Module Identifier MA46710  
Academic Year 2000/2001  
Co-ordinator Mr D A Jones  
Semester Intended For Use In Future Years  
Next year offered N/A  
Next semester offered N/A  
Pre-Requisite MA10020 , MA11110 , MA11310  
Course delivery Lecture   19 x 1hour lectures  
  Seminars / Tutorials   3 x 1hour example classes  
Assessment Exam   2 Hours (written examination)   75%  
  Project report     25%  
  Resit assessment   2 Hours (written examination) Project passed: assessment as above, project mark carried forward. Project failed: 2 hour written examination - 100%   100%  

General description
Queuing Theory is an application of mathematics and probability theory that arises directly from a practical situation, viz the development and dissipation of queues. Whilst mathematics can go a long way to analysing such situations, some complex systems defy analytical treament, and Simulation is concerned with ways in which practical situations can be 'mimicked' mathematically. This course introduces these two areas.

To introduce the student to the basic theory of queues and to the technique of simulation.

Learning outcomes
On completion of this module, a student should be able to:

1. INTRODUCTION: Random events. Queues and their characteristics. Markovian arrival processes. Queue model notation.
2. THE SIMPLE QUEUE: Simple Markovian (M/M/1) Queue; basic theory; steady state solutions. Waiting times and their districution. The output process.
3. GENERALISED MARKOVIAN SYSTEMS: Queues where arrival and service rates are dependent on system size. Examples will include limited waiting rooms, multiple server queues, self-service queues, telephone exchange design, machine minding, server fatigue, etc
4. NON-MARKOVIAN QUEUES: The method of stages; Erlangian sitributions. Pollaczek-Khintchine methods. Priority queues.
5. INTRODUCTION TO SIMULATION: Random numbers. Inverse transform theorem. Composition methods. Acceptance-rejection techniques. Simulating a queue.
6. PROJECT: Detailed study of a specific queueing situation to be completed by the end of the semester, with most of the work being in the second half.

Reading Lists
** Recommended Text
H A Taha. Operations Research, an introduction. Maxwell-Macmillan