M/M/1 queue with bi-level network process and bi-level vacation policy with balking

Abstract

In this article, an M/M/1 queueing model with bi-level network service provider, balking process and bi-level vacation policy that comprises of working vacation and complete vacation after fixed service, is developed. Matrix form expressions have been derived for the distributions of the queued customers with some performance metrics with the help of matrix geometric method. The maximum entropy principle is also used to derive the distributions of the steady state probabilities of queue size. The cost function has been formed to optimize the decision variables of the system. We perform the cost optimization by employing the steepest descent search method. Numerical illustrations along with the sensitivity analysis have been drawn to validate the model. Finally, the conclusions of the investigation done are drawn by mentioning the novel features and future scope.

Keywords:

• Bi-level service process
• bi-level vacation policy
• working vacation
• matrix geometric method
• maximum entropy principle
• steepest descent method

Acknowledgements

The author Anshul Kumar would like to thank Council of Scientific and Industrial Research (CSIR), India for awarding senior research fellowship (SRF) with grant code 9013-12-061.

Additional information

Funding

The author Anshul Kumar would like to thank Council of Scientific and Industrial Research (CSIR), India for awarding senior research fellowship (SRF) with grant code 9013-12-061.