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NETW 7
odel
and
Simulat
Amr El Mo
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People and Resources
• Instructor: Amr El Mougy
• Email: [email protected]
• Office hours: Monday 2:00-3:00, Thursday 3:00-4:00
• Office: C7.312
• TA: Maggie Mashaly
• Email: [email protected]
• Office hours:
• Office:
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Assessment
Assignments
10%
Quizzes (best 2/3)
10%
Project
15%
Mid-term
25%
Final
40%
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Pre-Requisites
•
Probability• MS-Excel
• Programming skills
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Textbook• Author: Averill M. Law
• Title: “Simulation Modeling and Analysis”, Fourth Edition
• Publisher: McGraw-Hill Higher Education
• Year: 2007
Notes:
- The codes in this book are written in C++. However, simulationthe course will be done using Excel. Ideas from this book will b
- Part of the contents of the slides are copyrighted to Dr. Akram
- These slides are not meant to be comprehensive lecture noonly remarks and pointers. The material presented here is notstudying for the course. Your main sources for studying are and your own lecture notes
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Course Outline
• Introduction to simulation
• Simulation examples in Excel spreadsheets
• General principles of simulation
• Statistical models in simulation
• Queuing models• Random number generation
• Random variate generation
• Monte-Carlo simulation
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Lecture (1)
Introduction to
Systems andSimulation
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Systems
Systems: a group of objects joined together in sregular interaction or interdependence towards accomplishment of some purpose
Example: A production system
manufacturing automobiles.Machines, components and
workers operate jointly to
produce vehicles
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System Environment• A system is affected by changes that occur outside its bound
Such changes are said to occur in the system environment• The boundary between the system and its environment
depend on the purpose of the study
• Example: Bank System
- There is a limit on the maximum interest rate that can
be paid- For a study of a single bank, this would be an example of a
imposed by the environment
- For a study of the effect of monetary laws on the banking
the setting of the limit would be an activity of the system
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Entity
Attribute
StateActivity
Event
System Components
System
Object of interest
in the system
Propert
entity
The collection o
necessary to des
at a particular ti
objectives of the
An action that takes place
over a period of specified
length and changes the
state of the system
An instantaneous
occurrence that may
change the state of
the system
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System Components
Endogenous:Activities and events occurring
within a system
Exogenous:Activities and events occurring outside the sy
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ExampleAttribu
Balance in the cust
Activity:
Making deposits
State Variables:
# busy tellers, # customers
waiting in line or being served,
arrival time of next customer
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Examples
System Entities Attributes Activities Events
Railway Passengers Origin, destination TravelingArrival at station,
arrival at
destination
N
w
Production MachinesSpeed, capacity,
breakdown rate
Welding,
stampingBreakdown
(
Communications Messages Length, destination TransmittingArrival at
destination
Inventory Warehouse Capacity Withdrawal Demand
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Types of Systems
Discrete CState variables change
instantaneously at
separated points in time
Example: Bank
Number of customerschanges only when
customer arrives or departs
St
co
ti
Ex
Poco
re
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Note
•
It is often possible to use discrete event simulatioapproximate the behaviour of a continuous systegreatly simplifies the analysis
“ Few systems in practice are wholly discrete or
continuous. But since one type of change domina
most systems, it will usually be possible to classif
system as being discrete or continuous” [Law, 200
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Ways to Study a System [Law
System
Experiment
with the
Actual System
Experiment
with a Model
of the System
Physical
Model
Mathematical
Model
Analytical
SolutionSimu
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Why are Models Used?
