Introduction to Discrete Event Simulation Customer population Service system Served customers...
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Introduction to Discrete Event Simulation Customer Customer population population Service system Service system Served Served customers customers Waiting line Priori ty rule Service facilit ies Figure C.1 Figure C.1 Lotfi K. Gaafar
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Transcript of Introduction to Discrete Event Simulation Customer population Service system Served customers...
Introduction to Discrete Event Simulation
Customer Customer populationpopulation
Service systemService system
Served Served customerscustomers
Waiting line
Priority rule
Service facilities
Figure C.1Figure C.1Lotfi K. Gaafar
What is Simulation?
“Simulation is the process of designing a model of a real system and conducting experiments with this model for the purpose either of understanding the behavior of the system or of evaluating various strategies (within the limits imposed by a criterion or set of criteria) for the operation of the system.”
- R.E. Shannon
What is a System?
A system is defined as a group of objects that are joined together in some regular interaction or interdependence toward the accomplishment of some purpose.
A system that does not vary with time is static whereas one that varies is dynamic.
Components of a System
An entity is an object of interest in the system (flows through the system).
An attribute is a property of an entity. A given entity can possess many attributes.
A variable is a global value used to track various system activities.
An activity represents a time period of specified length.
A resource carries out an activity.
A Queue is a waiting space for entities when resources are busy.
The state of a system is defined to be that collection of variables (e.g. entities, attributes, activities) necessary to describe the system at any time, relative to the objectives of the study. The progress of the system is studied by following the changes in the state of the system.
An event is defined as an instantaneous occurrence that may change the state of the system.
What is a Model?
A model is a high level specification to abstract from reality a description of a dynamic system.
Types of models:
physical : scale models, prototype plants, ...
mathematical : analytical queuing models, linear programs, simulation, etc.
Modeling is a way of thinking and reasoning about systems.
Use of a Model
To study system behavior in the design stage, before such systems are built.
To communicate a system design
To predict the performance of new systems under varying sets of circumstances.
“What if” questions about the real-world system.
Simulation Potential
Specifying performance requirements
Evaluating design alternatives
Comparing two or more systems
Determining the optimal value of a parameter (system tuning)
Finding the performance bottleneck (bottleneck identification)
Characterizing the load on the system (workload characterization)
Determining the number and sizes of components (capacity planning)
Predicting the performance at future loads (forecasting)
Why use Simulation
Study none existing systems
Faster experiments
Cheaper experiments
Avoid political problems
Try wild ideas
Experiment under extreme conditions
Training
Support operational decisions
STEPS IN SIMULATION STUDY
Problem Definition
Knowledge/data Acquisition
Model Building
Model Implementation
Model Verification/validation
Experiment Design
Simulation Runs
Output Analysis
Problem Solution
Ways to Study a System
The Queuing Model
Customer Customer populationpopulation
Service systemService system
Served Served customerscustomers
Waiting line
Priority rule
Service facilities
Figure C.1Figure C.1
M/M/1 Queue: Analytical Solution
= Average utilization of the server == Average utilization of the server =
LL = Average number of customers in the service system = = Average number of customers in the service system = ––
LLqq = Average number of customers in the waiting line = = Average number of customers in the waiting line = L L
WW = Average time spent in the system, including service = = Average time spent in the system, including service =11
––
WWqq = Average waiting time in line = = Average waiting time in line = W W
Arrival Rate Service Rate
Exponential arrivals and service timesExponential arrivals and service times
Excel Simulation
Use ‘–*ln(R)’ to generate obsevaions from the exponential distribution, where is the average and R is a random number between 0 and 1 generated using the RAND() function of Excel.
