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The Longer Queue Model

Published online by Cambridge University Press:  27 July 2009

Leopold Flatto
Leopold Flatto
Affiliation:
AT&T Bell Laboratories Murray Hill, New Jersey 07974
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Abstract

Two queues forming two independent Poisson processes are served by one server with exponential service time. The server always works on the longer queue and, in case that they are of equal length, chooses either one with probability ½. Let πij be the probability that the two queue lengths equal i andj at equilibrium and π(z, w) = ∑πi j Ziwj. We determine π(z, w) and derive from this asymptotic formulas forπij as i, j → ∞. These asymptotic formulas are used to study the interdependence of the queue lengths. In particular, we obtain limit laws for the queue lengths conditioned on each other.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 3 , Issue 4 , October 1989 , pp. 537 - 559
Copyright
Copyright © Cambridge University Press 1989

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