31 Consider a queueing system in which each service time, independent of the past, has mean Let Wn and Dn denote, respectively, the amounts of time customer n spends in the system and in queue Hence, Dn Wn Sn where Sn is the service time of customer n Therefore, E Dn E Wn If we use simulation to estimate E Dn , should we (a) use the simulated data to determine Dn, which is then used as an estimate of E Dn or (b) use the simulated data to determine Wn and then use this quantity minus as an estimate of E Dn Repeat for when we want to estimate E Wn

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Question: 31. Consider a queueing system in which each service time, independent of the past, has mean . Let Wn and Dn denote, respectively, the amounts

31. Consider a queueing system in which each service time, independent of the past, has mean μ. Let Wn and Dn denote, respectively, the amounts of time customer n spends in the system and in queue. Hence, Dn = Wn − Sn where Sn is the service time of customer n. Therefore, E[Dn] = E[Wn] − μ

If we use simulation to estimate E[Dn], should we

(a) use the simulated data to determine Dn, which is then used as an estimate of E[Dn]; or

(b) use the simulated data to determine Wn and then use this quantity minus μ as an estimate of E[Dn]?

Repeat for when we want to estimate E[Wn].

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