Article ID: | iaor2014439 |
Volume: | 19 |
Issue: | 2 |
Start Page Number: | 154 |
End Page Number: | 173 |
Publication Date: | Jan 2014 |
Journal: | International Journal of Operational Research |
Authors: | Jain Madhu, Singh Charan Jeet, Kumar Binay |
Keywords: | bulk queues, vacation models |
In this paper, a single server queueing model, wherein the units arrive in bulk with varying arrival rates in Poisson process, is considered. It is assumed that the service time of units is arbitrarily distributed. Also, we incorporate the optional deterministic vacations for the server. The server may take a vacation of a fixed duration at the completion of each service or may continue to be available in the system for the next service. At busy and vacation states, the customers may balk from the system with different balking probabilities. By using the basic assumptions of probability reasoning and supplementary variable technique, the steady state behaviour of the system is studied and various performance measures are obtained. In order to obtain the approximate values of the system state probabilities, the principle of maximum entropy is also employed. To verify the tractability of the performance measures obtained, the numerical illustrations are provided. Further, the sensitivity analysis is carried out to examine the system performance with respect to different parameters.