Learning-based superposition for the analysis of feed-forward queueing networks with non-Markovian arrivals

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. Experiments indicate that the neural framework achieves errors on the order of 1%–5% for steady-state predictions across the tested networks, while classical methods often exhibit much larger errors, typically tens of percent and in some regimes exceeding 100%. This gap persists across varying SCV and utilization levels, with the learning-based approach remaining stable even under high variability and strong dependence, where traditional approximations significantly deteriorate.