POISSON HYPOTHESIS FOR INFORMATION NETWORKS. I

被引：15
|
作者：
Rybko, Alexander [1 ]
Shlosman, Senya [2 ]
机构：
[1] Russian Acad Sci, Inst Informat Transmiss Problems, Moscow, Russia
[2] CNRS, Ctr Phys Theor, UMR 6207, F-13288 Marseille 9, France
来源：
MOSCOW MATHEMATICAL JOURNAL | 2005年 / 5卷 / 03期
关键词：
Mean-field models; server; waiting time; phase transition; limit theorem; self-averaging property; attractor;
D O I：
10.17323/1609-4514-2005-5-3-679-704
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we study the Poisson Hypothesis, which is a device to analyze approximately the behavior of large queuing networks. We prove it in some simple limiting cases. We show in particular that the corresponding dynamical system, defined by the non-linear Markov process, has a line of fixed points which are global attractors. To do this we derive the corresponding non-linear equation and we explore its self-averaging properties. We also argue that in cases of heavy-tail service times the PH can be violated.
引用
收藏
页码：679 / 704
页数：26
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