Course pages 2015–16

# Computer Systems Modelling

**Principal lecturer:** Dr Richard Gibbens**Taken by:** Part II**Past exam questions**

No. of lectures: 12

Suggested hours of supervisions: 3

Prerequisite courses: 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.**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 queueing theory.**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, mean occupancy and mean residence time. [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]

## 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.

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.