Queue-Length Distribution for the Discriminatory Processor-Sharing Queue

Kiran M. Rege and Bhaskar Sengupta
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Kiran M. Rege: AT&T Bell Laboratories, Holmdel, New Jersey
Bhaskar Sengupta: NEC USA, Princeton, New Jersey

Operations Research, 1996, vol. 44, issue 4, 653-657

Abstract: In this paper, we study a multiple class discriminatory processor-sharing queue. The queue is assumed to have Poisson input and exponentially distributed service times. In this discipline there are K classes of customers. When there are n i customers present in the system of class i ( i = 1, …, K ), each member of class j receives a fraction of the server's capacity given by α j /∑ i =1 K n i α i . Thus, associated with class i customers is a weight α i which determines the level of service discrimination. For this problem, we find the moments of the queue-length distribution as a solution of linear simultaneous equations. We also prove a heavy traffic limit theorem for the joint queue-length distribution for this queue.

Keywords: probability; Markov processes; queue-length distribution; queues; limit theorems; heavy traffic (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:44:y:1996:i:4:p:653-657

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