# Unit information: Introduction to Queuing Networks 34 in 2015/16

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Unit name Introduction to Queuing Networks 34 MATHM5800 10 M/7 Teaching Block 1A (weeks 1 - 6) Dr. Ayalvadi Ganesh Not open MATH 21400 Applied Probability 2. None School of Mathematics Faculty of Science

## Description

Unit aims

To introduce stochastic models for the description and analysis of simple queues and queueing networks.

General Description of the Unit

Queues are a fact of life - banks, supermarkets, health care, traffic etc.! The modelling and evaluation of individual queueing systems (in terms of quantities such as customer arrival patterns, service demands, scheduling priorities for different customer classes, queue size and waiting times) has been a rich source of theory and application in applied probability and operational research. Networks of linked queueing systems have gained wide popularity for modelling and performance-evaluation purposes in telecommunications, computer technology and manufacturing.

The course will introduce relevant concepts in the context of a single server queue and look at simple parallel and tandem systems, before going on to develop models and performance criteria applicable to more general networks.

Relation to Other Units

The units Information Theory, Financial Mathematics, Queuing Networks and Complex Networks apply probabilistic methods to problems arising in various fields.

Further information is available on the School of Mathematics website: http://www.maths.bris.ac.uk/study/undergrad/

## Intended learning outcomes

Learning Objectives

Students who successfully complete this unit should be able to:

• identify the transition rates for simple Markov processes from an informal description of the system;
• construct Markov process models of simple queueing networks, specified in terms of the transition rates, and understand the basic properties of such models;
• define the concepts of reversed and reversible Markov processes and use them to construct equilibrium distributions for simple queueing networks;
• compute the distribution of the queue size as seen in equilibrium by arrivals and departures;
• use Little's theorem to compute appropriate performance measures for simple systems.

Transferable Skills

The ability to translate practical problems into mathematics and the construction of appropriate probabilistic models.

## Teaching details

Lectures and weekly problem sheets, from which work will be set and marked, with outline solutions handed out a fortnight later.

## Assessment Details

80% Examination and 20% Coursework.

The homework will be marked against the criteria on the 0-100 scale.

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

Students will be provided with comprehensive lecture notes.

Main text:

• F P Kelly, Reversibility and stochastic networks, Wiley, 1979.

Other recommended texts:

• I Mitrani, Modelling of computer and communication systems, Cambridge University Press, 1998.
• J Walrand, An introduction to queuing networks, Prentice-Hall International, 1988.
• M. Harchol-Balter, Performance modelling and design of computer systems, Cambridge University Press, 2013.