# Computer Laboratory

Course pages 2011–12

# Computer Systems Modelling

Principal lecturer: Dr Richard Gibbens
Taken by: Part II
Past exam questions
Information for supervisors (contact lecturer for access permission)

No. of lectures: 12
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. 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. [2 lectures]

• Birth-death processes, flow balance equations. Birth-death processes and their relation to queueing systems. The M/M/1 queue in detail: existence and when possible solution for equilibrium distribution, 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.
Mitzenmacher, M. & Upfal, E. (2005). Probability and computing: randomized algorithms and probabilistic analysis. Cambridge University Press.
Jain, A.R. (1991). The art of computer systems performance analysis. Wiley.
Kleinrock, L. (1975). Queueing systems, vol. 1. Theory. Wiley.

• © 2011 Computer Laboratory, University of Cambridge
Information provided by Dr Richard Gibbens