Two-State Retrial Queueing Model with Catastrophe

Abstract

The present paper discusses a two-state retrial queueing system with catastrophe. If a customer on arrival finds the server free then it is served immediately. Such customer is known as primary customer. Moreover, if the server is busy then the customer joins virtual queue and retries for service after a random amount of time. This customer is called a secondary customer. Primary and secondary customers both follow Poisson processes. Inter arrival times and service times both follow exponential distribution. Catastrophe occurs on a busy server and its occurrence follows a Poisson process. Catastrophe causes the failure of server and so the server is sent for repair after occurrence of catastrophe. The repair times are also exponentially distributed. Time dependent probabilities for
exact number of arrivals in the system and departures from the system when the server is idle or busy are obtained by using recursive approach. The probability of server being under repair is also obtained. Verification of results is done. Numerical results are generated and represented graphically to study the effect of various parameters.