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Transient characteristics of an M/M/∞ system

Part of: Markov processes Miscellaneous topics of analysis in the complex domain Computer system organization

Published online by Cambridge University Press:  01 July 2016

Fabrice Guillemin  and
Alain Simonian
Fabrice Guillemin*
Affiliation:
France Telecom
Alain Simonian*
Affiliation:
France Telecom
*
* Postal address: France Telecom, CNET Lannion-A, 2 Ave. P. Marzin, 22300 Lannion, France.
** Postal address: France Telecom, CNET Paris-A. 38–40 rue du Général Leclerc, 92131 Issy-les-Mlx, France.
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Abstract

Convergence results are given for transient characteristics of an M/M/∞ system such as the period of time the occupation process remains above a given state, the area swept by this process above this state and the number of customers arriving during this period. These results are precise in contrast to approximations derived in the framework of the Poisson clumping heuristic introduced by Aldous.

Keywords

TRANSIENT ANALYSISPOINT PROCESS THEORYANALYTIC FUNCTION THEORYSPECIAL FUNCTIONS

MSC classification

Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 30E15: Asymptotic representations in the complex domain 68M20: Performance evaluation; queueing; scheduling
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 27 , Issue 3 , September 1995 , pp. 862 - 888
Copyright
Copyright © Applied Probability Trust 1995 

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