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Some distributional approximations in Markovian queueing networks

Published online by Cambridge University Press:  01 July 2016

T. C. Brown and
P. K. Pollett
T. C. Brown
Affiliation:
University of Bath
P. K. Pollett*
Affiliation:
University of Cambridge
*
∗∗ Postal address: Statistical Laboratory, 16 Mill Lane, Cambridge CB2 1SB, U.K.
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Abstract

We consider single-class Markovian queueing networks with state-dependent service rates (the immigration processes of Whittle (1968)). The distance of customer flows from Poisson processes is estimated in both the open and closed cases. The bounds on distances lead to simple criteria for good Poisson approximations. Using the bounds, we give an asymptotic, closed network version of the ‘loop criterion' of Melamed (1979) for an open network. Approximation of two or more flows by independent Poisson processes is also studied.

Keywords

QUEUEING NETWORKSMIGRATION PROCESSPOISSON APPROXIMATIONSBOTTLENECKSLOOP CRITERIA

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 14 , Issue 3 , September 1982, pp. 654 - 671
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

a

Present address: Mathematics Department, Monash University, Clayton, VIC 3168, Australia.

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