MAT2216

Applied probability models

Associate Professor Philip Rayment

4 points - First semester - 2 hours of lectures and one 1-hour tutorial per week - Gippsland/Distance (odd-numbered years only) - Prerequisites: MAT1085 and MAT1060 - Prohibitions: MAS2021, MAT2211, GAS2713

Objectives For students to demonstrate an understanding of Markov chains in discrete and continuous time; obtain the equilibrium distribution of a Markov chain (where it exists) and (in particular) of a continuous-time-birth-death process; derive basic measures of effectiveness of some queuing models based on the birth-death process or the more general Markov process and apply these to the design and control of queues.

Synopsis This subject is designed to introduce students to simple random processes in discrete and continuous time, to develop the ability to build probabilistic models (specifically queuing models) and to build a basis for design and control of queues. Topics covered include an introduction to probability distributions and probability generating functions; random processes in discrete and continuous time; Markov chains and birth-death processes and stationary distributions; single and multiple server models under infinite and finite population, infinite and finite capacity requirements; advanced Markovian queuing models - bulk input, bulk service, Erlangian models, network, series and cyclic queues; introduction to models with general service patterns; applications to renewal, maintenance and replacement policies.

Assessment Two assignments: 40% Examination (3 hours): 60%

Recommended texts

To be advised on enrolment.

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