Randy Fritz has been collecting data at the TU student grill. He has found that, between 5:00 PM and 7:00 PM, students arrive at the grill at a rate of 20 per hour (Poisson distributed) and service time takes an average of 2 minutes (exponential distribution). There is only 1 server, who can work on only 1 order at a time.
a) What is the average number of customers in line?
b) The average time in minutes in the system?
c) Suppose that a second server can be added to team up with the first (and, in effect, act as one faster server). This would reduce the average service time to 90 seconds. The average time in the system in minutes is?
d) Suppose a second server is added and the 2 servers act independently, with each taking an average of 2 minutes. If a second teller is added, what is the average time a customer spends in the system in minutes is?