Optimal Prediction of Times and Queue Lengths in the GI-M-1 Queue

Article Abstract:

Optimal predictors for variables in a GI-M1 queue, number in the queue, time in the queue, and waiting in line, is presented. The conditional-expectation predictors and optimal linear predictors are derived and compared. Close relationships are found among the predictors and their performance of values, with prediction of number in queue from some previous number playing the key roles. Basic properties of the predictors are illustrated with examples.

Queues, Queuing Networks

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Simulating the GI-G-1 Queue in Heavy Traffic

Article Abstract:

The two problems of classical techniques in simulating queueing systems are the statistical dependence between successive observations and the inability to begin in the steady state. A simple method for simulating the GI-G1 queue is given. It retains the advantages of the regenerative method and reduces the estimator variance as the traffic intensity approaches one. Tables have numerical results.

Models, Simulation, Simulation Theory, Approximation, Variance Reduction, Traffic Monitoring

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