modeling & simulation: an introduction some slides in this presentation have been copyrighted to...
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Modeling & Simulation: An Introduction
Some slides in this presentation have been copyrighted to Dr. Amr Elmougy
© Tallal Elshabrawy
Systems
Systems:
A group of objects joined together in some regular interaction or interdependence towards the accomplishment of some purpose.
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Systems
Systems Environment:
A system is affected by changes that occur outside its boundaries. 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
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Boundary
System Environment
i/p
o/p
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System Components
System
Entity
Attribute
StateActivity
Event
Object of interest in the system
Property of an entity
Collection of variables necessary to describe the system at a particular time,
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 Example
Queuing System
Packet
Entity
Length, Destination
Attribute
Nof Packets
State
FIFO
Activity
Packet Arrival
Event
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Discrete Continuous
State variables change
instantaneously at separated points in time
State variables may change
constantly with respect to time
Types of Systems
Slotted ALOHA Vs Pure ALOHA
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Simulation of Continuous Systems
It is feasible to study continuous systems analytically
mathematically
However when it comes to simulation it is challenging.
Solutions: Approximate continuous system as a discrete event
simulation (Discretization)
Event-Driven Simulations
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System
Experiment with the
Actual System
Experiment with a Model of the System
Physical Model
Mathematical Model
Analytical Solution Simulation
Approaches to Studying Systems
NETW 707 Modeling & Simulation
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Why do we Need Modeling
It is not possible to experiment with the actual system, e.g.: the experiment is destructive
The system might not exist, i.e. the system is in the design stage
In essence it boils down to:
Time Cost Complexity
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A model is a representation of a system for the purpose of studying that system
It is only necessary to consider those aspects of the system that affect the problem under investigation
The model is a simplified representation of the system
The model should be sufficiently detailed to permit valid conclusions to be drawn about the actual system
Different models of the same system may be required as the purpose of the investigation changes
Models
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Modeling Examples
Grade of Service in 2G Cellular Networks
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Modeling Examples
Grade of Service in 2G Cellular Networks
Nof Channels
Aggregate Arrivals
All Servers Busy = Calls Blocked or Delayed
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Approaches to Solving Models
Mathematically:
Derivation of equations to answer questions regarding the model.
Derivation Process and Solving could be handled: Analytically: Derives closed form (hopefully concise)
expressions
Numerically: Utilizes the help of numerical approximations (by hand or by programming)
By Simulation: Building a program that tries to imitate the behavior of the model under study
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Introduction to Simulations
Simulation is the imitation of a real-world process or system over time [Banks et al.]
It is used for analysis and study of complex systems
Simulation requires the development of a simulation model
Computer-based experiments are conducted to describe, explain, and predict the behaviour of the real system
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Advantages of Simulations
Effects of variations in the system parameters can be observed without disturbing the real system
New system designs can be tested without committing resources for their acquisition
Hypotheses on how or why certain phenomena occur can be tested for feasibility
Time can be expanded or compressed to allow for speed up or slow down of the phenomenon under investigation
Insights can be obtained about the interactions of variables and their importance
Bottleneck analysis can be performed in order to discover where work processes are being delayed excessively
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Disadvantages of Simulations
Model building requires special training
Simulation results are often difficult to interpret. Most simulation outputs are random variables - based on random inputs – so it can be hard to distinguish whether an observation is the result of system inter-relationship or randomness
Simulation modeling and analysis can be time consuming and expensive
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The problem can be solved by common sense
The problem can be solved analytically
It is less expensive to perform direct experiments
Costs of modeling and simulation exceed savings
Resources or time are not available
Lack of necessary data
System is very complex or cannot be defined
When are Simulations not Necessary
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Modifying System Models
Adopting Distributed/Parallel Processing
Utilizing customized simulation packages for the system under study
Looping around Simulation Limitations
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Static Dynamic
Discrete Continuous
Classification of Simulation Models
Deterministic Stochastic
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Static
• Monte Carlo Simulation Represents a system snapshot at a particular point in time
Dynamic
• Represents systems as they change over time
Static and Dynamic models
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Deterministic• Contain no random
variables• Has a known set of
inputs that will result in a unique set of outputs
Stochastic• Has one or more
random variables• Random inputs lead to
random outputs• Random outputs only
estimates of the true characteristics of the system
Deterministic and Stochastic Models
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Discrete
• Simulation progress over discrete time instants
Continuous
• Simulation progresses over continuous time
Discrete and Continuous Models
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