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The serial correlation coefficients of waiting times in a stationary single server queue

Published online by Cambridge University Press:  09 April 2009

D. J. Daley
D. J. Daley
Affiliation:
Statistical Laboratory CambridgeEngland
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In a stationary GI/G/1 queueing system in which the waiting time variance is finite, it can be shown that the serial correlation coefficients {ρn} of a (stationary) sequence of waiting times are non-negative and decrease monotonically to zero. By means of renewal theory we find a representation for Σ∞0 ρn from which necessary and sufficient condition for its finiteness can be found. In M/G/1 rather more can be said: {ρn} is convex sequence, the asymptotic form of ρ n can be given in a nearly saturated queue, and a simple explicit expression for Σ∞0 ρn exists. For the stationary M/M/1 queue we find the ρn's explicitly, illustrate them numerically, and derive a representation which shows that {ρn} is completely monotonic.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 8 , Issue 4 , November 1968 , pp. 683 - 699
Copyright
Copyright © Australian Mathematical Society 1968

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