Weak convergence of high-speed network traffic models

被引：1

作者：

Resnick, S

Van den Berg, E

机构：

[1] Cornell Univ, Sch Operat Res & Ind Engn, Ithaca, NY 14853 USA

[2] Telecordia Technol, Morristown, NJ 07960 USA

来源：

JOURNAL OF APPLIED PROBABILITY | 2000年 / 37卷 / 02期

关键词：

fractional Brownian motion; Poisson process; Levy stable motion; high speed network; M-1; topology;

D O I：

10.1017/S0021900200015758

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider a network traffic model consisting of an infinite number of sources linked to a server. Sources initiate transmissions to the server at Poisson time points. The duration of each transmission has a heavy-tailed distribution. We show that suitable scalings of the traffic process converge to a totally skewed stable Levy motion in Skorohod space, equipped with the Skorohod M-1 topology. This allows us to prove a heavy-traffic theorem for a single-server fluid model.

引用

页码：575 / 597

页数：23

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