At the Order Fulfillment Center of a Major Mail-Order Firm

Essay

At the order fulfillment center of a major mail-order firm, customer orders, already packaged for shipment, arrive at the sorting machine to be sorted for loading onto the appropriate truck for the parcel's address. The arrival rate at the sorting machine is at the rate of 100 per hour following a Poisson distribution. The machine sorts at the constant rate of 125 per hour.
(a) What is the average number of packages waiting to be sorted?
(b) What is the average number of packages in the sorting system?
(c) How long must the average package wait until it gets sorted?
(d) What would L_q and W_q be if the service rate were exponential, not constant?