A manufacturing station operates in the following way. Items to be processed arrive at the station as a Poisson process with the mean time between arrivals equal to 5 minutes. Processing is done on machines that require an average time of 12 minutes per item. Three machines are provided to meet this load. Based on this data, the probabilities at the right are computed. In addition, we have that the expected number of items in the system is 4.986.

a. What is the expected number in the queue?

b. What is the throughput time for the items (this is the expected time between when the item enters the system to when it leaves the system)?

c. What is the probability that an arriving item will have to wait for processing?

d. Adjacent to the machines there is room for three waiting items. When that space is full, items are moved to separate storage to await processing. What is the probability that an arriving item will be stored in this separate storage?

e. If we add another machine to aid in the processing, how will the expected number of items actually being processed (not in the queue) change? (up, down, or stay the same)