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

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.