The covariance function of the virtual waiting-time process in an M / G /1 queue
Year: 1977
Type: article
Abstract: 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.
Source: Advances in Applied Probability
Author: Teunis J. Ott
Institution: Case Western Reserve University
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W2065690340