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Efficient estimators for simulated queueing systems
Averill M. Law
- 01 Jan 1974
46
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.
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Abstract: In this paper we consider efficient estimators for simulated queueing systems. 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. For single-server queues an estimator is introduced which is more efficient than the normal estimator of mean delay in queue.
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Citations
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A distributional form of Little's Law
J. Keilson,L. D. Servi +1 more
- 25 Aug 2011
TL;DR: For many system contexts for which Little's Law is valid a distributional form of the law is also valid as discussed by the authors, and this paper establishes the prevalence of such system contexts and makes clear the value of the distributional forms.
120
A distributional form of Little's Law
Julian Keilson,L. D. Servi +1 more
TL;DR: The distributional form of Little's Law is valid for a wide range of system contexts.
Simulation methods for queues: an overview
TL;DR: The main topics covered are: output analysis for simulation of transient and steady-state quantities, variance reduction methods that exploit queueing structure, and gradient estimation methods for performance parameters associated with queueing networks.
77
Simulation run lengths to estimate blocking probabilities
R. Srikant,Ward Whitt +1 more
TL;DR: In this article, the authors derived the asymptotic variance of four estimators for steady-state blocking probability in a multiserver loss system, exploiting diffusion process limits, which can be used to predict simulation run lengths required to obtain desired statistical precision before the simulation has been run.
Fundamental bounds on the accuracy of network performance measurements
Matthew Roughan
- 06 Jun 2005
TL;DR: The answer is somewhat counter-intuitive in that there are bounds on the accuracy of such measurements, no matter how many probes the authors can use in a given time interval, and thus arises a type of Heisenberg inequality describing the bounds in their knowledge of the performance of a network.
59
References
Regenerative Stochastic Processes
TL;DR: In this article, a wide class of stochastic processes, called regenerative, is defined, and it is shown that under general conditions the instantaneous probability distribution of such a process tends with time to a unique limiting distribution, whatever the initial conditions.
716
On the Characteristics of the General Queueing Process, with Applications to Random Walk
J. Kiefer,J. Wolfowitz +1 more
TL;DR: In this article, the authors studied the general queueing process for the case where a limiting distribution exists and gave necessary and sufficient conditions for the finiteness of various moments in the process.
On the relation between customer and time averages in queues
TL;DR: In this article, the authors gave conditions sufficient to obtain the formula L = λW, where L is the time average queue size, W is the expected wait in queue, and λ is the arrival rate of customers.
132
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.
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