A RANDOM MULTIPLE-ACCESS PROTOCOL WITH SPATIAL INTERACTIONS

被引：5

作者：

Bordenave, Charles

Foss, Serguei ^{[1
]}

Shneer, Vsevolod ^{[2
,3
]}

机构：

[1] Heriot Watt Univ, Dept Actuarial Math & Stat, Edinburgh EH14 4AS, Midlothian, Scotland

[2] EURANDOM, NL-5600 MB Eindhoven, Netherlands

[3] Eindhoven Univ Technol, NL-5600 MB Eindhoven, Netherlands

来源：

JOURNAL OF APPLIED PROBABILITY | 2009年 / 46卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

ALOHA protocols; spatial interaction; stability of processes; fluid limits; NETWORKS; CONVERGENCE; STABILITY;

D O I：

10.1239/jap/1253279855

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 analyse an ALOHA-type random multiple-access protocol where users have local interactions. We show that the fluid model of the system workload satisfies a certain differential equation. We obtain a sufficient condition for the stability of this differential equation and deduce from that a sufficient condition for the stability of the protocol We discuss the necessary condition. Furthermore, for the underlying Markov chain, we estimate the rate of convergence to the stationary distribution. Then we establish in interesting and unexpected result showing that the main diagonal is locally unstable if the input rate is sufficiently small. Finally, we consider two generalisations of the model.

引用

页码：844 / 865

页数：22

共 18 条

[1]

Abramson N., 1970, AFIPS CONF P, V36, P295

[2]

CODDINGION E, 1955, THEORY ORDINARY DIFF

[3] ON POSITIVE HARRIS RECURRENCE OF MULTICLASS QUEUEING NETWORKS: A UNIFIED APPROACH VIA FLUID LIMIT MODELS [J].