具有单重休假和Min(N,V)-策略控制的Geo/G/1离散时间排队的离去过程分析

数学物理学报 ›› 2016, Vol. 36 ›› Issue (2): 380-392.

• 论文 • 上一篇

具有单重休假和Min(N,V)-策略控制的Geo/G/1离散时间排队的离去过程分析

兰绍军¹, 唐应辉^1,2

1. 四川师范大学数学与软件科学学院成都 610066;
2. 四川师范大学基础教学学院成都 610066

收稿日期:2015-10-21 修回日期:2016-01-13 出版日期:2016-04-25 发布日期:2016-04-25
通讯作者: 唐应辉,tangyh@uestc.edu.cn E-mail:tangyh@uestc.edu.cn
作者简介:兰绍军,sjlan89@163.com
基金资助:
国家自然科学基金(71171138,71571127)资助

Analysis of the Departure Process for Geo/G/1 Discrete-Time Queue with Single Server Vacation and Min-Policy

Lan Shaojun¹, Tang Yinghui^1,2

1 School of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066;
2 School of Fundamental Education, Sichuan Normal University, Chengdu 610066

Received:2015-10-21 Revised:2016-01-13 Online:2016-04-25 Published:2016-04-25
Supported by:
Supported by the NSFC (71171138, 71571127)

摘要/Abstract

摘要：

该文研究服务员具有单重休假和系统采用Min(N,V)-策略控制的Geo/G/1离散时间排队系统的离去过程.首先,借助全概率分解方法,更新过程理论以及概率母函数技术,讨论了服务员在任意时刻点n⁺处于忙的瞬态概率和稳态概率.其次,得到了在时间段(0⁺,n⁺]内的平均离去顾客数的概率母函数表达式.同时给出了离去过程、服务员忙的状态过程和在服务员忙期中的服务更新过程三者之间的关系,这一关系表明了系统离去过程的特殊结构.特别地,直接获得了一些特殊离散时间排队系统的离去过程的相应结果.最后,给出了便于计算任意时间段(0⁺,n⁺]内平均离去顾客数的渐近展式.

关键词: 离散时间排队, Min(N, V)-策略, 单重休假, 离去过程, 离去平均数

Abstract:

In this paper we investigate the departure process for a Geo/G/1 discrete-time queueing system in which the server takes single server vacation and the system adopts Min(N, V)-policy. In this study, by employing the total probability decomposition law, renewal theory and probability generating function technique, the transient and the steady probability that the server is busy at any epoch n⁺ are derived. Furthermore, we also obtain the expression of the probability generating function for the expected number of departures occurring in the time interval (0⁺, n⁺] from any initial state. Meanwhile, the relationship among departure process, server busy-state process and the service renewal process in server busy period is found, which shows the especial structure of departure process. Especially, some corresponding results of departure process for special discrete-time queues are directly gained by the results obtained in this paper. Finally, the asymptotic expansion for calculating expected number of departures conveniently is presented.

Key words: Discrete-time queue, Min(N, V)-policy, Single server vacation, Departure process, Expected number of departures

中图分类号:

O226

兰绍军, 唐应辉. 具有单重休假和Min(N,V)-策略控制的Geo/G/1离散时间排队的离去过程分析[J]. 数学物理学报, 2016, 36(2): 380-392.

Lan Shaojun, Tang Yinghui. Analysis of the Departure Process for Geo/G/1 Discrete-Time Queue with Single Server Vacation and Min-Policy[J]. Acta mathematica scientia,Series A, 2016, 36(2): 380-392.

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具有单重休假和Min(N,V)-策略控制的Geo/G/1离散时间排队的离去过程分析

Analysis of the Departure Process for Geo/G/1 Discrete-Time Queue with Single Server Vacation and Min-Policy

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