Abstract
Let Xt
denote the waiting time of customer t in a stationary GI/G/1 queue, with traffic intensity τ; let ρn
denote the correlation between Xt
and Xt+n. For a rational GI/G/1 queue, in which the distribution of the difference between arrival and service intervals has a rational characteristic function, it is shown that, for large n, ρn
is asymptotically proportional to n–
3/2
e
–βn
, where β and the factor of proportionality are calculable. The asymptotic law n
–3/2
e–βn
applies also to the approach of the waiting-time distribution to the stationary state in an initially empty rational GI/G/1 queue, and to the correlations in the queueing systems recently analysed by Cohen [1]. Its more general applicability is discussed.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Cited by
5 articles.
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