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Title

Continuity theorems for the M/M/1/n queueing system

Author(s)

Abramov, Vyacheslav M.

Abstract

In this paper continuity theorems are established for the number of losses during a busy period of the M/M/1/n queue. We consider an M/GI/1/n queueing system where the service time probability distribution, slightly different in a certain sense from the exponential distribution, is approximated by that exponential distribution. Continuity theorems are obtained in the form of one or two-sided stochastic inequalities. The paper shows how the bounds of these inequalities are changed if further assumptions, associated with specific properties of the service time distribution (precisely described in the paper), are made. Specifically, some parametric families of service time distributions are discussed, and the paper establishes uniform estimates (given for all possible values of the parameter) and local estimates (where the parameter is fixed and takes only the given value). The analysis of the paper is based on the level crossing approach and some characterization properties of the exponential distribution.

Publication type

Journal article

Source

Queueing Systems, Vol. 59, no. 1 (May 2008), pp. 63-86

Publication year

2008

FOR Code(s)

0102 Applied Mathematics;  0103 Numerical and Computational Mathematics;  0104 Statistics

Keyword(s)

Branching process;  Busy period;  Continuity theorems;  Kolmogorov metric;  Loss systems;  M/GI/1/n and M/M/1/n queues;  Number of level crossings;  Stochastic inequalities;  Stochastic ordering

Publisher

Springer

ISSN

0257-0130

Publisher URL

http://dx.doi.org/10.1007/s11134-008-9076-7

Copyright

Copyright © 2008 Springer Science+Business Media, LLC. The accepted manuscript is reproduced in accordance with the copyright policy of the publisher. The definitive version is available at www.springer.com.

Research Projects

Queueing systems and their application to telecommunication systems and dams, Australian Research Council grant number DP0771338

Full text

Peer reviewed