Systems Modelling and Simulation

Systems Modelling and Simulation

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. Topics to be covered in this course include basics of discrete-event system simulation, mathematical and statistical models, simulation design, experiment design, and modelling of simulation data

Textbooks

The recommended textbooks for this course are:

• Discrete-Event System Simulation (Fourth Edition), Banks, Carson, Nelson, and Nicol, Prentice-Hall, 2005. Henceforth, referred to as [BCNN05].
• Simulation Modeling and Analysis (Third Edition), Law and Kelton, McGraw Hill, 2000. Henceforth, referred to as [LK00].

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.

Important Notes : -

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Outline (And Lecture Notes)

1. Introduction (1 week) What is simulation, when to use simulation, simulation terminology, application areas, model classification, types of simulation, steps in a simulation study, advantages/disadvantages of a simulation study Lecture slides: Introduction (PPT, PDF) Readings: Chapter 1 (omit Sections 1.3-1.5) from [LK00] or [BCNN05]
2. General Principles and Examples (1.5 weeks) Concepts of discrete-event simulation, list processing, examples: single-server queueing simulation, time-shared computer model, multi-teller bank with jokeying, job-shop model Lecture slides: Discrete-event simulation (PPT, PDF), single-server simulation (PPT, PDF), time-shared computer model, multi-teller bank (PPT, PDF) Readings: Section 1.3, Section 1.4, and Chapter 2 from [LK00] or Chapters 2 and 3 from [BCNN05]
3. Statistical Models (1.5 weeks) Review of basic probability and statistics, discrete distributions, continuous distributions, empirical distributions Lecture slides: Probability review part I (PPT, PDF), probability review part II (PPT, PDF), discrete and continuous distributions (PPT, PDF) Readings: Chapter 4, Sections 6.1, 6.2, 6.12 from [LK00] or Chapter 5 from [BCNN05]
4. Queueing Models (2 weeks) Queueing systems, important random processes, birth-death queueing systems, Markovian queues in equilibrium Lecture slides: Introduction to Queueing Systems (PPT, PDF) Readings: Our discussion on the Operational Laws is based on Chapter 33 of [Jain91] and Chapter 3 of [LZGS84]. The second text is available online. Please follow this link.
5. Generating Random-Numbers (1 week) Properties of random numbers, techniques for generating random numbers, testing random number generators Lecture slides: Random-Number Generation (PPT, PDF) Readings: Chapter 7 from [LK00] or [BCNN05]
6. Generating Random-Variates (1 week) Inverse-transform technique, acceptance-rejection technique, composition, convolution Lecture slides: Random-Variate Generation (PPT, PDF) Readings: Sections 8.1,8.2, and 8.3 from [LK00]; Cahpet 8 from [BCNN05]
7. Input Modelling (1 week) Data collection, assessing sample independence, hypothesizing distribution family with data, parameter estimation, goodness-of-fit tests, selecting input models in absence of data, models of arrival processes Lecture slides: Input modeling (PPT, PDF) Readings: Sections 6.4-6.6, 6.11, and 6.12 from [LK00] or Sections 9.1-9.4, and 9.6 from [BCNN05]
8. Output Data Analysis (1 week) Transient and steady-state behaviour of a stochastic process, types of simulations with regard to output analysis, statistical analysis for steady-state parameters Lecture slides: Input modeling (PPT, PDF) Readings: Sections 9.1-9.5 from [LK00] or Chapter 11 from [BCNN05]
9. Experiment Design and Sensitivity Analysis (1.5 weeks) Common mistakes in experimentation, types of experiment design, 2^k factorial designs, coping with many factors Lecture slides: Experiment design, performance evaluation, graphing tips etc. (PPT, PDF) NOTE: The example used in the lecture notes is derived from the paper Locality Characteristics of Web Streams Revisited by Aniket Mahanti, Anirban Mahanti, and Carey Williamson. This paper appeared in the Proceedings of the SCS Symposium on Performance Evaluation of Computer and Telecommunication Systems (SPECTS), Philadelphia, PA, July 2005. Readings: Sections 12.1-12.3 from [LK00]; additional material will be drawn from [Jain91].