Authorised by Academic Registrar, April 1996
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 develop the ability to build models with probability distributions (specifically queuing models) and to build a basis for design and control of queues. Topics covered include an introduction to probability distributions; Markov chains; 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. For internal students the program will usually involve two hours of lectures and a one-hour workshop per week. The workshop will involve case studies, problem solving and group work.
Assessment Two assignments: 40% + Examination: 60%