Analysis of the M/M/1 Queue with Processor Sharing via Spectral Theory

被引：0
|
作者：
Fabrice Guillemin
Jacqueline Boyer
机构：
[1] France Telecom R&D,
来源：
Queueing Systems | 2001年 / 39卷
关键词：
/; /1 queue; processor sharing; spectral theory; orthogonal polynomials; queue asymptotics;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We show in this paper that the computation of the distribution of the sojourn time of an arbitrary customer in a M/M/1 with the processor sharing discipline (abbreviated to M/M/1 PS queue) can be formulated as a spectral problem for a self-adjoint operator. This approach allows us to improve the existing results for this queue in two directions. First, the orthogonal structure underlying the M/M/1 PS queue is revealed. Second, an integral representation of the distribution of the sojourn time of a customer entering the system while there are n customers in service is obtained.
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页码：377 / 397
页数：20
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