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Queueing theory is one of the main tools for performance evaluation and dimensioning of production systems, inventory systems, telecommunication and computer communication networks, road traffic systems, and transport systems in general. This course treats queueing systems with an emphasis on the classical models. The theory is illustrated by problems drawn mainly from production and inventory control.

This course includes the classical theory for queueing systems:
- Basic terminology, Kendall's notation and Little's theorem.
- Discrete and continuous time Markov chains, birth-death processes, and the Poisson process.
- Markovian waiting systems with one or more servers, and systems with infinite as well as finite buffers and finite user populations (M/M/).
- Systems with general service distributions (M/G/1): the method of stages, Pollaczek-Khinchin mean-value formula and systems with priority and interrupted service.
- Loss systems according to Erlang, Engset and Bernoulli.

The theory is illustrated by examples from production and inventory control.

For a passing grade the student must:
- be able to use advanced queueing theory and methodology to formulate, analyze and solve business problems relating to operational and managerial decisions
- be able to derive and prove classical theorems in advanced queueing theory.

In more detail this means:
- to be able to formulate relevant business problems characterized by uncertainty in the availability and demand for capacity as queueing problems
- to understand and explain principles for analytical modeling of advanced queueing systems
- to be able to compute steady-state probability distributions of events as well as mean values of various performance measures as waiting times, queue lengths and costs
- to be able to use mathematical transforms (such as z-transform and Laplace-transform) to derive mean values of various performance measures
- to be able to use concepts related to stochastic processes in order to prove various properties of the system.

For a passing grade the student must be able to independently formulate, solve and interpret:
- birth and death processes, such as M/M/c, M/M/c/K, M/M/c/infinity/N.
- Markovian queues.
- M/G/1-queues.

For a passing grade the student must:
- be able to understand relations and limitations when advanced models are used to describe complex queueing systems
- be able to evaluate how various assumptions affect the performance of the queueing system.

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Inlämningsuppgifter

Assessment: Individual written home assignments together with an oral exam.

Underkänd, godkänd

Basic course in Mathematical statistics.

Basic courses in Probability theory, Queueing theory, and knowledge regarding mathematical transforms.

Kleinrock, L.: Queueing Systems. Volume 1: Theory.. Wiley, 1975. ISBN 0471491101.

The course will be given in the spring of 2013 and thereafter upon demand.

MIO005F

 -03-05

FN3/Per Tunestål