Question: Queue with impatient customers. Customers arrive at a single server at rate and require an exponential amount of service with rate . Customers waiting

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

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 any ı > 0 the system has a stationary distribution.

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

ı D .

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