Spectral expansion solutions for markov-modulated queues

Authors:
Isi Mitrani
Affiliations:
School of Computing Science, Newcastle University, UK
Venue:
Network performance engineering
Year:
2011

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Abstract

This tutorial deals with the solution of a large class of models where the behaviour of an unbounded queue is influenced by the evolution of a Markovian environment. The latter, in turn, may be affected by the state of the queue. Several examples of such models, with applications in the fields of computing, communication and manufacturing, are given. The spectral expansion method for obtaining exact solutions is described. A simple and easily computable approximation which is asymptotically exact in heavy traffic is also presented. Some illustrative examples are included.