# Students arrive at a rate of about three per minute according to a Poisson distribution. The single cashier takes about 15 seconds per customer, following an exponential distribution. a) What is the probability that the system is empty? b) How long will the average student have to wait before reaching the cashier? c) What is the expected number of students in the queue? d) What is the average number in the system?

from the companion website ://..com/___11/236/60528/15495221.cw/index.Go to practice problems of Module D. (We did problems 1 and 2 in class). Go to Problem 3 and consider that  = 0.0767 for 2 servers and a ratio lambda/mu of 0.66. Compute the values of Ls,  and  based on this number and the formulas on slides 35-36 from the material. Build a table to compare the 2 models, taking slide 39 as a template. Compute the cost of the system when there are 2 servers; which option would you choose between 1 server and 2 servers?The cafeteria line in the university student center is a self-serve facility in which students select the items they want and then form a single line to pay the cashier. Students arrive at a rate of about three per minute according to a Poisson distribution. The single cashier takes about 15 seconds per customer, following an exponential distribution. a) What is the probability that the system is empty? b) How long will the average student have to wait before reaching the cashier? c) What is the expected number of students in the queue? d) What is the average number in the system? e) If a second cashier is added and works at the same pace, how will the operating characteristics computed in parts (a), (b), (c), and (d) change? Assume customers wait in a single line and go to the first available cashier. (use the table from slide 40 to start)

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