Important: If you decide to take ST333 you cannot then take ST406. Bear this in mind when planning your module selection. Recall: an integrated Masters student must take at least 120 CATS of level 4+ modules over their 3rd & 4th years.
Commitment: 3 lectures per week, 1 example class per fortnight. This module runs in Term 1.
Prerequisite(s): ST202 Stochastic Processes.
Aims: To provide an introduction to concepts and techniques which are fundamental in modern applied probability theory and operations research:
- Models for queues, point processes, and epidemics.
- Notions of equilibrium, threshold behaviour, and description of structure.
These ideas have a vast range of applications, for example routing algorithms in telecommunications (queues), assessment of apparent spatial order in astronomical data (stochastic geometry), description of outbreaks of disease (epidemics). We will only be able to introduce each area - indeed each area could easily be the subject of a course on its own! But the introduction will provide you with a good base to follow up where and when required. (For example: a MORSE student graduating in 1996 found the next year their firm was asking them to address problems in queuing theory, for which ST333 provided the basis.) We will discuss these and other applications and show how the ideas of stochastic process theory help in formulating and solving relevant questions.
Objectives: At the end of the course students will:
- Be able to formulate continuous-time Markov chain models for applied problems.
- Be able to use basic theory to gain quick answers to important questions (for example, what is the equilibrium distribution for a specific reversible Markov chain?).
- Be able to solve for the transition probabilities for Markov chains on a finite state space.
- Understand how to use Markov chains in the modelling and analysis of queues and epidemics.
Assessment: 100% by 2-hour examination.
Deadlines: The module has non-credit bearing coursework with the following deadlines: Problem Sheet 1: Week 2, Problem Sheet 2: Week 4, Problem Sheet 3: Week 6, Problem Sheet 4: Week 8.
There will be problem classes associated with the course, and students will be expected to attend.
Feedback: Feedback on non-credit bearing coursework will be provided in the following problem class.
Examination Period: Summer