INTRODUCTION TO SIMULATION. WHAT IS SIMULATION? The imitation of the operation of a real-world...
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![Page 1: INTRODUCTION TO SIMULATION. WHAT IS SIMULATION? The imitation of the operation of a real-world process or system over time… –Most widely used tool (along.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649ccb5503460f94993f44/html5/thumbnails/1.jpg)
INTRODUCTION TO SIMULATION
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WHAT IS SIMULATION?
• The imitation of the operation of a real-world process or system over time…– Most widely used tool (along LP) for decision making
– Usually on a computer with appropriate software
– An analysis (descriptive) tool – can answer what if questions
– A synthesis (prescriptive) tool – if complemented by other tools
• Applied to complex systems that are impossible to solve mathematically
• This course focuses on one form of simulation modelling – discrete-event simulation modelling.
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APPLICATIONSSystems – facility or process, actual or planned
ExamplesManufacturing facilityBank operationAirport operations (passengers, security, planes, crews, baggage)Transportation/logistics/distribution operationHospital facilities (emergency room, operating room, admissions)Computer networkFreeway systemBusiness process (insurance office)Criminal justice systemChemical plantFast-food restaurantSupermarketTheme parkEmergency-response system
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SYSTEM• A set of interacting components or entities
operating together to achieve a common goal or objective.
• Examples:– A manufacturing system with its machine centers,
inventories, conveyor belts, production schedule, items produced.
– A telecommunication system with its messages, communication network servers.
– A theme park with rides, workers, …
REAL WORLD SYSTEMS OF INTEREST ARE HIGHLY COMPLEX!!!
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WHY & HOW TO STUDY A SYSTEM
System
Experimentwith the
actual system
Experiment with a mathematical model
of the system
MathematicalAnalysis
Simulation
Measure/estimate performanceImprove operationPrepare for failures
IE 325IE 202IE 303
…
IE 324
Experiment with a physical model
of the system
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MATHEMATICAL MODEL
• An abstract and simplified representation of a system• Specifies
– Important components
– Assumptions/approximations about how the system works
• Not an exact re-creation of the original system!• If model is simple enough, study it with Queueing Theory,
Linear Programming, Differential Equations...• If model is complex, Simulation is the only way!!!
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GETTING ANSWERS FROM MODELS
MODEL
Operating Policies
• Single queue, parallel servers
• FIFO
Input Parameters
• No of servers
• Inter-arrival Time Distribution
• Service Time Distributions
Output Parameters
• Waiting Times
• System Size
• Utilizations
(X) (Y)
Y = f (X)
ACTUAL SYSTEM
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STOCHASTIC MODELS
• Randomness or uncertainty is inherent
• Example: Bank with customers and tellers
ACTUAL SYSTEM
QUEUEING MODEL
IE325
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Static (Monte Carlo) Dynamic Systems
Represents the system at a particular point in time
IID observations
Represents the system behaviour over time
Continuous Simulation:
• (Stochastic) Differential Equations
Discrete Event Simulation:
• System quantities (state variables) change with events
• Estimation of
• Risk Analysis in Business
• Water Level in a Dam
CLASSIFICATION OF SIMULATION MODELS
• Queueing Systems
• Inventory Systems
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HOW TO SIMULATE• By hand
– Buffon Needle and Cross Experiments (see Kelton et al.)
• Spreadsheets
• Programming in General Purpose Languages– Java
• Simulation Languages– SIMAN
• Simulation Packages– Arena
Issue: Modeling Flexibility vs. Ease of Use
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ADVANTAGES OF SIMULATION• When mathematical analysis methods are not available, simulation may be the only investigation tool
• When mathematical analysis methods are available, but are so complex that simulation may provide a simpler solution
• Allows comparisons of alternative designs or alternative operating policies
• Allows time compression or expansion
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DISADVANTAGES OF SIMULATION
• For a stochastic model, simulation estimates the output while an analytical solution, if available, produces the exact output
• Often expensive and time consuming to develop• An invalid model may result with confidence in
wrong results.