•
It is not possible to experiment with the actual system, e.g.:experiment is destructive
• The system might not exist, i.e. the system is in the design s
Example: Bank
- Reducing the number of tellers to study the effect on the lewaiting lines may annoy the customers such that they will maccounts to a competitor
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Models
• A model is a representation of a system for the purp
studying that system• It is only necessary to consider those aspects of the s
that affect the problem under investigation
• The model is a simplified representation of the syste
•The model should be sufficiently detailed to permit vconclusions to be drawn about the actual system
• Different models of the same system may be requirepurpose of the investigation changes
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Types of Models
• A Mathematical Model utilizes symbolic notations and equrepresent a system
- Example: current and voltage equations are mathematical man electric circuit
• A Physical Model is a larger or smaller version of an object
- Example: enlargement of an atom or a scaled version of thesystem
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Classifications of Simulation Mo
Static Dynamic
Deterministic Stochastic
Discrete Continuous
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Static and Dynamic Models
Static
• i.e. Monte Carlo
Simulation – Represents
a system at a particular
point in time• Example: Simulation of
a coin toss game
Dynamic
• Represents syst
they change ove
• Example: The
simulation of afrom 9:00am – 4
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Deterministic and Stochastic Mo
Deterministic
• Contain no random variables
• Has a known set of inputs that
will result in a unique set of
outputs
• Example: Patients arriving at
the dentist’s office exactly at
their scheduled appointments
Stochastic
• Has one or more random
• Random inputs lead to r
outputs
• Random outputsonly
the true characteristics
• Example: random arriva
Output may be average
waiting customers, aver
time. This output is onlyestimate of the system
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Discrete and Continuous Mode
Discrete
• Not always used to simulate a
discrete system
• Example: Tanks and pipes may
be modeled discretely, even
though the flow is continuous
Continuou
• Not always used to
continuous system
• The choice of whether to use a discrete or continuous model
on the characteristics of the system and the objectives of the
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Introduction to Simulation
Simulation is the imitation of a real-world procsystem over time [Banks et al.]
It is used for analysis and study of complex syst
Simulation requires the development of a simu
model and then conducting computer-based expwith the model to describe, explain, and predictbehaviour of the real system
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When is Simulation Appropria
Simulation enables the study of, and intewith, the internal actions of a real system
The effects of changes in state variables omodel’s behaviour can be observed
The knowledge gained from the simulatiomodel can be used to improve the design real system under investigation
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When is Simulation Appropria
Changing inputs and observing outputs can prvaluable insights about the importance of varia
and how they interact
Simulations can be used to experiment with d
designs and policies before implementation soprepare for what might happen
Simulations can be used to verify analytic solu
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When is Simulation not Appropr
The problem can be solved by common senseThe problem can be solved analytically
It is less expensive to perform direct experime
Costs of modeling and simulation exceed savi
Resources or time are not available
Lack of necessary data
System is very complex or cannot be defined
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Advantages of Simulation
Effects of variations in the system parameters can be owithout disturbing the real system
New system designs can be tested without committingfor their acquisition
Hypotheses on how or why certain phenomena occurtested for feasibility
Time can be expanded or compressed to allow for speslow down of the phenomenon under investigationInsights can be obtained about the interactions of var
their importance
Bottleneck analysis can be performed in order to discowork processes are being delayed excessively
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Disadvantages of Simulation
Model building requires special trainingSimulation results are often difficult to interp
Most simulation outputs are random variableson random inputs – so it can be hard to distingwhether an observation is the result of systemrelationship or randomness
Simulation modeling and analysis can be timeconsuming and expensive
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Offsetting the Disadvantages Simulation
Utilize simulation packages that only need inptheir operation, e.g.: SIMULINK, MS-Excel
Many simulation packages have output analyscapabilities, e.g. MATLAB, Excel
Simulation has become faster due to advancehardware
St i Si l ti St d
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Steps in a Simulation Study
Phase I
• Problem formulation: statement of the problem
• Setting of objectives and overall design: questions to be answered by the simulation
Phase II
• Model conceptualization: abstract the essential features of the problem, select and modify basic as
characterize the system, start with a simple model, enrich and elaborate the model
• Data collection: start early because it may take a lot of time
• Model translation: programming
• Verification: is the computer program functioning properly
• Validation: does the model accurately represent the system
Phase III
• Experimental design: which alternatives (designs) to simulate
• Production runs and analysis: to estimate measures of performance for the system designs that hav
Measures of performance may depend on statistical analysis, e.g.: average, probability, frequency, e
• More runs? a sufficient number is needed to guarantee statistical accuracy
Phase IV
• Documentation
• Implementation
Problem Formulation1
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Setting of Objectives and
Overall Project Plan
Model Conceptualization
Model Translation
Verified
Validated
Experimental Design
Production Runs and Analysis
More Runs
Documentation
and Reporting
Data Collection
Yes
Yes
No
NoNo
2
3 4
5
6
7
8
9
10
11
Yes No
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