intro modeling simulation
TRANSCRIPT
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Prof M S Prasad,
@2008
Based on open literature and reports . For special system model see Session II
presentations.
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Introduction to Simulation
A Simulation is the imitation of the operation of areal-world process or system over time
ASystem is defined to be a set of elements whichinteract or interrelated in some fashion Elements having no relationship with the set of
elements that have been chosen as system can not affect
the system hence irrelevant A System may consist of sub systems or may be a part of
a larger system
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Elements that often make up thesystem are calledEntitiesEntities that comprise a system need
not be tangible e.g, a queuing systemis made up of customers, queue andservers
Customers and servers are physical
entities but queue itself is a concept
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More components of a systemAnAttribute is a property of a system
AnActivity represents a time period of specifiedlength
State of system is defined to be that collection ofvariables necessary to describe the system at any time ,relative to the objective of the study In the study of a bank possible state variables are number of
busy tellers, number of customers waiting in the queue orbeing served, arrival and service times of the next customer
An Event is defined as an instantaneous occurrencethat may change the state of the system
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More terms of a system Endogenous used to describe the activities and
events occurring within a system
Exogenous is used to describe activities and events inthe environment that affect the system
In the bank arrival of a customer is exogenous eventand completion of service of a customer is endogenousevent
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Examples: Production System Entities Machines
Attributes (property of an entity) Speed , Capacity,
Breakdown rateActivities (time period of specified length) Welding,
Cutting, Stamping
Events breakdown
State variables Status of machines busy, idle ordown
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Examples: Communications System Entities Messages
Attributes (property of an entity) Length ,
DestinationActivities (time period of specified length)
Transmitting
Events arrival at destination
State variables Number of messages waiting to betransmitted
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Examples: Inventory System Entities Warehouse
Attributes (property of an entity) Capacity
Activities (time period of specified length) Issue,Receipt
Events Demand
State variables Level of inventory, Backlogged
demands
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Introduction to modelA model is a system that is used as a surrogate for
another system
Reason for using a model Helps in understanding the behaviour of a real system
before it is built
Cost of building and experimenting with a model is less
Models can be used to mitigate risk pilots can be
taught how to cope with wind sheer while landing Models have the capability of scale time or space in
favourable manner wind sheer can be produced ondemand
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Types of ModelsBroadly there are two types
Physical
(Scale models, prototype plants,)
Mathematical
(Analytical queuing models, linearprograms, simulation)
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Ten Types of Models Iconic - physical models that are images of the
real world; dimensions are usually scaled up ordown; for example, models of cars might be
constructed and tested in a wind tunnelAnalog - model that substitutes one set of
properties for another; may be iconic ormathematical; electric resistance often used as ananalog of the friction of a fluid flowing in a pipe;
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Ten Types of Models Stochastic - probabilistic model that usesrandomness to account for non measurablefactors (e.g., weather)
Deterministic - model that does not userandomness but uses explicit expressions forrelationships
Discrete - model where state variables change insteps as opposed to continuously with time (e.g.,number of cattle in a barn); may be deterministicor stochastic
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Ten Types of Models Continuous - model whose state variables change
continuously with time (e.g., biomass in a field);usually sets of differential equations used; initial
conditions required (can be difficult to obtain for somesystems!)
Combined - model where some state variables changecontinuously and others change in steps at event
times; for example, a field of hay might be modeledusing a combined approach with the biomass modeledcontinuously during growth and then as a discreteevent when harvested
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Types of Models Mathematical - abstract model usually written in
equation form
Object-oriented - use objects that are abstractions of
real world objects and develop relationships andactions between objects; comes from field of artificialintelligence
Heuristic - heuristics (rules) are used to model the
system; comes from field of artificial intelligence.
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Static Model
Dynamic Model
Lumped & distributed Models :distributed model use Partial diff equation to Explain spacevarying parameters.
In Lumped model the space variations are defined
in finite numbers making it a differential eqn,
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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 whichwould be impossible, too expensive, or tooimpractical to perform on the system which itportrays.
The operation of the model can be studied, and,from this, properties concerning the behavior ofthe actual system can be inferred.
Introduction 16
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Applications:Designing and analyzing manufacturing systemsEvaluating H/W and S/W requirements for a
computer systemEvaluating a new military weapons system or tacticsDetermining ordering policies for an inventory
systemDesigning communications systems and message
protocols for them
Introduction 17
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Applications:(continued)Designing and operating transportation facilities such
as freeways, airports, subways, or ports
Evaluating designs for service organizations such ashospitals, post offices, or fast-food restaurants
Analyzing financial or economic systems
Introduction 18
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Types of Simulation Models
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System model
deterministic stochastic
static dynamic static dynamic
continuous discrete continuous discrete
Monte Carlo
simulation
Discrete-event
simulation
Continuous
simulation
Discrete-event
simulation
Continuous
simulation
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Stochastic vs. Deterministic
Stochastic simulation: a simulation that containsrandom (probabilistic) elements, e.g., Examples
Inter-arrival time or service time of customers at a restaurant orstore
Amount of time required to service a customer Output is a random quantity (multiple runs required to
analyze output)
Deterministic simulation: a simulation containing
no random elements Examples
Simulation of a digital circuit
Simulation of a chemical reaction based on differential equations
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Static vs. Dynamic Models Static models
Model where time is not a significant variable
Examples Determine the probability of a winning solitaire hand
Static + stochastic = Monte Carlo simulation Statistical sampling to develop approximate solutions to
numerical problems
Dynamic models Model focusing on the evolution of the system under
investigation over time
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Continuous vs. Discrete Discrete
State of the system is viewed as changing at discretepoints in time: arrival of a customer in a queuing system
An event is associated with each state transition Events contain time stamp
Continuous State of the system is viewed as changing continuously
across time: rise if water level in a dam System typically described by a set of differential
equations
Few systems in practice are wholly discrete orcontinuous
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Discrete & Continuous Systems Essential to remember that
A discrete simulation model is not always used to modela discrete system
Similarly, a continuous simulation model is not alwaysused for a continuous system
Simulation models may also be mixed both discreteand continuous
Choice of discrete or continuous simulationmodels is a function of Characteristics of the system
Objective of the study
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Discrete & Continuous Systems Communication channel
Modeled as discrete if characteristics of movement ofeach message is important
Modeled as continuous if f low of messages asaggregate over the channel is important
In this course we will study only
Models that are discrete, dynamic and stochastic
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Discrete event systems (DES) DES are dynamic systems which evolve in time by theoccurrence of events at possibly irregular timeintervals
DES abound in real-world applications Examples include traffic systems
flexible manufacturing systems
computer-communications systems
production lines flow networks.
