TRANSIENT ANALYSIS FOR EXPONENTIAL TIME-LIMITED POLLING MODELS UNDER THE PREEMPTIVE REPEAT RANDOM POLICY

被引：4

作者：

De Haan, Roland ^{[1
]}

Al Hanbali, Ahmad ^{[2
]}

Boucherie, Richard J. ^{[3
]}

Van Ommeren, Jan-Kees ^{[3
]}

机构：

[1] CQM, Eindhoven, Netherlands

[2] King Fahd Univ Petr & Minerals, Dept Syst Engn, Coll Comp Sci & Engn, POB 5063, Dhahran 31261, Saudi Arabia

[3] Univ Twente, Dept Stochast Operat Res, Twente, Netherlands

来源：

ADVANCES IN APPLIED PROBABILITY | 2020年 / 52卷 / 01期

关键词：

Queueing; polling systems; transient analysis; SYSTEMS;

D O I：

10.1017/apr.2019.51

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：

Polling systems are queueing systems consisting of multiple queues served by a single server. In this paper we analyze two types of preemptive time-limited polling systems, the so-called pure and exhaustive time-limited disciplines. In particular, we derive a direct relation for the evolution of the joint queue length during the course of a server visit. The analysis of the pure time-limited discipline builds on and extends several known results for the transient analysis of an M/G/1 queue. For the analysis of the exhaustive discipline we derive several new results for the transient analysis of the M/G/1 queue during a busy period. The final expressions for both types of polling systems that we obtain generalize previous results by incorporating customer routeing, generalized service times, batch arrivals, and Markovian polling of the server.

引用

页码：32 / 60

页数：29

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