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

David A. Stanford · Bernard Pagurek · C. Murray Woodside

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Advanced Queuing Theory Analysis Probability and Statistical Research Age of Information Optimization

Abstract

This paper presents optimal predictors for variables in a GI/M/1 queue, number in the queue, time in the queue, and waiting time. The conditional-expectation predictors and optimal linear predictors are derived and compared. Close relationships are found among the predictors and their performance values, with prediction of number in queue from some previous number playing the key role. Basic properties of the predictors are illustrated with examples.

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References

1977Fundamentals of Queueing Theory.1975Theory, Volume 1, Queueing Systems 1968The serial correlation coefficients of waiting times in a stationary single server queue 1971The Serial Correlation Coefficients of Waiting Times in the Stationary GI/M/1 Queue 1967The covariance function of the M/G/1 queuing system 1971The Correlation Coefficients of the Queue Lengths of Some Stationary Single Server Queues

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