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Simple Bounds and Monotnicity the Call Congestion of Finite Multiserver Delay Systems

Published online by Cambridge University Press:  27 July 2009

Nico M van Dijk ,
Pantelis Tsoucas  and
Jean Walrand
Nico M van Dijk
Affiliation:
Department of Actuarial Sciences and Econometrics Free University, Amsterdam, The Netherlands
Pantelis Tsoucas
Affiliation:
Department of Electrical Engineering and Computer Sciences and Electronics Research LaboratoryUniversity of California, Berkeley Berkeley, California 94720
Jean Walrand
Affiliation:
Department of Electrical Engineering and Computer Sciences and Electronics Research LaboratoryUniversity of California, Berkeley Berkeley, California 94720
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Abstract

Simple and insensitive lower and upper bounds are proposed for the call congestion of M/GI/c/n queues. To prove them we establish the general monotonicity property that increasing the waiting room and/or the number of servers in a /GI/c/n queue increases the throughput. An asymptotic result on the number of busy servers is obtained as a consequence of the bounds. Numerical evidence as well as an application to optimal design illustrates the potential usefulness for engineering purposes. The proof is based on a sample path argument.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 2 , Issue 1 , January 1988 , pp. 129 - 138
Copyright
Copyright © Cambridge University Press 1988

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