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On ross's conjectures about queues with non-stationary poisson arrivals

Published online by Cambridge University Press:  14 July 2016

D. P. Heyman
D. P. Heyman*
Affiliation:
Bell Laboratories
*
∗Postal address: Bell Laboratories, Bldg. WB, Room 1G311, Holmdel, NJ 07733, U.S.A.
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Abstract

Ross (1978) conjectured that the average delay in a single-server queue is larger when the arrival process is a non-stationary Poisson process than when it is a stationary Poisson process with the same rate. We present an example where equality obtains. When the number of waiting-positions is finite, Ross conjectured that the proportion of lost customers is greater in the nonstationary case. We present a counterexample to this conjecture.

Keywords

DELAYNON-STATIONARY ARRIVALSCOMPARISON WITH STATIONARY CASE
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 1 , March 1982 , pp. 245 - 249
Copyright
Copyright © Applied Probability Trust 1982 

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References

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