Computational algorithm and parameter optimization for a multi-server system with unreliable servers and impatient customers

被引：11

作者：

Wu, Chia-Huang ^{[2
]}

Ke, Jau-Chuan ^{[1
]}

机构：

[1] Natl Taichung Inst Technol, Dept Appl Stat, Taichung 404, Taiwan

[2] Natl Chiao Tung Univ, Dept Ind Engn & Management, Hsinchu, Taiwan

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2010年 / 235卷 / 03期

关键词：

Cost; Balk; Quasi-Newton method; Renege; Matrix analytic approach; MACHINE REPAIR PROBLEM; M/G/1 QUEUING SYSTEM; ADDITIONAL SERVER; SERVICE SUBJECT; COST-ANALYSIS; PHASES; BALKING; BREAKDOWNS; RELIABILITY; STARTUP;

D O I：

10.1016/j.cam.2010.06.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider an infinite capacity M/M/c queueing system with c unreliable servers, in which the customers may balk (do not enter) and renege (leave the queue after entering). The system is analyzed as a quasi-birth-and-death (QBD) process and the necessary and sufficient condition of system equilibrium is obtained. System performance measures are explicitly derived in terms of computable forms. The useful formulae for computing the rate matrix and stationary probabilities are derived by means of a matrix analytical approach. A cost model is derived to determine the optimal values of the number of servers, service rate and repair rate simultaneously at the minimal total expected cost per unit time. The parameter optimization is illustrated numerically by the Quasi-Newton method. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：547 / 562

页数：16

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