(Queue with impatient customers). Customers arrive at a single server at rate

[1] and require an exponential amount of service with rate

. Customers waiting in line are impatient and if they are not in service they will leave at rate ı independent of their position in the queue.

(a) Show that for anyı > 0 the system has a stationary distribution.

(b) Find the stationary distribution in the very special case in which

ı D

.