite length not known until it ends; duration determined by system conditions; i.e. by other events or activities; not scheduled or desired Conditional wait Time waiting in queue Time waiting on any other event

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Terminology: CLOCK

Variable representing simulated time Elapsed time in smallest time unit

necessary Updated with each new event time as

the event is executed

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Primary vs. Secondary Events

Primary Event Occurrence is scheduled Placed on FEL Arrival, Complete Service

Secondary Event Occurrence due to some other event or

condition Not on FEL Enter or Leave queue, Begin service

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Waits Conditional vs. Unconditional

Conditional Wait = Delay Caused by some other condition In Queue

Unconditional Wait = Activity Scheduled Service time

Example 2.6 – page 51

Computer technical support center is staffed by 2 people, Able & Baker, who take calls & answer questions to solve computer problems. Able is more experienced & faster. If both are idle, Able takes call. If both busy, caller placed on hold & calls are answered in the order received.

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State components from Example 2.6

System Model System State Entity Attributes List

Event Event notice Event list (FEL) Activity Delay Clock

Dynamic Relationships & Interactions Between Components

Consider the questions on page 91. Answers are necessary to

determine correct model.

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Time Management Methods

Determines how CLOCK is managed (updated)

Time Slice Approach Continuous Systems

vs.

Critical Event Approach Discrete Event Approach

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Time Slice Approach

Simulation is controlled by time Clock is incremented by fixed number of

time units (N) each time State of system is based on everything that

occurred in past N time units Typical for simulating continuous systems Able to easily compress or expand time by

varying N

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Critical Event Approach

Simulation is controlled by occurrence of “critical events”

Clock is incremented (updated) by variable amounts as determined by occurrence of next critical event

Critical events cause specific changes in state of the system

Used for discrete systems

Time Slice vs. Discrete Event:Examples

Discuss clock management & system updates…

Continuous Release of pollutants into a river Flood of city due to rain storm

Discrete Use of student computer lab Baggage check-in counter at airport

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Future Events List (FEL)

A set of all events that have been scheduled to occur at a future time

Arrange in chronological order Linked List t<= t1<= t2 <= t3<=…tn t is value of clock t1 is the imminent event

Future Events List

What are implementation options? Pros & Cons? Array

Ordered, Unordered Linked List

Ordered

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Event Scheduling – Time Advance Algorithm (main)

1. Remove imminent event

2. Advance Clock

3. Execute imminent event: update state

4. Generate future events (as necessary) & Place on FEL

5. Update Cumulative Statistics & counters

6. Repeat (1-5) until simulation ends

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Stop Event

An event whose occurrence causes termination of the simulation

EXAMPLES:

