Module Identifier MA38110
Module Title QUEUEING AND RELIABILITY
Co-ordinator Mr Alan Jones
Semester Semester 1
Other staff Dr John A Lane
Pre-Requisite MA11310
Course delivery Workload Breakdown   Lectures and tutorials: 22 hours Worksheets ( 4 x 5 ): 20 hours Private study: 56 hours Examinations: 2 hours
Assessment
Assessment TypeAssessment Length/DetailsProportion
Semester Exam2 Hours conventional 2-hour examination  100%
Supplementary Exam2 Hours conventional 2-hour examination  100%

#### Learning outcomes

On successful completion of this module students should be able to:
1. formulate and solve simple problems in random arrival modelling;

2. set up and solve the steady-state equations governing a simple queue;

3. formulate a given real situation as a queueing model;

4. appreciate the failings of the simplest models and what modified models are trying to cover;

5. evaluate and use the reliability function, hazard function, mean time to failure and reliable lifetime of lifetime distributions in common use;

6. evaluate the reliability of systems of independent components;

7. calculate and interpret simple bounds on reliability;
explain the notation used in fault trees and be aware of their uses.

#### Aims

IMAPS has for some years been able to offer a very limited range of modules for final year students. With the imminent arrival of more staff, it is now proposed to rectify this by introducing Level 3 modules that can be extended to cater for Level M students also. This module introduces the important area of stochastic Operational Research; its companion module, MAM8120 has some common lectures but extends the applications. It is intended to offer this module in alternate years.

#### Brief description

Queueing Theory is a classic application of probability that falls within the umbrella of stochastic operational research, motivated by practical problems. The module covers the basic models of Queueing Theory and the formulation of real scenarios in their terms.

The module also introduces students to the properties of lifetime distributions, to study the reliability of systems of components and to gain an appreciation of how high levels of reliability and safety may be achieved in practice.

#### Content

Random events
Modelling of Markovian arrival processes. Queues and their characteristics. Queue model notation.
The Simple Queue
Simple Markovian (M/M/1) Queue; basic theory; steady state solutions. Waiting times and their distribution. The output process.
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.
Statistical Failure Models
Reliability and hazard functions, mean time to failure, reliable lifetime; distributions (Exponential, Weibull, Gamma, Gumbel, Log Normal) competing risks; simple bounds on reliability.
Systems Reliability
Series, parallel, k out of n systems. Path and cut sets, monotonic systems, modules. Bounds on system reliability. Fault trees.

#### Module Skills

 Problem solving All situations considered are problem-based to a greater or lesser degree. Research skills Students will be encouraged to consult various books and journals for examples of application. Communication Students will be expected to submit written worksheet solutions Improving own Learning and Performance Feedback via tutorials Team work N\A Information Technology Extensive use of spreadsheets. Application of Number Throughout the module. Personal Development and Career planning Students will be exposed to an area of application that they have not previously encountered. Subject Specific Skills Modelling of practical situations in stochastic terms