*Lecturer: Mr T.L. Harris*
(`tlh20@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 computer and communications systems.

**Lectures**

**Introduction to modelling.**What is it, when is it useful? Overview of analytic techniques, operational analysis, simulation.**Simple queueing theory.**Stochastic processes, definition and examples. Restriction to tractable systems. Markov chains.**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 & applications.**Extensions to birth-death models: series and parallel stages; the Er-M-1 and M-Er-1 queues. Multiple queue systems.**The M/G/1 queue and its application.**The Pollaczek Khintshine formula; performance measures; the non-preemptive priority queue.**Operational analysis.**Simple operational quantities. Weakness of assumptions. Bottleneck analysis. Applicability.**Introduction to discrete event simulation.**Applicability to computer system modelling and other problems. Limitations of simulation models. The discrete event simulation algorithm; examples.**Random number generation methods, random variate generation.**Statistical measures for simulations, confidence intervals and stopping criteria. Distributed simulation.

**Objectives**

At the end of the course students should

- be able to build simple Markov models and understand the
assumptions which are used in their application to a real system
- be able to solve simple birth-death processes
- understand that in general, as utilisation of a system
approaches unity, its response time becomes unbounded
- 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.

Lazowska, E.D., Zahorjan, J., Graham, G.S. &
Sevcik, K.C. (1984). *Quantitative System Performance*. Prentice-Hall.