A Learning-Based Superposition Operator for Non-Renewal Arrival Processes in Queueing Networks
arXiv:2603.11118v1 Announce Type: new 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 correl
arXiv:2603.11118v1 Announce Type: new 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.
Executive Summary
This article proposes a novel learning-based superposition operator for non-renewal arrival processes in queueing networks, leveraging deep learning to accurately map low-order moments and autocorrelation descriptors of multiple arrival streams to those of their merged process. The operator outperforms classical renewal-based approximations and enables decomposition-based evaluation of feed-forward queueing networks with merging flows. Extensive computational experiments demonstrate its effectiveness across various variability and correlation regimes.
Key Points
- ▸ Development of a data-driven superposition operator for non-renewal arrival processes
- ▸ Use of deep learning to learn a compact representation of the merged process
- ▸ Ability to accurately reconstruct the first five moments and short-range dependence structure of the aggregate stream
Merits
Scalability
The proposed operator provides a scalable alternative to traditional analytical approaches, making it suitable for large-scale queueing networks
Accuracy
The operator demonstrates uniformly low prediction errors across heterogeneous variability and correlation regimes
Demerits
Limited Interpretability
The use of deep learning may limit the interpretability of the results, making it challenging to understand the underlying mechanisms
Expert Commentary
The proposed learning-based superposition operator represents a significant advancement in queueing theory, offering a scalable and accurate solution for analyzing non-renewal arrival processes. While the use of deep learning may raise concerns about interpretability, the results demonstrate the operator's effectiveness in capturing complex dependencies and variability. Further research is needed to explore the potential applications and limitations of this approach, but the initial findings are promising and warrant attention from both academia and industry.
Recommendations
- ✓ Further investigation into the interpretability of the deep learning model
- ✓ Exploration of the operator's applicability to other areas, such as stochastic processes and network optimization
