On the discrete-time Geo/G/1 queue with randomized vacations and at most J vacations

被引:20
作者
Wang, Tsung-Yin [1 ]
Ke, Jau-Chuan [2 ]
Chang, Fu-Min [3 ]
机构
[1] Natl Taichung Inst Technol, Dept Accounting Informat, Taichung 404, Taiwan
[2] Natl Taichung Inst Technol, Dept Appl Stat, Taichung 404, Taiwan
[3] Chaoyang Univ Technol, Dept Finance, Taichung 404, Taiwan
关键词
Busy period; Cost; Discrete-time queue; Markov chain; Randomized vacation; GI/GEO/1; QUEUE; SYSTEM; SCHEDULES; BALKING; POLICY;
D O I
10.1016/j.apm.2010.11.021
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
This paper examines a discrete-time Geo/G/1 queue, where the server may take at most J - 1 vacations after the essential vacation. In this system, messages arrive according to Bernoulli process and receive corresponding service immediately if the server is available upon arrival. When the server is busy or on vacation, arriving messages have to wait in the queue. After the messages in the queue are served exhaustively, the server leaves for the essential vacation. At the end of essential vacation, the server activates immediately to serve if there are messages waiting in the queue. Alternatively, the server may take another vacation with probability p or go into idle state with probability (1 - p) until the next message arrives. Such pattern continues until the number of vacations taken reaches J. This queueing system has potential applications in the packet-switched networks. By applying the generating function technique, some important performance measures are derived, which may be useful for network and software system engineers. A cost model, developed to determine the optimum values of p and J at a minimum cost, is also studied. (c) 2010 Elsevier Inc. All rights reserved.
引用
收藏
页码:2297 / 2308
页数:12
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