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On the ordering of tandem queues with exponential servers

Published online by Cambridge University Press:  14 July 2016

Tapani Lehtonen
Tapani Lehtonen*
Affiliation:
Helsinki School of Economics
*
∗Postal address: Helsinki School of Economics, Runebergink. 22–24, 00100 Helsinki 10, Finland.
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Abstract

We consider tandem queues which have a general arrival process. The queueing system consists of s (s ≧ 2) single-server service stations and the servers have exponential service-time distributions. Firstly we give a new proof for the fact that the departure process does not depend on the particular allocation of the servers to the stations. Secondly, considering the service rates, we prove that the departure process becomes stochastically faster as the homogeneity of the servers increases in the sense of a given condition. It turns out that, given the sum of the service rates, the departure process is stochastically fastest in the case where the servers are homogeneous.

Keywords

EXPONENTIAL DISTRIBUTIONDEPARTURE PROCESSSTOCHASTIC ORDER(WEAK) MAJORIZATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 23 , Issue 1 , March 1986 , pp. 115 - 129
Copyright
Copyright © Applied Probability Trust 1986 

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