9.4.3 Balking refers to the refusal of an arriving customer to enter the queue. Reneging refers to the departure of a customer in the queue before obtaining service.

Consider an M=M=1 system with reneging such that the probability that a specified single customer in line will depart prior to service in a short time interval

.t; tC1t] is rn.1t/Co.1t/ when n is the number of customers in the system.

(Note that r0 D r1 D 0.) Assume Poisson arrivals at rate  and exponential service times with parameter , and determine the stationary distribution when it exists.