Ensuring the conformance of a service system's end-to-end delay to service level agreement (SLA) constraints is a challenging task that requires statistical measures beyond the average delay. In this paper, we study the real-time prediction of the end-to-end delay distribution in systems with composite services such as service function chains. In order to have a general framework, we use queueing theory to model service systems, while also adopting a statistical learning approach to avoid the limitations of queueing-theoretic methods such as stationarity assumptions or other approximations that are often used to make the analysis mathematically tractable. Specifically, we use deep mixture density networks (MDN) to predict the end-to-end distribution of the delay given the network's state. As a result, our method is sufficiently general to be applied in different contexts and applications. Our evaluations show a good match between the learned distributions and the simulations, which suggest that the proposed method is a good candidate for providing probabilistic bounds on the end-to-end delay of more complex systems where simulations or theoretical methods are not applicable.

中文翻译：

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使用深度 MDN 的服务功能链端到端延迟的概率界限

确保服务系统的端到端延迟符合服务水平协议 (SLA) 约束是一项具有挑战性的任务，需要超出平均延迟的统计措施。在本文中，我们研究了具有复合服务（例如服务功能链）的系统中端到端延迟分布的实时预测。为了有一个通用的框架，我们使用排队理论对服务系统进行建模，同时还采用统计学习方法来避免排队理论方法的局限性，例如平稳性假设或其他近似值，这些方法通常用于使分析在数学上易于处理. 具体来说，我们使用深度混合密度网络 (MDN) 来预测给定网络状态的端到端延迟分布。因此，我们的方法足够通用，可以应用于不同的上下文和应用程序。我们的评估显示学习分布和模拟之间的良好匹配，这表明所提出的方法是提供模拟或理论方法不适用的更复杂系统的端到端延迟的概率界限的良好候选者。