Title: A heuristic algorithm for the optimization of a retrial system with Bernoulli vacation
Authors: Ke, Jau-Chuan
Wu, Chia-Huang
Pearn, Wen Lea
Department of Industrial Engineering and Management
Keywords: Bernoulli vacation schedule;matrix-geometric method;quasi-Newton method;retrial;single vacation policy
Issue Date: 1-Mar-2013
Abstract: In this study, we consider an M/M/c retrial queue with Bernoulli vacation under a single vacation policy. When an arrived customer finds a free server, the customer receives the service immediately; otherwise the customer would enter into an orbit. After the server completes the service, the server may go on a vacation or become idle (waiting for the next arriving, retrying customer). The retrial system is analysed as a quasi-birth-and-death process. The sufficient and necessary condition of system equilibrium is obtained. The formulae for computing the rate matrix and stationary probabilities are derived. The explicit close forms for system performance measures are developed. A cost model is constructed to determine the optimal values of the number of servers, service rate, and vacation rate for minimizing the total expected cost per unit time. Numerical examples are given to demonstrate this optimization approach. The effects of various parameters in the cost model on system performance are investigated.
URI: http://dx.doi.org/10.1080/02331934.2011.579966
ISSN: 0233-1934
DOI: 10.1080/02331934.2011.579966
Volume: 62
Issue: 3
Begin Page: 299
End Page: 321
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