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STEPS IN A SIMULATION STUDY
Problemformulation
Setting ofobjectivesand overallproject plan
Modelconceptualization
Datacollection
Modeltranslation
Verified?
No
Validated?
No
No ExperimentalDesign
Production runsand analysis
More runs?
Documentationand reporting
No
Implementation
Yes
YesYes
Yes
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PROBLEM FORMULATION
• A statement of the problem– the problem is clearly understood by the simulation
analyst– the formulation is clearly understood by the client
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SETTING OF OBJECTIVES & PROJECT PLAN
Project Proposal• Determine the questions that are to be answered
• Identify scenarios to be investigated
• Decision criteria
• Determine the end-user
• Determine data requirements
• Determine hardware, software, & personnel requirements
• Prepare a time plan
• Cost plan and billing procedure
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STEPS IN A SIMULATION STUDY
Problemformulation
Setting ofobjectivesand overallproject plan
Modelconceptualization
Datacollection
Modeltranslation
Verified?
No
Validated?
No
No ExperimentalDesign
Production runsand analysis
More runs?
Documentationand reporting
No
Implementation
Yes
YesYes
Yes
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MODEL CONCEPTUALIZATION
Assumed system
Conceptual model
Real World System
Logical model
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CONCEPTUAL MODEL
• Abstract essential features– Events, activities, entities, attributes, resources,
variables, and their relationships– Performance measures – Data requirements
• Select correct level of details (assumptions)
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LEVELS OF DETAIL
• Low levels of detail may result in lost of information and goals cannot be accomplished
• High levels of detail require:– more time and effort– longer simulation runs– more likely to contain errors
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Accuracy of the model
Scope & level of details
Scope & level of details
Cost of model
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COMPONENTS OF A SYSTEM
Entity: is an object of interest in the system
– Dynamic objects — get created, move around, change status, affect and are affected by other entities, leave (maybe)
– Usually have multiple realizations floating around
– Can have different types of entities concurrently
Example: Health Center
Patients
Visitors
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COMPONENTS OF A SYSTEM
Attribute: is a characteristic of all entities, but with a specific value “local” to the entity that can differ from one entity to another.
Example: Patient
Type of illness,
Age,
Sex,
Temperature,
Blood Pressure
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COMPONENTS OF A SYSTEM
Resources: what entities compete for– Entity seizes a resource, uses it, releases it– Think of a resource being assigned to an entity, rather than an
entity “belonging to” a resource– “A” resource can have several units of capacity which can be
changed during the simulation
Example: Health Center
Doctors, Nurses
X-Ray Equipment
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COMPONENTS OF A SYSTEMVariable: A piece of information that reflects some characteristic of the whole system, not of specific entities– Entities can access, change some variables
Example: Health Center
Number of patients in the system,
Number of idle doctors,
Current time
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• State: A collection of variables that contains all the information necessary to describe the system at any time
Example: Health Center
{Number of patients in the system,
Status of doctors (busy or idle),
Number of idle doctors,
Status of Lab equipment, etc}
COMPONENTS OF A SYSTEM
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• Event: An instantaneous occurrence that changes the state of the system
Example: Health Centre
Arrival of a new patient,
Completion of service (i.e., examination)
Failure of medical equipment, etc.
COMPONENTS OF A SYSTEM
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COMPONENTS OF A SYSTEM
Activity: represents a time period of specified length.
Example: Health Center
Surgery,
Checking temperature,
X-Ray.
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LOGICAL (FLOWCHART) MODEL
• Shows the logical relationships among the elements of the model
Q(t)> 0 ?
3
YESNO
2 Departure event
Q(t)=Q(t)-1B(t)=0
Generate service & schedule new departure
Collect & update statistics TB, TQ, TL, N
L(t)=L(t)-1
L : # of entities in systemQ : # of entities in queueB : # of entities in server
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STEPS IN A SIMULATION STUDY
Problemformulation
Setting ofobjectivesand overallproject plan
Modelconceptualization
Datacollection
Modeltranslation
Verified?
No
Validated?
No
No ExperimentalDesign
Production runsand analysis
More runs?
