Random Processes III
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Description
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.
Objective
To introduce students to fundamental methods for modelling random processes. On
completion of this subject, students should be familiar with: The definition of
a continuous-time Markov chain and analysis of transient behaviour, the
stationary distribution, hitting probabilities and expected hitting times.
Stochastic modelling of traffic streams. Evaluation of delay, congestion and
buffer size performance measures for simple queues and single network links.
Evaluation of exact and approximate performance measures for loss networks.
Students will be expected to draw together many aspects of the above in
completing a project.
Content
Topics covered are: Continuous-time Markov-chains: definition and basic
properties, transient behaviour, the stationary distribution, hitting
probabilities and expected hitting times, reversibility; 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; Queueing Networks: Kendall's notation, Jackson
networks, mean value analysis; Loss Networks: truncated reversible processes,
circuit-switched networks, reduced load approximations.
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| Year |
Semester |
Level |
Units |
| 2012 |
2 |
3 |
3 |
Delivery
36 hours of lectures and tutorials.
Assessment
Ongoing assessment 30%, exam 70%.
Graduate attributes
Linkage past
Prerequisite is Mathematics IB or Mathematics IIM. Students who have completed one or more of
Operations Research II,
Introduction to Mathematical Statistics II and
Probability and Statistics II will have a better background
than students who have not completed these subjects. Students who have completed
Applied Probability III will be well prepared to take this subject.
Linkage present
A sister unit is Applied Probability III. Other units relating to
Operations Research are Optimisation III,
Stochastic Decision Theory III and
Variational Methods and Optimal Control III.
This subject is also part of the core at third-year level for the BE (Telecomms)
degree.
Linkage future
Many Masters and PhD in IT&T topics require a knowledge of the concepts in this course. They are also required in many positions in the IT&T industry.
Restrictions
None.
Recommended text
None, notes will be provided. References: Introduction to Probability Models (various editions), Sheldon Ross, Academic Press (1972-2000), 519.2 R826i
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