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- W2325344952 abstract "Consider a stable GI/G/ 1 queue with non-lattice interarrival time distribution. Let G and H be the limiting actual and virtual waiting time distributions respectively. Two separate statements of the relationship between G and H are found in a classical theorem of Takàcs and a more recent (and previously unpublished) theorem of Hooke. A simplified proof of Takàcs's theorem, based on a sample path relationship between the virtual and actual waiting time processes, has recently been advanced. This paper gives a similar proof of Hooke's theorem, based on the same sample path relationship, and demonstrates the utility of the result in analyzing the special case of Poisson input. In particular, by combining the Takàcs and Hooke results one can obtain the Pollaczek–Khintchine formula without any reference to the imbedded Markov chain." @default.
- W2325344952 created "2016-06-24" @default.
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- W2325344952 date "1976-12-01" @default.
- W2325344952 modified "2023-09-26" @default.
- W2325344952 title "On the virtual and actual waiting time distributions of a GI/G/1 queue" @default.
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- W2325344952 doi "https://doi.org/10.1017/s0021900200104541" @default.
- W2325344952 hasPublicationYear "1976" @default.
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