Title :
A Discrete-Time Queue with Modified Vacation Policy
Author :
Wang, Tsung-Yin ; Ke, Jau-Chuan ; Chang, Fu-Min
Author_Institution :
Dept. of Accounting Inf., Nat. Taichung Inst. of Technol., Taichung, Taiwan
Abstract :
This paper examines a discrete-time Geo/Geo/1 queue, in which the server operates a randomized vacation policy with at most J vacations. After all messages are served in the queue, the server leaves for a vacation immediately. If there are some messages waiting in the queue upon the server returning from a vacation, it serves the waiting messages immediately. If no messages present in the queue, the server takes another vacation with probability p or goes into idle state with probability (1-p) until the next message arrives. By using the supplementary technique, the joint generating functions of the server state together with the system queue length and waiting time in the queue, vacation period, idle period, and busy period are derived. We also derive the distribution of the messages in the system at the busy initiation epoch and its expected length. Finally, a cost model developed to determine the optimum values of p and J at a minimum cost is also studied.
Keywords :
queueing theory; discrete time Geo/Geo/1 queue; modified vacation policy; queue length system; randomized vacation policy; Computational modeling; Cost function; Joints; Maintenance engineering; Mathematical model; Queueing analysis; Servers; Busy cycle; Cost; Markov chain; Vacation; Waitin time;
Conference_Titel :
Computational Sciences and Optimization (CSO), 2011 Fourth International Joint Conference on
Conference_Location :
Yunnan
Print_ISBN :
978-1-4244-9712-6
Electronic_ISBN :
978-0-7695-4335-2
DOI :
10.1109/CSO.2011.27