Lecturer

Professor P. Taylor, Melbourne, Semester 2.

Syllabus

Continuous time Markov chains: transient behaviour, classical queueing examples, the stationary distribution, hitting probabilities, expected hitting times. Applications to models of practical systems. Students are encouraged, in particular, to draw together many aspects of the above in completing their mini-projects. Queueing networks: Tandem networks, Burkes Theorem, Jackson networks, reversibility and the reversed process. Renewal theory: description, renewal theorem, foward and backward recurrence times, the ``bus-stop" paradox.

Generic skills

 

References

References

• Goodman, R. (1988) Intrduction to Stochastic Models, Benjamin-Cummings.
• Kleinrock, L. (1975/6) Queuing Systems - Vol.~1 Theory and Vol.~2 Computer applications, Wiley.
• Karlin, S. and Taylor, H.M. (1975) A First Course in Stochastic Processes, Academin Press.
• Karlin, S. and Taylor, H.M. (1981) A Second Course in Stochastic Processes, Academin Press.
• Kelly, F.P. (1979) Reversibility and Stochastic Networks, Wiley.
• Xiuli Chao, Masakiyo Miyazawa and Michael Pinedo (1999)Queuing networks: Customers, Signals and Product Form Solutions, Wiley.

Last updated: 30 October 2002.