Markovian queueing model with catastrophe, unreliable and backup server

Abstract

In this article, we considered a finite size Markovian queue with single server. When the server breaks down, in order to facilitate the customer, backup server is provided. When system happened to undergo catastrophe, the customers are being removed and by restoration time the system get back to its normal state. Here, we have analysed the number of times the system reached its capacity. By utilising matrix geometric method, model has been solved and measures of effectiveness are done. Also numerical examples and graphical representation are given.