ANALYSIS OF AN M/M/1 QUEUEING SYSTEM WITH IMPATIENT CUSTOMERS AND A VARIANT OF MULTIPLE VACATION POLICY

被引：23

作者：

Yue, Dequan ^{[1
]}

Yue, Wuyi ^{[2
]}

Saffer, Zsolt ^{[3
]}

Chen, Xiaohong ^{[4
]}

机构：

[1] Yanshan Univ, Dept Stat, Coll Sci, Qinhuangdao 066004, Peoples R China

[2] Konan Univ, Dept Intelligennce & Informat, Kobe, Hyogo 6588501, Japan

[3] Budapest Univ Technol & Econ, Dept Telecommun, Budapest, Hungary

[4] Yanshan Univ, Coll Sci, Qinhuangdao 066004, Peoples R China

来源：

JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION | 2014年 / 10卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Queue; a variant of multiple vacation; impatience; probability generating function; mean system size; QUEUES;

D O I：

10.3934/jimo.2014.10.89

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, we consider an M/M/1 queueing system with impatient customers and a variant of multiple vacation policy, where we examine the case that customer impatience is due to the servers' vacation. Whenever a system becomes empty, the server takes a vacation. However, the server is allowed to take a maximum number K of vacations if the system remains empty after the end of a vacation. This vacation policy includes both a single vacation and multiple vacations as special cases. We derive the probability generating functions of the steady-state probabilities and obtain the closed-form expressions of the system sizes when the server is in different states. We further make comparisons between the mean system sizes under the variant vacation policy and the mean system sizes under the single vacation policy or the multiple vacation policy. In addition, we obtain the closed-form expressions for other important performance measures and discuss their monotonicity with respect K. Finally, we present some numerical results to show the effects of some parameters on some performance measures.

引用

页码：89 / 112

页数：24

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