A variant of the conditional expectation variance reduction technique and its application to the simulation of GI/G/1 queues

Article Abstract:

The conditional expectation (CE) variance reduction technique is well-known but unpopular due to its model-dependency and the lack of a general method to find a random variable Y for all computed variables of Y. A modified version of the CE technique, the Partial Conditional Expectation (PCE), provides the capacity to obtain a consistent estimator for computing the waiting time in queue for a single-server queueing system in simulations of a GI/G/1 queue. An improved version of the estimator can be derived by further consideration of the system. The two estimators preform better than the classical estimator and variance reduction obtained from the two estimators is particularly significant with low traffic.

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Simulating GI-G-K queues in heavy traffic

Article Abstract:

Waiting times in heavy traffic queues are analyzed for length of time, queue length, and expected service backlog. The method used to measure these factors is called an error estimator because it estimates the error involved in the use of Kingman's heavy traffic approximation. The error estimator method is superior to the regenerative error method because it retains the advantages of the latter while substantially lowering variances when heavy traffic is involved. The regenerative method is more versatile in some situations, however.

Methods, Work measurement

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Importance sampling for stochastic simulations

Article Abstract:

Importance sampling is an effective technique for increasing the efficiency of Monte Carlo algorithms for the numerical analysis of integrals. The original random mechanism in the simulation can be replaced in order to solve problems arising from the simulation of stochastic systems for application to GI/G/1 queueing problems, including: discrete time Markov chains; continuous-time Markov chains; and generalized semi-Markov processes.

Stochastic analysis, Samples (Merchandising), Samples (Products)

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