Title: The multi-server retrial system with Bernoulli feedback and starting failures
Authors: Yang, Dong-Yuh
Ke, Jau-Chuan
Wu, Chia-Huang
Department of Industrial Engineering and Management
Keywords: 90C53;90B22;68M20;60K25;cost;starting failure;matrix-geometric method;retrial queue;Bernoulli feedback
Issue Date: 4-May-2015
Abstract: In this paper, we present a detailed analysis of a multi-server retrial queue with Bernoulli feedback, where the servers are subject to starting failures. Upon completion of a service, a customer would decide either to leave the system with probability p or to join the retrial orbit again for another service with complementary probability 1-p. We analyse this queueing system as a quasi-birth-death process. Specifically, the equilibrium condition of the system is given for the existence of the steady-state analysis. Applying the matrix-geometric method, the formulae for computing the rate matrix and stationary probabilities are obtained. We further develop the matrix-form expressions for various system performance measures. A cost model is constructed to determine the optimal number of servers, the optimal mean service rate and the optimal mean repair rate subject to the stability condition. Finally, we give a practical example to illustrate the potential applicability of this model.
URI: http://dx.doi.org/10.1080/00207160.2014.932908
ISSN: 0020-7160
DOI: 10.1080/00207160.2014.932908
Volume: 92
Begin Page: 954
End Page: 969
Appears in Collections:Articles