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Batch service queue with change over times and Bernoulli schedule vacation interruption

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Abstract

In this paper, we model a discrete-time renewal input queue with change over times and Bernoulli schedule vacation interruption under batch service (a, c, b) policy. The service, working vacation and change over times are geometrically distributed. At the instants of a service completion, the vacation is interrupted and the server is resumed to a regular busy period with probability 1 − q if there are c or more customers in the system, or continues the vacation with probability q. Employing the supplementary variable and recursive techniques, we have derived the steady state queue length distributions at various epochs. Some performance measures and a cost model have been presented and an optimum service rate has been obtained using geneticalgorithm. Numerical results showing the effect of the parameters of the modelon the key performance measures are presented.

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Acknowledgments

The authors would like to thank the Editor and the referees for their valuable comments and suggestions which helped in improving the quality of presentation of this paper. The first author also wishes to thank the support from University Grants Commission (UGC), New Delhi, India, under the minor research project: F.No. 41-1389/2012 (SR).

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  1. Department of Applied Mathematics, Andhra University, Visakhapatnam, 530003, India

    P. Vijaya Laxmi & D. Seleshi

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  1. P. Vijaya Laxmi
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  2. D. Seleshi
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Correspondence to P. Vijaya Laxmi.

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Laxmi, P.V., Seleshi, D. Batch service queue with change over times and Bernoulli schedule vacation interruption. OPSEARCH 51, 354–375 (2014). https://doi.org/10.1007/s12597-013-0149-y

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