Requests arrive at a server at an average of 3 per minute, and each takes an average of 15 seconds to process. Treating the server as an M/M/1 queue, which of the following is the average time from the arrival of a request until its processing is finished (the average response time)?

Answer: C. 60 seconds

The utilization is ρ = 3 per minute × 15 seconds ÷ 60 seconds = 0.75. The average waiting time is Wq = ρ/(1 − ρ) × Ts = 0.75/0.25 × 15 = 45 seconds, and adding the processing time of 15 seconds gives an average response time of 45 + 15 = 60 seconds. Ts/(1 − ρ) = 15/0.25 = 60 seconds gives the same result.

• A. This is 15 ÷ 0.75 = 20, dividing by ρ instead of 1 − ρ.
• B. 45 seconds is only the time spent waiting in the queue, Wq, without adding the 15-second processing time.
• C. Correct. 45 + 15 = 60 seconds.