4.4. A small grocery store has a single checkout counter with a full-time cashier. Customers arrive at the checkout according to a Poisson process of rate A per hour. When there is only a single customer at the counter, the cashier works alone at a mean service rate of a per hour. Whenever there is more than one customer at the checkout, however, a "bagger" is added, increasing the service rate to /3 per hour. Assume that service times are exponentially distributed and determine the stationary distribution of the queue length.