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The matrix M/M/∞ system: retrial models and Markov Modulated sources

Part of: Special processes Computer system organization

Published online by Cambridge University Press:  01 July 2016

J. Keilson  and
L. D. Servi
J. Keilson*
Affiliation:
University of Rochester
L. D. Servi*
Affiliation:
GTE Laboratories
*
∗Postal address: University of Rochester, Dept of Statistics, Rochester, NY 14627, USA.
∗∗Postal address: GTE Laboratories Incorporated, 40 Sylvan Road, Waltham, MA, USA.
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Abstract

The matrix-geometric work of Neuts could be viewed as a matrix variant of M/M/1. A 2 × 2 matrix counterpart of Neuts for M/M/∞ is introduced, the stability conditions are identified, and the ergodic solution is solved analytically in terms of the ten parameters that define it. For several cases of interest, system properties can be found from simple analytical expressions or after easy numerical evaluation of Kummer functions. When the matrix of service rates is singular, a qualitatively different solution is derived. Applications to telecommunications include some retrial models and an M/M/∞ queue with Markov-modulated input.

Keywords

RETRIAL QUEUEING MODELSM/M/∞MATRIX METHODS

MSC classification

Primary: 68M20: Performance evaluation; queueing; scheduling
Secondary: 60K25: Queueing theory
Type
Research Article
Information
Advances in Applied Probability , Volume 25 , Issue 2 , June 1993 , pp. 453 - 471
Copyright
Copyright © Applied Probability Trust 1993 

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Footnotes

This work was conducted while JK was a senior staff scientist at GTE Laboratories.

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