The University of Southampton

MATH3013 Simulation & Queues

Module Overview

Queueing theory has many practical applications and some queueing systems, including complex ones, can be studied analytically. This module covers the main mathematical techniques and is centred in investigations of long-run behaviour. This part of the module contains some very interesting mathematics including investigations of long-run behaviour of underlying stochastic processes. It also provides motivation for the use of simulation in complex problems where analytical solution can become difficult. Simulation is one of the most widely used Operational Research techniques in industry, business and government organisations. This module aims to provide a good understanding of the theory of simulation and the skills in its practical application. There will be several computer laboratory sessions during the module. Students will gain experience and skills in using simulation software packages or libraries. The course work, which is a major component of the module, applies these skills in the study of a practical real-life example. The module will lead on from the material presented in Computer Tools for Operational Research, and will include continuous and discrete simulation. Statistical methods are required for the good use of simulation models and the module will cover elements of the design of simulation experiments, variance reduction and the analysis and interpretation of results.

Aims and Objectives

Module Aims

To provide a good understanding of the modelling of queues, using both queueing theory and computer simulation.

Learning Outcomes

Learning Outcomes

Having successfully completed this module you will be able to:

  • Use simulation for the solution of complex discrete and continuous models;
  • Understand and apply the main analytical techniques used in the study of queues
  • Appreciate the restrictions of analytical solutions for real problems
  • Implement simulation models
  • Understand the basic issues and methodologies used in modelling real problems
  • Understand the statistical aspects of simulation.


Simulation: Discrete-event modelling techniques. Generation of random numbers and tests of randomness. Inverse transform, acceptance/rejection, and composite methods of random variate generation. Design of simulation experiments. Simple Monte Carlo examples. Variance reduction methods. Queues: Poisson process. Differential-difference methods. Examples of queues. Steady-state distribution. Waiting-time distribution. Little's Law. Generating-function methods(if time permits). SIMUL8: Use of the package to model discrete-event systems

Learning and Teaching

Teaching and learning methods

Lectures, exercise classes, computer laboratories, private study.

Independent Study106
Total study time150

Resources & Reading list

Cox DR & Smith WL - Queues. 

Law AM (2007). Simulation Modeling and Analysis. 

Pidd M (1994). Computer Simulation in Management Science. 

Wolf RW (1989). Stochastic Modeling and the Theory of Queue. 



MethodPercentage contribution
Coursework 40%
Exam  (2 hours) 60%


MethodPercentage contribution
Exam  (2 hours) %

Repeat Information

Repeat type: Internal & External

Linked modules


To study this module, you will need to have studied the following module(s):

MATH2013Introduction to Operational Research
MATH2011Statistical Distribution Theory
MATH2010Statistical Methods I


Costs associated with this module

Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.

In addition to this, students registered for this module typically also have to pay for:

Books and Stationery equipment

Course texts are provided by the library and there are no additional compulsory costs associated with the module.

Please also ensure you read the section on additional costs in the University’s Fees, Charges and Expenses Regulations in the University Calendar available at

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