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Some reflections on the Renewal-theory paradox in queueing theory

1998
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Journal of Applied Mathematics and Stochastic Analysis
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The classical renewal-theory (waiting time, or inspection) paradox states that the length of the renewal interval that covers a randomly-selected time epoch tends to be longer than an ordinary renewal interval. This paradox manifests itself in numerous interesting ways in queueing theory, a prime example being the celebrated Pollaczek-Khintchine formula for the mean waiting time in theM/G/1queue. In this expository paper, we give intuitive arguments that "explain" why the renewal-theory paradox

doi:10.1155/s104895339800029x
fatcat:jspmlotc7zfqbhzju5xujpa6n4