Discrete-time renewal input bulk service queue with changeover time

Abstract

In this paper, we model a discrete-time infinite buffer renewal input single server queue with changeover time under (a, c, b) policy. The service and changeover time are geometrically distributed. The server begins service if there are at least c customers in the queue and the services are performed in batches of minimum size a and maximum size b (a ≤ c ≤ b). At the instant of service completion, if the queue size is less than c but not less than a secondary limit a, the server continues to serve and it will be in the changeover period if the queue size is a − 1. Employing the supplementary variable and recursive techniques, we have derived the steady state queue length distributions at pre-arrival and arbitrary epochs. Based on the queue length distributions, some performance measures and cost functions have been discussed. Using a genetic algorithm, the optimum value of the service rate at minimum cost has been evaluated. Numerical results showing the effect of model parameters on the key performance measures are presented. Finally, we have derived the steady state queue length distributions of the continuous-time counterpart of our model.

Keywords:

• discrete-time
• infinite buffer
• batch service
• changeover time
• cost

Acknowledgements

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