On an unreliable-server retrial queue with customer feedback and impatience

•A feedback retrial system with unreliable servers and impatient customers is studied.•We develop a recursive solver algorithm for calculating the stationary distribution.•We derive a cost function to optimize the system parameters.•We employ three heuristic algorithms to implement optimization task...

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Bibliographic Details
Published in:Applied Mathematical Modelling 2018-03, Vol.55, p.171-182
Main Authors: Chang, Fu-Min, Liu, Tzu-Hsin, Ke, Jau-Chuan
Format: Article
Language:English
Subjects:
Customer feedback
Feedback
Impatience
Mathematical models
Optimization
Optimization algorithms
Pattern search
Policies
Probability
Quasi Newton methods
Queueing
Queues
Search methods
Studies
Unreliable-server
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Summary:•A feedback retrial system with unreliable servers and impatient customers is studied.•We develop a recursive solver algorithm for calculating the stationary distribution.•We derive a cost function to optimize the system parameters.•We employ three heuristic algorithms to implement optimization tasks.•A comparison is made to justify the correctness of approximate optimal solution. Analysis of an unreliable-server retrial queue with customer's feedback and impatience is presented. Truncated classical and constant retrial policies are taken into account. This system is analyzed as a process of quasi-birth-and-death (QBD). The quasi-progression algorithm is applied to compute the rate matrix of QBD model. A recursive solver algorithm for computing the stationary probabilities is also developed. To make the investigated system viable economically, a cost function is developed to decide the optimum values of servers, mean service rate and mean repair rate. Quasi-Newton method, pattern search method and Nelder–Mead simplex direct search method are employed to implement the optimization tasks. Under optimum operating conditions, numerical results are provided for a comparison of retrial policies. We also give a potential application to illustrate the system's applicability.
ISSN:0307-904X
1088-8691
0307-904X
DOI:10.1016/j.apm.2017.10.025