Course Description:
The syllabus consists of introduction to system, modelling and simulation of different types of systems. It includes the modelling of systems, its validation, verification and analysis of simulation output. It comprises the concept of queuing theory, random number generation as well as study of some simulation languages.
Course Objectives:
To make students understand the concept of simulation and modelling of real time systems.
Course Contents:
Unit 1: Introduction to Simulation (6 Hrs.)
System and System Environment
Concept of system and system environment
Components of System
System, entities, attributes, events, state variables and other terms related to system
Discrete and Continuous System
Introduction and examples
System Simulation, Model of a System, Types of Model
Introduction to system simulation and system model, different types of models and examples (physical/ mathematical, static/dynamic, discrete/continuous, deterministic/stochastic)
Use of Differential and Partial differential equations in Modelling
Brief review of how differential and partial differential equations can be used in system- modelling
Advantages, Disadvantages and Limitations of Simulation, Application Areas
Advantages, Disadvantages, Limitations and Applications of system simulation
Phases in Simulation Study
Study of different phases during simulation
Unit 2: Simulation of Continuous and Discrete System (7 Hrs.)
Continuous System Models Analog Computer, Analog Methods, Hybrid Simulation, Digital-Analog Simulators, Feedback Systems
Concept, examples, use of differential equations for modelling continuous system
Discrete Event Simulation, Representation of time, Simulation Clock and Time Management
Concept of discrete event simulation, time representation and management
Arrival Processes - Poisson Processes, Non-stationary Poisson Processes, Batch Arrivals
Concept of arrival pattern, generation of arrival pattern using Poisson and Non-stationary Poisson with example, Introduction to batch arrival processes
Models of Gathering statistics
Different statistics (like counts, summary measures, utilization, occupancy, distributions etc) that are needed to generate report and methods to gather such statistics
Probability and Monte Carlo Simulation
Concept with an example
Unit 3: Queuing System (6 Hrs.)
Characteristics and Structure of Basic Queuing System, Models of Queuing System
Concept of Basic Queuing System, Its Characteristics, Discipline, Models and related terms
Queuing notation
Kendall’s notation for queuing system
Single server and Multiple server Queuing Systems
Concept and examples of single server and multiple server queue
Measurement of Queuing System Performance, Elementary idea about networks of Queuing with particular emphasis to computer system
Performance evaluation of queuing system (M/M/1) in terms of parameters like average number of customers, average time spent in system and in queue per customer, server utilization, cost of waiting time and idle time, with numerical examples
Elementary idea about network of queuing with particular emphasis to computer system
Introduction of network of queues
Applications of queuing system
Examples of computer system related queuing systems and other applications of queuing system
Unit 4: Markov Chains (2 Hrs.)
Features, Process Examples, Applications
Concept, Features, Examples, Applications of Markov Chains
Unit 5: Random Numbers (7 Hrs.)
Random Numbers and its properties, Pseudo Random Numbers
Concept, properties and types of random numbers
Methods of generation of Random Number
Linear Congruential Method (mixed and multiplicative), Mid square method
Tests for Randomness - Uniformity and independence
- Uniformity testing – K-S Test and Chi – square test
- Independent testing – Gap test, Auto correlation test, Poker test upto 4 digits
Random Variate Generation
Random variate generation via inverse transform technique and acceptance-rejection technique
Unit 6: Verification and Validation (4 Hrs.)
Design of Simulation Models Verification of Simulation Models, Calibration and Validation of the models, Three-Step Approach for Validation of Simulation Models, Accreditation of Models
Concept of Model Building; verification; validation and calibration; three step approach, Introduction to accreditation of models
Unit 7: Analysis of Simulation Output (4 Hrs.)
- Confidence Intervals and Hypothesis Testing, Estimation Methods (Point Estimation and confidence interval with examples), Simulation run statistics, Replication of runs, Elimination of initial bias
Unit 8: Simulation of Computer Systems (9 Hrs.)
- Simulation Tools
- Simulation Languages - GPSS
- study and use of language with related problem
- study of different blocks of GPSS blocks
- concept of queue, storage, facility, multi-server queue, decision making
- Case Studies of different types of Simulation Models, Construction of sample mathematical models
Laboratory Work:
After completing this course, students should have practical knowledge regarding simulation of some real time systems (continuous and discrete event systems), Queuing Systems, Random Number generations as well as study of Simulation Tools and Language. Verification and validation of models can be done, the analysis of outputs produced in the laboratory exercise can also be performed. The laboratory work should include:
- Implement different methods of random number generation
- Simulating games of dice that generate discrete random variate, using random number generation
- Testing of random numbers (K-S and Chi Square Test)
- Implementing applications of Monte Carlo methods
- Implement applications of Markov’s chain
- Simulation of single queue server system
- GPSS models - queue, storage, facility, multi-server queue, decision making problems
Text Books:
- Jerry Banks, John S. Carson, Barry L. Nelson, David M. Nicole, “Discrete Event system simulation”, 5th Edition, Pearson Education
Reference Books:
- Geoffrey Gordon: System Simulation
- Law, “Simulation Modeling and Analysis”, 5th Edition, McGraw-Hill