A queue with working breakdowns

In this paper, we consider a new class of queueing models with working breakdowns. The system may become defective at any point of time when it is in operation. However, when the system is defective, instead of stopping service completely, the service continues at a slower rate. Using the probability generating function, we give the joint distribution of the server state and the number of customers in the system in steady state. We also derive the necessary and sufficient condition for the existence of the steady state. We study the waiting time distribution of our model. Finally, some performance measures and numerical examples are presented.