Assignment:
Bill Youngdahl has been collecting data at the TU student grill. He has found that, between 5:00 p.m. and 7:00 p.m., students arrive at the grill at a rate of 25 per hour (Poisson distributed) and service time takes an average of 2 minutes (negative exponential distribution). There is only 1 server, who can work on only 1 order at a time.
a) What is the average number of students in line?
b) What is the average time a student is in the grill area?
c) Suppose that a second server can be added to team up with the first (and, in effect, act as 1 faster server). This would reduce the average service time to 90 seconds. How would this affect the average time a student is in the grill area?
d) Suppose a second server is added and the 2 servers act independently, with each taking an average of 2 minutes. What would be the average time a student is in the system?
Provide complete and step by step solution for the question and show calculations and use formulas.