*Lecturer: Dr R.J. Gibbens*
(`rg31@cl.cam.ac.uk`)

*No. of lectures:* 8

*Prerequisite course: Probability*

**Aims**

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

**Lectures**

**Introduction to modelling.**Overview of analytic techniques, operational analysis 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 the generation of random variates.**Statistical measures for simulations, confidence intervals and stopping criteria.**Operational analysis.**Simple operational quantities. Bottleneck analysis. Applicability and assumptions.**Simple queueing theory.**Stochastic processes, definition and examples. Markov chains. Advantages and limitations of analytic approaches.**Birth-death processes, general 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.**The M/G/1 queue and its application.**The Pollaczek-Khintchine formula; performance measures.

**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 able to perform a bottleneck analysis of a system
- be aware of the issues in building a simulation of a computer
system

**Recommended books**

Kleinrock, L. (1975). *Queueing Systems, vol. *1*. Theory*. Wiley.

Leung, C. (1988). *Quantitative Analysis of
Computer Systems*. Wiley.

Jain, A.R. (1991). *The Art of Computer Systems
Performance Analysis*. Wiley.