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On fluctuation problems in the theory of queues

Published online by Cambridge University Press:  01 July 2016

Lajos Takács
Lajos Takács*
Affiliation:
Case Western Reserve University, Cleveland, Ohio
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Abstract

This paper gives a survey of the historical development of the solutions of various fluctuation problems in the theory of queues from the point of view of the mathematical methods used. These methods include Markov chains, Markov processes, integral equations, complex functions, generating functions, Laplace transforms, factorization of functions, operator calculus, Banach algebras and some particular methods, such as calculus of finite differences and combinatorics. In addition, the paper contains several recent results of the author for semi-Markov queuing processes.

Keywords

QUEUING PROCESSESRECURRENT QUEUESSEMI-MARKOV QUEUESQUEUE SIZEWAITING TIMEBUSY PERIODSDISTRIBUTIONSLIMIT DISTRIBUTIONS
Type
Research Article
Information
Advances in Applied Probability , Volume 8 , Issue 3 , September 1976 , pp. 548 - 583
Copyright
Copyright © Applied Probability Trust 1976 

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