This module runs in Term 1 and is available for students on a course where it is a listed option and as an Unusual Option to students who have completed the prerequisite modules.
The ideas presented in this module 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 graduate found that 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.
Prerequisites: ST202 Stochastic Processes
Results from this module may be partly used to determine of exemption eligibility in the Institute and Faculty of Actuaries (IFoA) modules CS2.
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.
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
1: Continuous time Markov Chains.
Terms used in the analysis of continuoustime Markov chains: Markov property, transition probability function, standing assumptions, ChapmanKolmogorov equations, Qmatrix, Kolmogorov forward and backward differential equations, equilibrium distribution. The simplest case: finite statespace Markov chains. The "switcher" example. Exact transition densities for processes on a small number of states. The strong Markov property.
2: Linear BirthDeath processes.
Poisson (counting) process: construction, ideas of independent increments, superposition, counts and thinning. Pure birth process, linear birthdeath process, birthdeathimmigration process: construction using "microscopic model", derivation of extinction and equilibrium probabilities. Generalized birthdeath processes.
3: Queuing theory.
The Markov singleserver (M/M/1) queue. The concept of detailed balance. Measures of effectiveness. Multiserver (M/M/cl/c2) queues. Erlang's formula. Queues with general servicetime distribution (M/G/l) and their embedded Markov chains. Little's formula, PollaczekKhintchine formula.
4: Other Markov properties.
Stopping times. Strong Markov property. Holding theorem.
5: Epidemics.
Deterministic Epidemic model. Stochastic model without removals. Stochastic model with removals.
By the end of the module, students should be able to:
View reading list on Talis Aspire
TBC
TBC
Type  Required  Optional 

Lectures  30 sessions of 1 hour (20%)  2 sessions of 1 hour 
Seminars  5 sessions of 1 hour (3%)  
Private study  115 hours (77%)  
Total  150 hours 
Completion of noncredit bearing coursework, weekly revision of lecture notes and materials, wider reading, practice exercises and preparing for examination.
No further costs have been identified for this module.
You must pass all assessment components to pass the module.
Students can register for this module without taking any assessment.
Weighting  Study time  

Oncampus Examination  100%  
The examination paper will contain four questions, of which the best marks of THREE questions will be used to calculate your grade. ~Platforms  Moodle

Weighting  Study time  

Oncampus Examination  Resit  100%  
The examination paper will contain four questions, of which the best marks of THREE questions will be used to calculate your grade. ~Platforms  Moodle

Opportunities will be provided to submit noncredit bearing coursework for which feedback will be provided in the following problem class.
Solutions and cohort level feedback will be provided for the examination.
If you take this module, you cannot also take:
This module is Optional for:
This module is Core option list A for:
This module is Option list A for:
This module is Option list B for:
This module is Option list F for: