Analysis of Queues in a Random Environment with Impatient Customers

被引：7

作者：

Yu, Sen-lin ^{[1
]}

Liu, Zai-ming ^{[1
]}

机构：

[1] Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

来源：

ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES | 2017年 / 33卷 / 04期

基金：

中国国家自然科学基金;

关键词：

random environment; Markov modulated; queues; impatient customers; MODULATED SERVICE RATES; M/M/1; QUEUE; VACATIONS; SINGLE;

D O I：

10.1007/s10255-017-0701-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study M/M/c queues (c = 1, 1 < c < infinity and c = infinity) in a Markovian environment with impatient customers. The arrivals and service rates are modulated by the underlying continuous-time Markov chain. When the external environment operates in phase 2, customers become impatient. We focus our attention on the explicit expressions of the performance measures. For each case of c, the corresponding probability generating function and mean queue size are obtained. Several special cases are studied and numerical experiments are presented.

引用

页码：837 / 850

页数：14

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