Conservation equations and variance reduction in queueing simulations
John S. Carson,Averill M. Law +1 more
- 05 Dec 1977
- pp 186-189
42
TL;DR: In this paper, the authors consider the GI/G/s queue and show that it is more efficient to estimate w, Q, and L from an estimate of d than it is to estimate them directly.
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Abstract: We consider the efficient estimation of mean delay in queue, d, mean wait in system, w, time average number in queue, Q, and time average number in system, L, for simulated queueing systems. We prove for the GI/G/s queue that it is more efficient to estimate w, Q, and L from an estimate of d than it is to estimate them directly. This generalizes previous results for the M/G/l queue and also confirms empirical studies on other GI/G/s queues.
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A central-limit-theorem version of L =λ W
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TL;DR: This work has shown that when the arrival rateλ is known and the interarrivai times and waiting times are negatively correlated, it is more asymptotically efficient to estimate the long-run time-average queue lengthL indirectly by the sample-average of the waiting times, invokingL=λW, than it is to estimate it by the samples of the queue length.
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A perspective on variance reduction in dynamic simulation experiments
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54
References
•Book
Efficient estimators for simulated queueing systems
Averill M. Law
- 01 Jan 1974
TL;DR: It is shown to be more efficient to estimate all of the usual first moment measures of performance from an estimate of mean delay in queue than to estimate them directly.
46
Derivation of Confidence Intervals for Work Rate Estimators in a Closed Queuing Network
TL;DR: Confidence intervals are derived for a class of new work rate estimators in a closed queuing network and it is demonstrated that a substantial reduction in the length of confidence intervals is obtainable by use of the proposed estimators.
12
Embedded renewal processes in the GI/G/s queue
TL;DR: In this paper, the stable GI/G/s queuing problem is studied and functional limit theorems for time-average or cumulative processes associated with a large class of GI/g/s queues in light traffic are implied.
Simulating Stable Stochastic Systems, I: General Multiserver Queues
TL;DR: A technique is introduced for analyzing simulations of stochastic systems in the steady state, with the existence of a random grouping of observations which produces independent identically distributed blocks from the start of the simulation.
Technical Note-A Last Word on L = λW
TL;DR: This note gives a rigorous proof of the queuing formula L = λW, using as hypotheses only that the limiting averages, λ and W, exist and are finite.