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

• URL: http://arxiv.org/abs/2603.11118v1
• Date: Wed, 11 Mar 2026 13:46:32 GMT
• Title: A Learning-Based Superposition Operator for Non-Renewal Arrival Processes in Queueing Networks
• Abstract summary: Superposition of arrival processes is a fundamental yet analytically intractable operation in queueing networks.<n>We propose a scalable data-driven operator that maps low-order moments and autocorrelation descriptors of multiple arrival streams to those of their merged process.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The superposition of arrival processes is a fundamental yet analytically intractable operation in queueing networks when inputs are general non-renewal streams. Classical methods either reduce merged flows to renewal surrogates, rely on computationally prohibitive Markovian representations, or focus solely on mean-value performance measures. We propose a scalable data-driven superposition operator that maps low-order moments and autocorrelation descriptors of multiple arrival streams to those of their merged process. The operator is a deep learning model trained on synthetically generated Markovian Arrival Processes (MAPs), for which exact superposition is available, and learns a compact representation that accurately reconstructs the first five moments and short-range dependence structure of the aggregate stream. Extensive computational experiments demonstrate uniformly low prediction errors across heterogeneous variability and correlation regimes, substantially outperforming classical renewal-based approximations. When integrated with learning-based modules for departure-process and steady-state analysis, the proposed operator enables decomposition-based evaluation of feed-forward queueing networks with merging flows. The framework provides a scalable alternative to traditional analytical approaches while preserving higher-order variability and dependence information required for accurate distributional performance analysis.

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