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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

Fond, S. and Ross, S. M. (1978) A heterogeneous arrival and service loss model. Naval Res. Logist. Quart. 25, 483–488.Google Scholar
Heyman, D. P. and Stidham, S. (1980) The relation between customer and time averages in queues. Operat. Res. 28, 983–994.CrossRefGoogle Scholar
Niu, S.-C. (1980) A single server queueing loss model with heterogeneous arrival and service. Operat. Res. 28, 584–593.Google Scholar
Prabhu, N. U. (1965) Queues and Inventories. Wiley, New York.Google Scholar
Rolski, T. (1981) Queues with non-stationary input stream: Ross's conjecture. Adv. Appl. Prob. 13, 603–618.Google Scholar
Ross, S. (1978) Average delay in queues with non-stationary Poisson arrivals. J. Appl. Prob. 15, 602–609.Google Scholar
Takács, L. (1969) On Erlang's formula. Ann. Math. Statist. 40, 71–78.Google Scholar