Computer Laboratory

Course pages 2016–17


Computer Systems Modelling

Lecturer: Professor I.M. Leslie

No. of lectures: 12

Suggested hours of supervisions: 3

Prerequisite courses: Mathematical Methods for Computer Science


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.


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

  • Introduction to discrete event simulation. Basic approaches and applications to the modelling computer systems.

  • Random number generation methods and simulation techniques. Statistical aspects of simulations: confidence intervals, stopping criteria, variance reduction techniques. [2 lectures]

  • Simple stochastic processes. Introduction and examples. The Poisson process. [2 lectures]

  • Birth-death processes, flow balance equations. Birth-death processes and their relation to queueing systems. The M/M/1 queue in detail: the equilibrium distribution with conditions for existence and common performance metrics. [2 lectures]

  • Queue classifications, variants on the M/M/1 queue and applications to queueing networks. Extensions to variants of the M/M/1 queue. Queueing networks. [2 lectures]

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


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.
Harchol-Balter, M. (2013). Performance modeling and design of computer systems: queueing theory in action. Cambridge University Press.
Jain, A.R. (1991). The art of computer systems performance analysis. Wiley.
Kleinrock, L. (1975). Queueing systems, vol. 1. Theory. Wiley.
Mitzenmacher, M. & Upfal, E. (2005). Probability and computing: randomized algorithms and probabilistic analysis. Cambridge University Press.