1. Clock time exceeds value N

2. Number of events exceeds value N

3. Queue reaches length L

~~~ Others ???

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Critical Events

In a basic queuing system, there are 2 critical events.

What are they? 1. ????? 2. ?????

These are events in FEL

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Arrival Event Processing

ARRIVAL*

BEGIN SERVICE*

ENTER QUEUE

ServerBUSY?

No Yes

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Complete Service Event Processing

Complete Service

AnotherIN Q?

YESNO Remove from Q

Begin Service*

Server Idle

Generating Events Initialize

Stop event (if stopping on TIME) First Arrival (of each type)

Next Arrival As an Arrival is removed

Complete Service As an arrival Begins Service

Note * on flowcharts new event generated

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Queuing System Components

Queue Calling population Discipline Capacity

Arrivals Times, rates Nature of

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Queuing System Components

Services Times Nature of

System Number of queues Number of servers State variables Capacity Nature of Arrivals/ Departures

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Characteristics

Key elements: Customers and Servers Calling Population: set of potential

customers - finite vs. infinite System Capacity: the total number which

may wait and be served at any given time Finite vs. infinite Arrival rate vs. effective arrival rate

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Characteristics (cont.)

Arrival Process Characterized by inter-arrival times of

successive customers Scheduled vs. random 1 at a time or batches Poisson Arrivals – independence Examples

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Introduction to Queuing Models Queue = Waiting line Customer = any entity that may

request “service” from a system Typical Measures of System

Performance Server utilization Length of waiting lines Delays of customers

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Queuing Models (cont.)

Input Parameters Arrival rates Service demand Service rate Number & arrangements of

servers

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Start-up vs. Wind-down Conditions

Start-up What is state of system when simulation

starts? Empty? Full? Initialization?

Wind-down How is simulation stopped? Are customers left in system? What do you

do with them?

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Queuing Models

Mathematical Analysis vs. Simulation Analysis Topics to be addressed

Dynamic behavior General characteristics Meaning and relationships of the important

performance measures Estimation of performance measures Effect of varying input parameters Mathematical solutions to basic models

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Queue Attributes

# of Phases or Stations (sequential) # of Channels (parallel) # of Servers Blockers-non blocking stations Capacity Discipline (FIFO, LIFO, Priority, etc.)

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Queue Behavior

Balk: upon arrival, customer decides not to enter the system

Renege: after being in queue for some period of time, customer leaves system

Jockey: to change queues after entering one queue

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Queue Behavior

Priority: a number affecting the processing of customers

Preempt: to stop serving one customer before completion in order to begin serving another customer

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Single Server-Single Queue

Arrive Server DepartQueue

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Parallel Servers – Same Type Single Queue

Arrive

DepartQS

S

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Parallel Servers & QueuesDifferent Servers

A1 Q1 S1 D

A2 Q2 S2 D

A1 & A2 have different arrival rates.

S1 & S2 are different types w/ different rates.

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Parallel Servers

S1

S2

Arrive

DepartQ

S1 & S2 provide same service but may have different service rates. Choice between S1 & S2 may be rule-based or random.

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Sequential Servers

Q1 S1 Q2 S2

A D

Each customer must receive both services.

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Goals of Simulation

Common Questions1. Average Queue Length?

2. Amount (%) of server Idle Time? (Utilization)

3. Mean Waiting time of Customers?

4. Others?

Consider

Information Cost Value

Simulation Methodology

1. Plan

2. Model

3. Validate & Verify

4. Simulate

5. Apply

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Simulation Methodology

1. Plan Define problem & factors that affect the

system Estimate resources needed to observe

system and collect data Determine feasibility of continuing

Consider reduction Collect info.- interviews, literature

search, observation

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Methodology (cont.)

2. Model Construct a REPRESENTATION

consisting of the minimal set possible

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Methodology (cont.)

3. Validate and Verify Validate: to ensure that the model accurately

represents the system Verify: to ensure that the program accurately

represents the model How? – historical data & predictions

Statistical tests Sensitivity Analysis

Reasons for Failure to validate or verify

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Methodology (cont.)

4. Apply What is output? How should the results be

interpreted? How can we use the results? How can we communicate the results

to others?

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Steady State

The system is running in such a way that state variables (statistics) experience only small variations

Must consider “start- up” & “wind- down” conditions

How can steady state be recognized? Why do we care?

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Conway’s Method(Determining Steady State)

Take snapshots of some stats – independent, not cumulative

Rule: throw out first intervals such that they are min or max. When first interval is not, then in steady state.

Limits: Sensitive to interval size.

Which stats should be considered?

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Emshoff & Sisson Method(Determining Steady State)

Apply Conway to reduce the number of intervals. Look at the individual points in the set. Determine the % of values above & below the mean. Use Chi Square test to determine if the next interval is likely to come from the previous cumulative population.

Allows for gradual changes in data, but spots dramatic or sudden changes.

World Views (3)

1. Event Scheduling

2. Process Interaction

3. Activity Scanning

Way we view of the model & Interactions Languages may favor one view View may be hidden from user

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Event Scheduling (variable time advance)

Approach we have been discussing Schedule & Process each individual event,

updating System State as each is processed

Typical approach for simulation in high-level language Main: loops, removing events from FEL &

calling functions Functions: begin-service, enter-queue, end-

service, etc. 55

Process Interaction (variable time advance)

View entities in terms of process they follow; their life cycle

Process: time sequenced list of events, activities, & delays, including demands for resources, that define the life cycle of entity as it moves through system

Underlying support is likely event-based Simscript language

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Process Example

Customer A Definition Arrive at business Get in Queue A Request Service A Receive Service A End Service A Leave business

Customer B Definition Arrive at business Get Cart Get in Queue A Request Service A Receive Service A End Service A Return Cart Leave business

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Activity Scanning (time-slice)

Uses fixed time increment & rule-based approach to determine when activities begin

At each time advance, conditions for each activity checked, if true then activity starts

Simple, can be modular, easily maintainable

Repeated scanning can make simulation run slowly

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Other World Views

Hybrids Some languages, systems support

multiple views Many simulation environments “hide”

approach with GUI

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Next!

Read Implementation Paper posted on Class Web Site

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