Supervised ML for Solving the GI / GI /1 Queue

Opher Baron (), Dmitry Krass (), Arik Senderovich () and Eliran Sherzer ()
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Opher Baron: Rotman School Of Management, University of Toronto, Toronto, Ontario M5S 3E6, Canada
Dmitry Krass: Rotman School Of Management, University of Toronto, Toronto, Ontario M5S 3E6, Canada
Arik Senderovich: School of Information Technologies (ITEC), York University, Toronto, Ontario M3J 1P3, Canada
Eliran Sherzer: Rotman School Of Management, University of Toronto, Toronto, Ontario M5S 3E6, Canada

INFORMS Journal on Computing, 2024, vol. 36, issue 3, 766-786

Abstract: We apply supervised learning to a general problem in queueing theory: using a neural net , we develop a fast and accurate predictor of the stationary system-length distribution of a GI / GI /1 queue—a fundamental queueing model for which no analytical solutions are available. To this end, we must overcome three main challenges: (i) generating a large library of training instances that cover a wide range of arbitrary interarrival and service time distributions, (ii) labeling the training instances, and (iii) providing continuous arrival and service distributions as inputs to the neural net. To overcome (i), we develop an algorithm to sample phase-type interarrival and service time distributions with complex transition structures. We demonstrate that our distribution-generating algorithm indeed covers a wide range of possible positive-valued distributions. For (ii), we label our training instances via quasi-birth-and-death(QBD) that was used to approximate PH / PH /1 (with phase-type arrival and service process) as labels for the training data. For (iii), we find that using only the first five moments of both the interarrival and service times distribution as inputs is sufficient to train the neural net. Our empirical results show that our neural model can estimate the stationary behavior of the GI / GI /1—far exceeding other available methods in terms of both accuracy and runtimes.

Keywords: GI / GI /1 queue; neural networks; sampling; phase type (search for similar items in EconPapers)
Date: 2024
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