2 results
The covariance function of the virtual waiting-time process in an M/G/1 queue
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- Journal:
- Advances in Applied Probability / Volume 9 / Issue 1 / March 1977
- Published online by Cambridge University Press:
- 01 July 2016, pp. 158-168
- Print publication:
- March 1977
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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.
and 
if and only if the service-times have a finite fourth moment.The stable M/G/1 queue in heavy traffic and its covariance function
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- Journal:
- Advances in Applied Probability / Volume 9 / Issue 1 / March 1977
- Published online by Cambridge University Press:
- 01 July 2016, pp. 169-186
- Print publication:
- March 1977
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- Article
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