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Journal Article

On Ross's Conjectures about Queues with Non-Stationary Poisson Arrivals

D. P. Heyman
Journal of Applied Probability
Vol. 19, No. 1 (Mar., 1982), pp. 245-249
DOI: 10.2307/3213936
Stable URL: http://www.jstor.org/stable/3213936
Page Count: 5

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Topics: Poisson process, Counterexamples, Random variables
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On Ross's Conjectures about Queues with Non-Stationary Poisson Arrivals
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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.

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