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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Popis
Shrnutí: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.
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content type line 23
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2010.06.005