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Probability, Statistics and Queueing

A web server holds an average of 12 requests, counting those being processed and those waiting. Requests arrive at 40 per second and are processed at the same rate (steady state). Which of the following is the average time a request spends in the server, found from Little's law?

  1. A0.3 seconds
  2. BAbout 3.3 seconds
  3. C480 seconds
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Answer: A. 0.3 seconds

Rearranging Little's law L = λW (average number in the system = arrival rate × average time in the system) gives W = L ÷ λ. W = 12 ÷ 40 = 0.3 seconds. Little's law holds in a stable steady state regardless of the distributions of arrivals and service times.

  • A. Correct. 12 ÷ 40 = 0.3 seconds.
  • B. This is 40 ÷ 12 ≈ 3.3, dividing the wrong way round.
  • C. This is 12 × 40 = 480, calculating L × λ instead of L ÷ λ.
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