Question: (a) Consider an M/M/k system, where the processing rate at each server is = 1. Fix the system utilization at = 0.95. For k =

(a) Consider an M/M/k system, where the processing rate at each server is = 1. Fix the system utilization at = 0.95. For k = 1, 2, 4, 8, 16, 32 and adjusting the arrival rate to keep the utilization fixed at 0.95, compute the probability that an arriving job has to wait and the mean response time. Provide an intuitive explanation for the trends in your results. (b) For the case with k = 32, how many servers would the square-root staffing rule suggest if the goal was to keep the probability that an arriving job waits to be less than 20 percent? For your choice, calculate the probability that an arriving job waits (exactly, using the M/M/k formulas).

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