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

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.