Approximate sojourn time distribution of a discriminatory processor sharing queue with impatient customers
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We consider a two-class processor sharing queueing system scheduled by the discriminatory processor sharing discipline. Poisson arrivals of customers and exponential amounts of service requirements are assumed. At any moment of being served, a customer can leave the system without completion of its service. In the asymptotic regime, where the ratio of the time scales of the two-class customers is infinite, we obtain the conditional sojourn time distribution of each class customers. Numerical experiments show that the time scale decomposition approach developed in this paper gives a good approximation to the conditional sojourn time distribution as well as the expectation of it.
KeywordsDiscriminatory processor sharing Impatient customers Sojourn time distribution Time scale decomposition method
The author would like to thank the associate editor and the anonymous referees for their comments and suggestions on the first draft of this paper. Their suggestions have greatly improve the quality of the paper. This research was supported by the 2014 Research Fund of University of Seoul.
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