Course overview
This course introduces students to the fundamental concepts of random processes, particularly continuous-time Markov chains, and related structures. These are the essential building blocks of any random system, be it a telecommunications network, a hospital waiting list or a transport system. They also arise in many other environments, where you wish to capture the development of some element of random behaviour over time, such as the state of the surrounding environment.
Topics covered are: Continuous-time Markov-chains: definition and basic properties, transient behaviour, the stationary distribution, hitting probabilities and expected hitting times, reversibility; Queueing Networks: Kendall's notation, Jackson networks, mean; Loss Networks: truncated reversible processes, circuit-switched networks, reduced load approximations. Basic Queueing Theory: arrival processes, service time distributions, Little's Law; Point Processes: Poisson process, properties and generalisations; Renewal Processes: preliminaries, renewal function, renewal theory and applications, stationary and delayed renewal processes.
Course learning outcomes
- Demonstrate understanding of the mathematical basis of continuous-time Markov chains
- Demonstrate the ability to formulate continuous-time Markov chain models for relevant practical systems
- Demonstrate the ability to apply the theory developed in the course to problems of an appropriate level of difficulty
- Develop an appreciation of the role of random processes in system modelling
- Demonstrate skills in communicating mathematics orally and in writing
Fee calculator
To display course fees, please select your status and program below:
We’re updating this Fee Calculator. It currently shows fees for programs only. Please check the relevant program for full fee details.
Study Abroad student tuition fees are available here.
Only some Postgraduate Coursework programs are available as Commonwealth Supported. Please check your program for specific fee information.
The Student Contribution amount displayed below is for students commencing a new program from 2021 onwards. If you are continuing in a program you commenced prior to 1 January 2021, or are commencing an Honours degree relating to an undergraduate degree you commenced prior to 1 January 2021, you may be charged a different Student Contribution amount from the amount displayed below. Please check the Student Contribution bands for continuing students here. If you are an international student, or a domestic student studying in a full fee paying place, and are continuing study that you commenced in 2025 or earlier, your fees will be available here before enrolments open for 2026.