Documentationand reporting
No
Implementation
Yes
YesYes
Yes
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DATA COLLECTION & ANALYSIS
• Collect data for input analysis and validation• Analysis of the data
– Determine the random variables
– Fit distribution functions
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STEPS IN A SIMULATION STUDY
Problemformulation
Setting ofobjectivesand overallproject plan
Modelconceptualization
Datacollection
Modeltranslation
Verified?
No
Validated?
No
No ExperimentalDesign
Production runsand analysis
More runs?
Documentationand reporting
No
Implementation
Yes
YesYes
Yes
![Page 32: INTRODUCTION TO SIMULATION. WHAT IS SIMULATION? The imitation of the operation of a real-world process or system over time… –Most widely used tool (along.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649ccb5503460f94993f44/html5/thumbnails/32.jpg)
MODEL TRANSLATION
• Simulation model executes the logic contained in the flow-chart model
Coding
General Purpose Language Special Purpose Simulation Language/Software
JAVA, C++, Visual BASIC
Examples:
SIMAN, ARENA, EXTEND
Examples:
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ARENA EXAMPLE
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JAVA EXAMPLEpublic static void main(String argv[]){
Initialization();
//Loop until first "TotalCustomers" have departedwhile (NumberofDepartures < TotalCustomers){
Event evt = FutureEventList[0]; //get imminent eventremovefromFEL(); //be rid of itClock = evt.get_time(); //advance in timeif (evt.get_type() == arrival) ProcessArrival();else ProcessDeparture();
}
ReportGeneration();}
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STEPS IN A SIMULATION STUDY
Problemformulation
Setting ofobjectivesand overallproject plan
Modelconceptualization
Datacollection
Modeltranslation
Verified?
No
Validated?
No
No ExperimentalDesign
Production runsand analysis
More runs?
Documentationand reporting
No
Implementation
Yes
YesYes
Yes
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VERIFICATION AND VALIDATION
• Verification: the process of determining if the operational logic is correct.– Debugging the simulation software
• Validation: the process of determining if the model accurately represents the system.– Comparison of model results with collected data from
the real system
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VERIFICATION AND VALIDATION
Conceptual model
Logical model
Simulation model
Real World System
VERIFICATION
VALIDATION
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STEPS IN A SIMULATION STUDY
Problemformulation
Setting ofobjectivesand overallproject plan
Modelconceptualization
Datacollection
Modeltranslation
Verified?
No
Validated?
No
No ExperimentalDesign
Production runsand analysis
More runs?
Documentationand reporting
No
Implementation
Yes
YesYes
Yes
![Page 39: INTRODUCTION TO SIMULATION. WHAT IS SIMULATION? The imitation of the operation of a real-world process or system over time… –Most widely used tool (along.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649ccb5503460f94993f44/html5/thumbnails/39.jpg)
EXPERIMENTAL DESIGN
• Alternative scenarios to be simulated
• Type of output data analysis (steady-state vs. terminating simulation analysis)
• Number of simulation runs
• Length of each run
• The manner of initialization
• Variance reduction
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ANALYSIS OF RESULTS
• Statistical tests for significance and ranking– Point Estimation– Confidence-Interval Estimation
• Interpretation of results
• More runs?
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STEPS IN A SIMULATION STUDY
Problemformulation
Setting ofobjectivesand overallproject plan
Modelconceptualization
Datacollection
Modeltranslation
Verified?
No
Validated?
No
No ExperimentalDesign
Production runsand analysis
More runs?
Documentationand reporting
No
Implementation
Yes
YesYes
Yes
![Page 42: INTRODUCTION TO SIMULATION. WHAT IS SIMULATION? The imitation of the operation of a real-world process or system over time… –Most widely used tool (along.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649ccb5503460f94993f44/html5/thumbnails/42.jpg)
DOCUMENTATION & REPORTING
• Program Documentation– Allows future modifications
– Creates confidence
• Progress Reports– Frequent reports (e.g. monthly) are suggested
– Alternative scenarios
– Performance measures or criteria used
– Results of experiments
– Recommendations
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IMPLEMENTATION