Queue-length distribution for the discriminatory processor-sharing queue

• 成果类型: Article
• 署名作者: Rege, KM; Sengupta, B
• 署名单位: NEC Corporation
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.44.4.653
• 发表日期: 1996
• 页码: 653-657
• 关键词: probability; Markov processes; queue-length distribution; queues; limit theorems; heavy traffic

摘要

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