Customers arrive at a single convenience store check out counter according to a Poisson process with an average of 10 customers per hour. Customers are served one after the other. When there is only 1 customer in the system, the expected processing time is 10 minutes. When there are more than 1 customers, an assistant helps the server out so that the service time reduces to 5 minutes for each customer. In both cases the service times are exponential. Draw the rate diagram and obtain the steady-state distribution of the number of customers in the system. Also, derive L and W for the system.
L=long-run average number of customers in the system, W=the average time a customer spends in the system.