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Valid for year : 2009
 
NMAC22 Queueing Theory, 6 ECTS credits.
/Köteori/

For:   I   Ii   IMM   Mat   MMAT  

 

Prel. scheduled hours: 38
Rec. self-study hours: 122

  Area of Education: Science

Subject area: Mathematics
  Advancement level (G1, G2, A): A

Aim:
The aim of the course is give a working knowledge of standard queueing models and some of their applications and a description of the underlying theory. By the end of the course, the student is expected to know something of:
  • the theory of Markov Chains: classification of states, ergodicity, time reversibility.
  • Little's formula and its applications.
  • The basic Markov queuing models and situations to which they may be applied.
  • Markovian queueing models (E_r/M/1, M/E_r/1, hyperexponential arrival and hyperexponential service distributions).
  • Networks of queueing systems (Burke's Theorem, Jackson Networks).
  • The Pollaczek-Khinchine formula and its applications
  • M/G/1 systems and priority queueing systems.
  • How to use the GPSS queueing simulation programme.
Prerequisites: (valid for students admitted to programmes within which the course is offered)
Probability Theory

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
Organisation:
The teaching consists of lectures and tutorials. There will also be a short queueing simulation assignment.
Course contents:
The Poisson process, Discrete time Markov Chains (with Applications to some queueing problems), Continuous time Markov Chains, classification of states, expected time spent in states, ergodicity, steady state probabilities, time reversibility. Little's Formula, Markov queueing systems: one server, several servers, finite and infinite carrying capacity, Erlang´s formulae, Markovian queuing systems (E_r/M/1, M/E_r/1, hyperexponential arrival and service distributions), networks of queueing systems Burke's theorem, Jackson Networks, M/G/1 systems, Pollaczek - Khinchine formula, priority queueing systems, use of probability generating functions, simulation of queueing systems.
Course literature:
A Compendium containing lecture notes and examples (required).
Sheldon Ross, "Introduction to Probability Models" (current edition)(recmmended)
Examination:
A written examination
Computer exercises
 5 ECTS
1 ECTS
 


Course language is English.
Department offering the course: MAI.
Director of Studies: Torbjörn Larsson
Examiner: John M. Noble
Link to the course homepage at the department


Course Syllabus in Swedish

Linköping Institute of Technology
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Contact: TFK , val@tfk.liu.se
Last updated: 02/09/2011