# Question

Consider the M/M/s model.

(a) Suppose there is one server and the expected service time is exactly 1 minute. Compare L for the cases where the mean arrival rate is 0.5, 0.9, and 0.99 customers per minute, respectively. Do the same for Lq, W, Wq, and P{W > 5}. What conclusions do you draw about the impact of increasing the utilization factor p from small values (e.g., p = 0.5) to fairly large values (e.g., p = 0.9) and then to even larger values very close to 1 (e.g., p = 0.99)?

(b) Now suppose there are two servers and the expected service time is exactly 2 minutes. Follow the instructions for part (a).

(a) Suppose there is one server and the expected service time is exactly 1 minute. Compare L for the cases where the mean arrival rate is 0.5, 0.9, and 0.99 customers per minute, respectively. Do the same for Lq, W, Wq, and P{W > 5}. What conclusions do you draw about the impact of increasing the utilization factor p from small values (e.g., p = 0.5) to fairly large values (e.g., p = 0.9) and then to even larger values very close to 1 (e.g., p = 0.99)?

(b) Now suppose there are two servers and the expected service time is exactly 2 minutes. Follow the instructions for part (a).

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