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On joint queue-length characteristics in infinite-server tandem queues with heavy traffic

Published online by Cambridge University Press:  01 July 2016

Volker Schmidt
Volker Schmidt*
Affiliation:
Mining Academy of Freiberg
*
∗Postal address: Bergakademie Freiberg, Sektion Mathematik, Bernhard-von-Cotta-Str. 2, DDR-9200 Freiberg, GDR.
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Abstract

For m infinite-server queues with Poisson input which are connected in a series, a simple proof is given of a formula derived in [3] for the generating function of the joint customer-stationary distribution of the successive numbers of customers a randomly chosen customer finds at his arrival epochs at two queues of the system. In this connection, a shot-noise representation of the queue-length characteristics under consideration is used. Moreover, using this representation, corresonding asymptotic formulas are derived for infinite-server tandem queues with general high-density renewal input.

Keywords

QUEUEING NETWORKCORRELATION COEFFICIENTHIGH DENSITYLIMIT THEOREM
Type
Research Article
Information
Advances in Applied Probability , Volume 19 , Issue 2 , June 1987 , pp. 474 - 486
Copyright
Copyright © Applied Probability Trust 1987 

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