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

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 equilibri...

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Vydáno v:	Journal of computational and applied mathematics Ročník 235; číslo 3; s. 547 - 562
Hlavní autoři:	Wu, Chia-Huang, Ke, Jau-Chuan
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Kidlington Elsevier B.V 01.12.2010 Elsevier
Témata:	Algorithms Balk Calculus of variations and optimal control Computation Cost Cost engineering Customers Exact sciences and technology Mathematical analysis Mathematical models Mathematics Matrix analytic approach Numerical analysis Numerical analysis. Scientific computation Numerical methods in mathematical programming, optimization and calculus of variations Numerical methods in optimization and calculus of variations Optimization Quasi-Newton method Queues Renege Sciences and techniques of general use Servers Renege Balk Matrix analytic approach Quasi-Newton method Cost Necessary and sufficient condition Quasi Newton method Optimization method Probability distribution Algorithm Numerical analysis System performance Queueing system Applied mathematics Variational calculus Queue Mathematical programming
ISSN:	0377-0427, 1879-1778
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Abstract	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.
AbstractList	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. 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.
Author	Ke, Jau-Chuan Wu, Chia-Huang
Author_xml	– sequence: 1 givenname: Chia-Huang surname: Wu fullname: Wu, Chia-Huang organization: Department of Industrial Engineering and Management, National Chiao Tung University, Taiwan, ROC – sequence: 2 givenname: Jau-Chuan surname: Ke fullname: Ke, Jau-Chuan email: jauchuan@ntit.edu.tw organization: Department of Applied Statistics, National Taichung Institute of Technology, No. 129, Sec. 3, Sanmin Road, Taichung, 404, Taiwan, ROC
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Cites_doi	10.1007/BF02579061 10.1093/biomet/44.3-4.360 10.1016/0026-2714(94)00152-E 10.1016/0305-0548(92)90010-3 10.1016/S0307-904X(02)00133-6 10.1016/S0026-2714(96)00018-2 10.1007/BF02613734 10.2307/3215393 10.1016/j.peva.2008.04.004 10.1016/j.apm.2006.02.012 10.1016/j.cor.2005.05.013 10.1016/j.apm.2008.08.006 10.1007/s001860200206 10.1016/j.amc.2003.06.022 10.1051/ro:2004021 10.1111/j.2517-6161.1962.tb00438.x 10.1016/j.apm.2006.08.016 10.1016/j.camwa.2004.06.024 10.1057/palgrave.jors.2600702 10.1016/0026-2714(92)90008-9 10.1016/0026-2714(95)00069-E 10.1287/opre.11.1.88 10.1287/opre.11.6.928 10.1016/j.cie.2006.04.004 10.1016/j.cie.2006.11.005 10.1016/0026-2714(94)00079-4
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Snippet	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... 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...
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SubjectTerms	Algorithms Balk Calculus of variations and optimal control Computation Cost Cost engineering Customers Exact sciences and technology Mathematical analysis Mathematical models Mathematics Matrix analytic approach Numerical analysis Numerical analysis. Scientific computation Numerical methods in mathematical programming, optimization and calculus of variations Numerical methods in optimization and calculus of variations Optimization Quasi-Newton method Queues Renege Sciences and techniques of general use Servers
Title	Computational algorithm and parameter optimization for a multi-server system with unreliable servers and impatient customers
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