**PRE-REQUISITES**

Much of the material needed as background reading for this course will be provided on-line. Topics included will be elements of stochastic processes, simple queueing systems, aspects of inventory control, maintenance and reliability processes.

**AIM**

The course aims to provide an appreciation of the theory which has been developed to model real-life situations which have a probabilistic entity. On completion of the course, delegates should be better prepared to understand the more sophisticated models that appear in the literature.

**L****EARNING OUTCOMES
**On completion of the block, students will be expected to:

- understand the basics of stochastic processes, with particular relevance to queueing theory, inventory control, maintenance and reliability,
- be aware of the rich diversity of scenarios to which stochastic modelling may be applied,

be conscious of the relationships and complementarities between analytic and simulation modelling.

**PRINCIPAL TOPICS OF STUDY**

*Markov Chains*. Markov processes, finitely many states, continuous-time chains, random walks, branching processes, renewal processes.*Queueing Systems and Networks*. Queues with general arrival and service patterns, queues in series and in parallel, batch arrivals and services, phase-type service distributions, numerical approaches to transient behaviour.*Maintenance, reliability and renewal processes*. Replacement decisions (age, preventative, block, etc), inspection criteria, stochastic comparisons of system reliabilities and maintenance policies, scheduling and sequencing decisions, continuous and discrete renewal and repair processes and their computational requirements.*Stochastic models of inventory control*. Review of deterministic models as approximations to stochastic situations, Newsboy-type problems, time-varying demands, stochastic demand with constant lead-times, stochastic lead-times.*Brownian Motion*. Local properties of Brownian paths, canonical processes, Gaussian processes, filtration and stopping times.*Case studies*. Each of the above topics will be illustrated by case studies of applications from fields such as finance, telecommunications, epidemics, transport, healthcare.

**ASSESSMENTS**

Assessments, which will be formative in nature, will be held each day. They will take a variety of formats, and will typically last about half-an-hour. Feedback will be provided before the end of the course.