Cost-minimization analysis of a working vacation queue with N-policy and server breakdowns

被引:54
|
作者
Yang, Dong-Yuh [1 ]
Wu, Chia-Huang [2 ]
机构
[1] Natl Taipei Univ Business, Inst Informat & Decis Sci, Taipei 100, Taiwan
[2] Natl Chiao Tung Univ, Dept Ind Engn & Management, Hsinchu 30050, Taiwan
关键词
Quasi-birth-death process; Matrix-geometric method; N-policy; Particle swarm optimization; Working vacation; RELIABLE SERVER; M/G/1; QUEUE; SYSTEM; STARTUP;
D O I
10.1016/j.cie.2015.01.017
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
This paper investigates the N-policy M/M/1 queueing system with working vacation and server breakdowns. As soon as the system becomes empty, the server begins a working vacation. The server works at a lower service rate rather than completely stopping service during a vacation period. The server may break down with different breakdown rates during the idle, working vacation, and normal busy periods. It is assumed that service times, vacation times, and repair times are all exponentially distributed. We analyze this queueing model as a quasi-birth-death process. Furthermore, the equilibrium condition of the system is derived for the steady state. Using the matrix-geometric method, we find the matrix-form expressions for the stationary probability distribution of the number of customers in the system and system performance measures. The expected cost function per unit time is constructed to determine the optimal values of the system decision variables, including the threshold N and mean service rates. We employ the particle swarm optimization algorithm to solve the optimization problem. Finally, numerical results are provided, and an application example is given to demonstrate the applicability of the queueing model. (C) 2015 Elsevier Ltd. All rights reserved.
引用
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页码:151 / 158
页数:8
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