Prerequisite course: Probability, Mathematical Methods for Computer Science

Aims

The aims of this course are to introduce the concepts and principles
of analytic modelling and simulation, with particular emphasis on
understanding the behaviour of computer and communications systems.

Lectures

Introduction to modelling.
Overview of analytic techniques and simulation. Little's law.

Introduction to discrete event simulation.
Applicability to computer system modelling and other
problems. Advantages and limitations of simulation
approaches.

Random number generation methods and simulation techniques.
Review of statistical distributions.
Statistical measures for simulations, confidence intervals and
stopping criteria. Variance reduction techniques. [2 lectures]

Simple queueing theory. Stochastic processes:
introduction and examples. The Poisson process. Advantages and
limitations of analytic approaches.

Birth-death processes, flow balance
equations.
Relation to queueing systems. The M/M/1 queue in
detail: solution for state occupancy, average queue
length, average residence time. General observations.

Queue classifications, variants on the
M/M/1 queue and applications.
Extensions to birth-death models. Queueing networks. [2 lectures]

The M/G/1 queue and its application.
The Pollaczek-Khintchine formula; performance
measures. [2 lectures]

Case studies. Performance modeling of real-world
distributed systems. Workload characterization. Model development
and validation. Performance prediction. Use of queueing Petri net
models. [2 lectures]

Objectives

At the end of the course students should

be able to build simple Markov models and
understand the critical modelling assumptions

be able to solve simple birth-death
processes

understand that in general as the utilization
of a system increases towards unity then the response
time will tend to increase -- often dramatically so

understand the tradeoffs between different types of
modelling techniques

be aware of the issues in building a simulation of a computer
system and analysing the results obtained

Reference books

* Ross, S.M. (2002). Probability models for computer science. Academic Press.
Jain, A.R. (1991). The art of computer systems performance analysis. Wiley.
Kleinrock, L. (1975). Queueing systems, vol. 1. Theory. Wiley.