University of Malta

Study-Unit Description
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TITLE Queuing Theory and Markov Chains

LEVEL 02 - Years 2, 3 in Modular Undergraduate Course


DEPARTMENT Statistics and Operations Research


- Introduction to Queuing Theory, Birth-and-Death Processes
- Poisson Process and M/M/1 Model in Detail
- Other Markovian Models: Multichannel, Limited Capacity and Population
- Summary of Results for Other Single Queue Models
- Open and Closed Jackson Networks
- Simulation Techniques in Queueing Theory

Markov Chains

- Definition of Markov chains within the context of Stochastic Processes
- Transition probability matrices,
- Chapman-Kolmogorov theorem
- Classification of states
- Asymptotic results for irreducible, recurrent, aperiodic Markov chains
- Stationary distributions
- Simulation and Monte Carlo
- Introduction to Continuous-time Markov chains
- Applications mainly from computer science will be discussed throughout the course.

Study-unit Aims

Set within the language of probability and analytical tools of stochastic processes , the course is intended to give students with a specific background what they need within the time-frame and background limitations of the courses they are following. A number of key results in the theory of both topics, on which the models mentioned are based, were selected and inserted in the course so that students will understand what these results say. They should also know when and how to use them and when not.

Learning Outcomes

1. Knowledge & Understanding: By the end of the study-unit the student will:

- Understand how the language and mathematics used in theories of queuing and Markov chains can help formulate problems in computer science and related areas.
- Understand thoroughly what theoretical results say about the behaviour and properties of queuing and Markov chain systems and the conditions under which they hold.
- Be in a position to see how a deeper engagement with sophistication of the theory can help in more intricate applications.

2. Skills: By the end of the study-unit the student will be able to:

- Appreciate how theoretical results can be used to help with modeling and with deducing behaviour of certain probabilistically evolving systems.
- Apply results learnt in more intricate applications.
- Judge accurately whether a particular system satisfies the conditions under which result entertained hold.

Main Text/s and any supplementary readings

- Gross, D., Harris, C.M. (2008) Fundamentals of Queueing Theory, John Wiley & Sons.
- Tijms, H.C. (2003) A First Course in Stochastic Models, John Wiley & Sons.
- Prabhu, N.U. (1997) Foundations of Queueing Theory, International Series in OR & Management Sciences.
- Allen, A.O. (2009) Probability, Statistics and Queueing Theory, Academic.
- Banks, J., Carson, J.S., Nelson, B. and Nicol, D. (2004) Discrete Event Simulation, Prentice-Hall Inc.
- Kelton, W.D. (2006) Simulation with Arena, McGraw-Hill.
- Belch G., Greiner S., de Meer H., Trivedi K.S., (2006) Queueing Networks and Markov Chains- Modeling and Performance Evaluation with Computer Science Applications, Wiley.
- Stewart, W. (2009) Probability, Markov Chains, Queues, and Simulation, Princton University Press.
- Haggstrom O., (2002) Finite Markov Chains And Algorithmic Applications , Cambridge University Press.
- Stirzaker D., (2005) Stochastic Processes and Models, Oxford University Press.

ADDITIONAL NOTES Pre-requisite Qualifications: Pure or Applied Mathematics at the level requested for entry to Technology courses.

Co-requisite Study-unit: SOR1201

Students taking Statistics as one of the principal subject areas cannot take this study-unit.

STUDY-UNIT TYPE Lecture and Tutorial

Assessment Component/s Resit Availability Weighting
Computer-based Examination (2 Hours) Yes 100%

LECTURER/S David Paul Suda

The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints.
Units not attracting a sufficient number of registrations may be withdrawn without notice.
It should be noted that all the information in the study-unit description above applies to the academic year 2017/8, if study-unit is available during this academic year, and may be subject to change in subsequent years.
MSc (Research) and PhD application deadlines
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