Consider an M/M/1 queue with arrival rate and processing rate , and the following modification in its operational dynamics: Each customer joining the station will renege (i.e., depart without service) with probability ah + o(h) while waiting in the queue for a time interval of length h, independently of the other customers in the queue. But once a customer makes it to the server, she will receive full service and then depart from the system.

Consider the special case where a = (i.e., the customer reneging rate is equal to the server processing rate). Argue that in this case the CTMC will always be stable, and characterize the corresponding limiting distribution.

For the special case above, what is the \steady-state" probability that a customer who gets into the station will renege?