The covariance function of the virtual waiting-time process in an M/G/1 queue
Keyword(s):
Let R(t) be the covariance function of the stationary virtual waiting-time process of a stable M/G/1 queue. It is proven that if R(t) exists, i.e., if the service-times have a finite third moment, then R(t) is positive and convex on [0, ∞), with an absolutely continuous derivative R’ and a bounded, non-negative second derivative R″. Also, and R″ cannot be chosen monotone. Contrary to a finding by Beneš [1] it is proven that if and only if the service-times have a finite fourth moment.
1977 ◽
Vol 9
(01)
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pp. 158-168
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1977 ◽
Vol 9
(01)
◽
pp. 169-186
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1989 ◽
Vol 21
(02)
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pp. 485-487
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1974 ◽
Vol 11
(02)
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pp. 355-362
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Keyword(s):
Keyword(s):
1972 ◽
Vol 9
(01)
◽
pp. 117-128
◽
Keyword(s):