An optional service Markovian queue with working disasters and customer’s impatience

Abstract

In this paper, we develop a new class of Markov model with working disasters, second optional service, and reneging of customers. The disasters can occur during regular busy period. Whenever a disaster occurs, server continues to serve the customers with a lower service rate instead of completely stopping the service and after the completion of disaster recovery it switches to the regular busy period. Steady-state solution of the model is obtained by using probability generating function technique and stability condition is derived. Further, some important performance measures are presented. A cost model is developed in order to obtain the optimal service rates during first essential service, second optional service and during disaster period using quadratic fit search method. At the end, we provide some numerical examples to visualize the applicability of the model in practical situations.