A mathematical framework for delay analysis in single source networks

S. Samaranayake, Axel Parmentier, Ethan Xuan, A. Bayen
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引用次数: 3

Abstract

This article presents a mathematical framework for modeling heterogeneous flow networks with a single source and multiple sinks. The traffic is differentiated by its destination (i.e. Lagrangian flow) and different flow groups are assumed to satisfy the first-in-first-out (FIFO) condition at each junction. We show that our model leads to a well-posed problem for computing the dynamics of the system and prove that the solution is unique through a mathematical derivation of the model properties. The framework is then used to analytically prescribe the delays at each junction of the network and across any sub-path, which is one of the contributions of the article. This is a critical requirement when solving control and optimization problems over the network, such as system optimal network routing and solving for equilibrium behavior. In fact, the framework provides analytical expressions for the delay at any node or sub-path as a function of the inflow at any upstream node. Furthermore, the model can be solved numerically using a very simple and efficient feed forward algorithm. We demonstrate the versatility of the framework by applying it to a diverge junction with complex junction dynamics.
单源网络时延分析的数学框架
本文提出了一个单源多汇异构流网络建模的数学框架。根据目的地(即拉格朗日流)对流量进行区分,并假设不同的流组在每个路口满足先进先出(FIFO)条件。我们证明了我们的模型导致了一个计算系统动力学的适定问题,并通过模型性质的数学推导证明了解是唯一的。然后使用该框架分析规定网络的每个节点和任何子路径上的延迟,这是本文的贡献之一。这是解决网络控制和优化问题时的关键要求,例如系统最优网络路由和求解平衡行为。实际上,该框架提供了任何节点或子路径上的延迟作为任何上游节点流入的函数的解析表达式。此外,该模型可以用一种非常简单而高效的前馈算法进行数值求解。我们通过将其应用于具有复杂结动力学的发散结来证明该框架的多功能性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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