1. Modeling & Simulation: An Introduction Some slides in this presentation have been copyrighted to Dr. Amr Elmougy

2. © Tallal Elshabrawy Systems Systems: A group of objects joined together in some regular interaction or interdependence towards the accomplishment of some purpose. 2

3. © Tallal Elshabrawy 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 3 Boundary System Environment i/p o/p

4. © Tallal Elshabrawy System Components System EntityAttributeStateActivityEvent 4 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

5. © Tallal Elshabrawy System Components Example Queuing System Packet Entity Length, Destination Attribute Nof Packets State FIFO Activity Packet Arrival Event 5

6. © Tallal Elshabrawy DiscreteContinuous 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

7. © Tallal Elshabrawy 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 7

8. © Tallal Elshabrawy Approaches to Studying Systems 8 NETW 707 Modeling & Simulation

9. © Tallal Elshabrawy 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: 9 TimeCostComplexity

10. © Tallal Elshabrawy  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

11. © Tallal Elshabrawy Modeling Examples 11 Grade of Service in 2G Cellular Networks

12. © Tallal Elshabrawy Modeling Examples 12 Grade of Service in 2G Cellular Networks Nof Channels Aggregate Arrivals All Servers Busy = Calls Blocked or Delayed

13. © Tallal Elshabrawy 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 13

14. © Tallal Elshabrawy 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

15. © Tallal Elshabrawy 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

16. © Tallal Elshabrawy 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

17. © Tallal Elshabrawy  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

18. © Tallal Elshabrawy  Modifying System Models  Adopting Distributed/Parallel Processing  Utilizing customized simulation packages for the system under study Looping around Simulation Limitations

19. © Tallal Elshabrawy Static Dynamic DiscreteContinuous Classification of Simulation Models DeterministicStochastic

20. © Tallal Elshabrawy 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

21. © Tallal Elshabrawy 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

22. © Tallal Elshabrawy Discrete Simulation progress over discrete time instants Continuous Simulation progresses over continuous time Discrete and Continuous Models