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Systems Modelling and Simulation 2007

Systems Modelling and Simulation (Mahanti:L01, Winter 2007)

Systems modelling and simulation techniques find application in fields as diverse as physics, chemistry, biology, economics, medicine, computer science, and engineering. The purpose of this course is to introduce fundamental principles and concepts in the general area of systems modelling and simulation

Textbooks

The required textbooks for this course are:
  • Discrete-Event System Simulation: A First Course, Leemis and Park, Prentice-Hall, 2006. Henceforth, referred to as [LP06].
  • Introduction to Probability Models (9th Edition), Sheldon Ross, 2006. Henceforth, referred to as [SR06].
Note that lectures will be drawn from the above textbooks as well as other sources (e.g., books, research literature, etc). Other textbooks that I will be referring to include:
  • [Jain91] The Art of Computer Systems Performance Evaluation, Raj Jain, John Wiley and Sons, Inc., 1991.
  • [LZGS84] Computer Systems Analysis Using Network Models, Edward Lazowska, John Zahorjan, Scott Graham, and Kenneth Sevcik, Prentice-Hall Inc., 1984. (out-of-print, but available online)
  • [Kl75] Queueing Systems - Volume I: Theory, Leonard Kleinrock, John Wiley and Sons, Inc., 1975.
  • [DS02] Probability and Statistics (Third Edition), Morris H. DeGroot and Mark J. Schervish, Addision-Wesley, 2002.
  • [BCNN05] Discrete-Event System Simulation (Fourth Edition), Banks, Carson, Nelson, and Nicol, Prentice-Hall, 2005.
  • [LK00] Simulation Modeling and Analysis (Third Edition), Law and Kelton, McGraw Hill, 2000.

Important Notes : -

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Tentative Course Outline

  1. Introduction Topics: Introduction with focus on terminology: System, system state, analytic modelling, and simulation; Notes: Introduction
  2. Introduction and refresher of basic probability theory Topics: Experiment, sample space, events, review of set theory, probability: definition, property, and interpretation, conditional probability, independent events, law of total probability, Bayes' rule, counting methods Notes: Probability theory refresher Readings: Chapter 1 SR06 textbook
  3. Random variables Topics: Discrete random variables, common discrete distributions (Bernoulli, Binomial, Geometric, Poisson) and their application to modelling, continuous random variables, common continuous distributions (uniform, normal, pareto, exponential) and their application to modelling Notes: Discrete RV, Continuous RV Readings: Chapters 2 and 3 from the SR06 textbook; also look at Chapter 4 in the LP06 textbook
  4. Random number generation Topics: Properties of random numbers, techniques for generating random numbers, testing random number generators, Inverse-transform technique, acceptance-rejection technique, algorithms for generating random number that have well-known discrete and continuous distributions Notes: Random Numbers and Variates Readings: Chapters 2, 6, and 7 from the LP06 textbook
  5. Introduction to Discrete Event Simulation Topics:What is DES?, Time advance mechanism, components of a DES program, performance measures, hand simulation of a single server service center Notes: DES Notes
  6. Fundamental laws and queueing models Topics: Introduction to operational (or fundamental) laws, utilization law, forced flow law, service demand law, little's law, interactive response time law Notes: Fundamental Laws
  7. Stochatic processes
  8. Input data modelling
  9. Output data analysis
  10. Experiment design and analysis

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