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

TL;DR

This paper introduces a deep learning-based superposition operator that accurately predicts the moments and dependence structure of merged non-renewal arrival processes in queueing networks, improving over classical methods.

Contribution

A novel data-driven superposition operator using deep learning to model complex non-renewal arrival process merging in queueing networks.

Findings

Achieves low prediction errors across various regimes.

Outperforms classical renewal-based approximations.

Enables scalable analysis of queueing networks with merging flows.

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.