BSC4024106 Project Details
| Supervisor | Paul M. E. Shutler |
| Project Code | BSC4024106 |
| Title of Project | Analysis of Queueing Systems |
| Description | This project is about analysing certain kinds of queueing systems and their generalisations. The simplest queueing system consists of “customers” who arrive at random, a “server” who serves them one at a time, customers who cannot immediately be served because the server is busy form an orderly queue, the time the server takes to serve each customer can vary, and where each customer leaves the system as soon as their service is over. What one would like to know are things like: how long on average each customer has to wait in the queue before being served, and how long on average is the queue, both as a function of the arrival rate of the customers and of the distribution of the times the server takes to serve them. Although this sounds relatively simple in principle, in practice things are much more interesting, and sometimes the results obtained are quite counter intuitive. Moreover, queueing systems and their generalisations are ubiquitous in our modern world, not just when obvious queues form, such as in the canteen or at the bank, but also in cases where the queue is not so obvious such as in machine repairs or certain kinds of retail or inventory problems. The overall aims of this project are that the student should (a) learn how to analyse theoretically the performance of different kinds of queueing systems, (b) compare these theoretical predictions with results obtained from computer simulations, and if possible (c) gather some data from the real world (such as the queues in NIE Canteen!) and compare these with both theory and simulation. |
| Pre-requisites | • There are no mathematical prerequisites beyond the courses already taken in Years 1 and 2. • Some prior experience with a programming language would be an advantage as there will be an opportunity for the student to earn extra credit by writing their own computer simulation code, but if time is short, prewritten simulation code will be made available. • A willingness to spend a few hours collecting real world data from such public venues as canteens, banks, supermarkets, etc. for which prior official permission may be required. |
| References | The following books in NIE library include chapters on queueing theory which prospective students can read to gain a more detailed understanding of what is involved with this project: 1. Winston Operations Research: Applications and Algorithms T57.6 Win 2. Hillier and Lieberman Introduction to Operations Research T75.6 Hil 3. Taha Operations Research: An Introduction T57.6 Tah In practice, however, either one of the following texts, copies of which can be loaned out to the student for the duration of the project, or notes provided by the supervisor, will be used: 4. Bunday An Introduction to Queueing Theory 5. Bunday Basic Queueing Theory |