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Optimal prediction of times and queue lengths in the M/G/1 queue. (English) Zbl 0642.60090

Summary: This paper presents optimal mean-square predictors for several variables in a FIFO M/G/1 queue. In particular, conditional expectation predictors are derived for the number in the queue, time in the queue, and the waiting time, with a previous number in the queue as the basis for the prediction. The relationships between the predictors are derived, and the basic properties are illustrated with examples.

MSC:

60K25 Queueing theory (aspects of probability theory)
60G25 Prediction theory (aspects of stochastic processes)
90B22 Queues and service in operations research
68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
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