NeuraliNQ: a neural network method for the transient performance analysis in non-Markovian Queues

Spyros Garyfallos (), Yunan Liu (), Pere Barlet-Ros () and Albert Cabellos-Aparicio ()
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Spyros Garyfallos: Universitat Politécnica de Catalunya
Yunan Liu: Amazon, Supply Chain Optimization Technology
Pere Barlet-Ros: Universitat Politécnica de Catalunya
Albert Cabellos-Aparicio: Universitat Politécnica de Catalunya

Queueing Systems: Theory and Applications, 2025, vol. 109, issue 4, No 1, 42 pages

Abstract: Abstract Many empirical studies have confirmed that service-time and patience-time distributions in service systems (e.g., call centers and health care) are far from exponentially distributed. Because non-Markovian queues are rarely amenable to analytic solutions, performance analysis often resorts to approximating methods such as heavy-traffic fluid limits or computer simulations. In this paper, we contribute to the literature on transient performance analysis of non-Markovian queues by developing a new neural networks method, dubbed Neural network in non-Markovian Queue (NeuraliNQ); we specifically focus on queues with customer abandonment. NeuraliNQ is an offline supervised learning method that uses synthetic training data to learn the system’s intrinsic characteristics. In real-time applications, NeuraliNQ can recurrently estimate the transient system waiting time performance in a finite time window. Our results confirm that NeuraliNQ is able to achieve the proper balance between efficiency and accuracy: on the one hand, it is four orders of magnitude computationally more efficient than Monte-Carlo simulations; on the other hand, it yields higher solution accuracy than standard approximation methods such as the heavy-traffic fluid model, especially when the system scale is not too large.

Keywords: Non-Markovian queues; Transient performance analysis in queues; Neural networks in queues; Recurrent neural network (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11134-025-09952-3

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