用深度学习模拟复杂排队网络的流量叠加,精度远超传统方法。
A Learning-Based Superposition Operator for Non-Renewal Arrival Processes in Queueing Networks
- 基于深度学习构建流量叠加算子,输入多源流的低阶统计特征
- 能准确重建聚合流前五阶矩和短程相关性,误差极低
- 适合需要高阶统计特性的排队网络性能分析场景
在非更新型到达过程的排队网络中,流量叠加是基础但难以解析处理的操作。传统方法或将其简化为更新型近似,或依赖计算成本高昂的马尔可夫表示,或仅关注均值性能。本文提出一种可扩展的数据驱动叠加算子,将多个到达流的低阶矩和自相关描述符映射到其聚合过程的对应特征。该算子为深度学习模型,基于合成生成的马尔可夫到达过程(MAPs)训练,对精确叠加结果已知的情况进行学习,能够准确重构聚合流的前五阶矩及短程依赖结构。大量实验表明,在异质波动与相关性条件下,预测误差始终很低,显著优于经典更新近似方法。当与学习型离去过程及稳态分析模块结合时,该算子可实现具有汇流的前馈排队网络的分解式评估。该框架为传统解析方法提供了可扩展替代方案,同时保留了高阶变异性与依赖信息,满足精准分布性能分析需求。
原文摘要 · Abstract (English)
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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