# Computer Laboratory

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: 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 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]

## 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.

• © 2016 Computer Laboratory, University of Cambridge
Information provided by Dr Richard Gibbens