Asymptotic correlation in a queue
1969 ◽
Vol 6
(03)
◽
pp. 573-583
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Keyword(s):
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.
1979 ◽
Vol 16
(02)
◽
pp. 393-401
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1980 ◽
Vol 17
(03)
◽
pp. 814-821
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1976 ◽
Vol 80
(3)
◽
pp. 521-525
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1962 ◽
Vol 2
(3)
◽
pp. 345-356
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Keyword(s):
1972 ◽
Vol 9
(01)
◽
pp. 87-102
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Keyword(s):