An M /M /1 Queueing System with Server on Attacks and Repair

Abstract

We consider a M /M /1 queueing model of a communication system subject to random attacks on service station. In such attack system, the time interval between any two attacks is an exponentially distributed random variable with mean1/ . When the server fails by an attack, any customer getting service at that time becomes damaged. The failed server is immediately taken for repair and the damaged customer is washed out. Customers in the queue waiting for service are not washed out. The repair time of the server undergoing repair is assumed to be an exponentially distributed random variable with mean1/ . During repair time, the customers are allowed to wait for service maintain First Come First Served order. After the completion of repair, the server returns to the work-station immediately without any delay, even if there is no customer to render service. We derive explicit form of the state probabilities of the attack system in the long run. We also obtain measures of system performance and the model is validated by a numerical illustration.