Random Processes (Masters) (862G1)

Key facts

Details for course being taught in current academic year
Level M  -  15 credits  -  spring term

Course description

Course outline

The Poisson process. Birth processes; death processes; birth and death processes, including Extinction probabilities and embedded processes; the immigration-death process including the Equilibrium process.

Queueing theory; the simple M/M/1 queue, multiple servers (M/M/n), different distributions of service time (M/D/1 and M/G/1 queues), equilibrium distribution of queues.

Renewal processes; discrete and continuous time renewal processes, the equilibrium renewal processes.

Epidemic models; the simple epidemic, the general epidemic.

Learning outcomes

By the end of the course, a successful student should be able to:

1) understand the assumptions underlying continuous time models and how the models are formed;
2) understand the concept of a rate of a continuous time process;
3) be able to analyse the models mathematically and to isolate the important factors;
4) know how to relate continuous time processes to discrete analogues and embedded processes;
5) understand the Markov property and be able to identify when it applies and be able to analyse the models and apply them to different examples.

Assessments

Timing

Submission deadlines may vary for different types of assignment/groups of students.

Weighting

Coursework components (if listed) total 100% of the overall coursework weighting value.

Teaching methods

How to read the week pattern

The numbers indicate the weeks of the term and how many events take place each week.