Module Overview

Queueing Theory and Markov Processes

This module builds and expands upon the material covered in queueing theory and Markov processes in Stage 2.   It introduces the concept of multiple server models and variable arrival and service rates.  It introduces the learner to the topic of Markov processes and its applications and to the formulation and solution of related models.  Case studies of both topics are covered.

Module Code

MATH 4825

ECTS Credits


*Curricular information is subject to change



Queueing models

Introduction to queueing models. Poisson arrival patterns and exponential service times.

Types of queues & queue behaviour

Single and multiple servers, infinite and finite capacity. Balking and reneging.

Steady-state solutions

Derivation of steady-state solutions for various queueing systems.

Queueing system performance measures

Derivation and analysis of mean queueing times, mean number of customers in the queue.

Markov chains

Definition of Markov chains and their properties.

State space formulation for Markov chains

Formulation of a Markov chain and properties and use of transition matrices.


Classification of states of a Markov chain

Limiting distributions

Derive limiting distributions of a Markov chain.

Lectures supported by problem-solving and tutorial sessions.

Module Content & Assessment
Assessment Breakdown %
Formal Examination75
Other Assessment(s)25