Learning Lindley’s Recursion

Lindley's recursion is one of the most important formula's in queueing theory and applied probability. In this paper, we leverage stochastic simulation and current machine learning methods to learn the Lindley recursion directly from waiting time data of the G/G/1 queue. To this end, we use methods such as Gaussian Processes, k-Nearest Neighbors and Deep neural networks to learn the Lindley recursion. We also analyze specific parameter regimes for the M/M/1 to understand where learning the Lindley recursion may be easy or hard. Finally, we compare the machine learning methods to see how well we can predict the Lindley recursion multiple steps into the future with missing data.