Question: The Block Blaster DVD store has only one cashier working at a time. Assume that the customers arrive to the cashier according to a Poisson process with average rate of 1 customer/min. When comparing the service times of two cashiers that work different shifts, some differences in service time distributions were noted. Cashier A has an exponentially distributed service time with mean of 0.5 min per customer. Cashier B also has a mean service time 0.5 min per customer, but the time distribution is uniform on the interval [0.2, 0.8] min.
The management of Block Blaster wants to know if these differences in service time distributions affect the expected number of customers waiting in line and the associated expected time in the queue. If there are differences, the management team wants to know which cashier performs the best so that the other cashier may learn from the best practice performance, and the overall process can be improved.