Aims & Learning Objectives:
Aims: To study further Markov processes in both discrete and continuous time. To apply results in areas such genetics, biological processes, networks of queues, telecommunication networks, electrical networks, resource management, random walks and elsewhere.
On completing the course, students should be able to
* Formulate appropriate Markovian models for a variety of real life problems and apply suitable theoretical results to obtain solutions
* Classify a variety of birth-death processes as explosive or non-explosive
* Find the Q-matrix of a time-reversed chain and make effective use of time reversal.
Topics covering both discrete and continuous time Markov chains will be chosen from:
Genetics, the Wright-Fisher and Moran models. Epidemics. Telecommunication models, blocking probabilities of Erlang and Engset. Models of interference in communication networks, the ALOHA model. Series of M/M/s queues. Open and closed migration processes. Explosions. Birth-death processes. Branching processes. Resource management. Electrical networks. Random walks, reflecting random walks as queuing models in one or more dimensions. The strong Markov property. The Poisson process in time and space. Other applications.