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## Computer Systems Modelling

Lecturers: Dr R.J. Gibbens and Dr S. Kounev

No. of lectures: 12

Prerequisite course: 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.

• Birth-death processes, 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. [2 lectures]

• The M/G/1 queue and its application. The Pollaczek-Khintchine formula; performance measures. [2 lectures]

• Case studies. Performance modeling of real-world distributed systems. Workload characterization. Model development and validation. Performance prediction. Use of queueing Petri net models. [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.
Jain, A.R. (1991). The art of computer systems performance analysis. Wiley.
Kleinrock, L. (1975). Queueing systems, vol. 1. Theory. Wiley.    Next: Computer Vision Up: Lent Term 2008: Part Previous: Comparative Architectures   Contents