A Learning-Based Superposition Operator for Non-Renewal Arrival Processes in Queueing Networks

Researcher Eliran Sherzer has introduced a novel, data-driven approach to a fundamental problem in queueing theory: predicting the behavior of merged, non-renewal arrival streams. Classical methods for modeling these complex flows are either analytically intractable, rely on oversimplified renewal approximations, or require computationally prohibitive Markovian representations. Sherzer's solution is a deep learning model trained on synthetically generated Markovian Arrival Processes (MAPs), where exact superposition is known. This model acts as a 'superposition operator,' learning to map low-order moments and autocorrelation descriptors from multiple input streams to accurately predict the characteristics of their aggregate.

The operator's key achievement is its ability to reconstruct the first five moments and the short-range dependence structure of the merged process with high accuracy. Extensive computational experiments show it achieves uniformly low prediction errors across a wide range of variability and correlation scenarios, substantially outperforming traditional renewal-based approximations. By integrating this operator with other learning-based modules for departure-process and steady-state analysis, the framework enables a practical, decomposition-based method for evaluating complex feed-forward queueing networks. This provides a scalable, data-driven alternative to purely analytical approaches while preserving the higher-order variability information crucial for accurate performance analysis in real-world systems like data centers, telecommunications, and logistics networks.