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Discrete event systems (DES) Most of these systems can be modeled in terms of
discrete events whose occurrence causes the system tochange from one state to another
In designing, analyzing and operating such complexsystems, one is interested not only in performanceevaluation but also in sensitivity analysis andoptimization.
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Discrete event system simulation (DESS)
It is modeling of systems in which the state variablechanges only at a discrete set of points in time
Simulation models are analyzed by numerical
methods rather than by analytical methodsAnalytical methods apply deductive reasoning to solve
Differential calculus can be used to calculate EOQ
In case of simulation model is run rather thansolved
An artificial history of the system is generated (withthe help of computer) based on system characteristicsand observations are collected to be analyzed
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Steps in Simulation Study
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Problem Formulation
Setting objectives & Plan
Data Collection
Model Conceptualization
Verify model
Validate model
Fundamentallyan iterative
processModel Translation
Experimental Design
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Steps in Simulation Study
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Production run & Analysis
More runs?
Documentation & Reporting
Implementation
From previous slide
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Problem Formulation Initial step
Identify controllable and uncontrollable inputs
Identify constraints on the decision variables Define measure of system performance and an
objective function
Develop a preliminary model structure to
interrelate the inputs and the measure ofperformance
May be the problem needs reformulation as thestudy progresses
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Setting Objectives & PlanWhat do you (or the customer) hope to accomplish
with the model May be an end in itself
Predict the weather Train personnel to develop certain skills (e.g., driving)
More often a means to an end Optimize a manufacturing process or develop the most costeffective means to reduce traffic congestion in some part of a city
Often requires developing a business case to justifythe cost Improved efficiency will save the company $$$
Example: electronics Even so, may be hard to justify in lean times
Goals may not be known when you start theproject! One often learns things along the way
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Develop Conceptual Model An abstract (i.e., not directly executable) representationof the system
What should be included in model? What can be leftout?
What abstractions should be used Level of detail Often a variation on standard abstractions Example: transportation
Fluid flow? Queuing network? Cellular automation?
What metrics will be produced by the model? Appropriate choice depends on the purpose of the model
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Data Collection Regardless of the method used to collect the data, the
decision of how much to collect is a trade-off betweencost and accuracy
Constant inter play between construction of the modeland the collection of needed input
Changes with the degree of complexity of the model
Data should be collected for the validation as well
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Model translation Model requires great deal of information and
computation
Needs to be translated into computer recognizableformat using either special purpose or general purposelanguages
Focus of this course will be using Excel for model
buildingArena characteristics will be introduced
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Verification & Validation
Verification focuses on the internal consistency of amodel
Validation is concerned with the correspondencebetween the model and the reality
Validation is applied to those processes which seek todetermine whether or not a simulation is correct withrespect to the "real" system
Validation is concerned with the question "Are we
building the right system?
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Verification & ValidationVerification seeks to answer the question "Are we
building the system right?"
Verification checks that the implementation of the
simulation model (program) corresponds to the modelValidation checks that the model corresponds to
reality
Calibration checks that the data generated by the
simulation matches real (observed) data.
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Experimental DesignAlternatives to be simulated must be determined
Good experimental design Randomization
Replication Local control
For each system decisions needed Length of the initialization period
Length of the simulation run
Number of replication
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Production runs and analysis To measure performance of the simulation system so
designed
Also to determine if more runs needed till results areconsistent
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Documentation & Reporting Two types
Program
Needed if it is to be used again
May need to be applied for different system by differentpeople
For modification
Progress
Provides important written history of simulation project Should be frequent as the project progresses
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Implementation Success depends how well previous steps were
followed .
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M S Prasad : An avid researcher in the field ofSignal processing & Image processing, applicableto defence system. He has been designer of on Board computer
Navigation system, Multiple Target tracking for missiles he started thedigital GIS system in the country and has been responsible for having
a total digital military Ops room . In his span of career , he has beenNetwork security auditor for UNO classified organisations.He is the inventor most secure strategic system for India alongwithPositive Activation& Safing System.(PASS)
He holds 4 patents and has been awarded twice the Best scientist by defenceResearch organisation. Lately he is the chief evangelist of Cloud Security in ASIA.He is recipient of numerous national & International awards. He has published 28 papersin referred journals and 3 in Monographs
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Thanks