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

arXiv: https://arxiv.org/abs/2603.11118 · HTML: https://mlsanity.com/paper/2603.11118/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 17 references that are in the map.
- First posted on arXiv 11 Mar 2026.

## Builds on (most cited first, 2 of 2)

- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Approximating G(t)/GI/1 queues with deep learning](https://mlsanity.com/paper/2407.08765/) (2024)

## Abstract (arXiv)

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.