基于Wardrop原理建模需求不确定下的网络拥塞
Modeling Network Congestion under Demand Uncertainty Using Wardrop Principles
AI总结：
针对需求不确定下多商品交通网络的最坏拥塞问题，基于Wardrop原理建立双层模型，提出混合整数非线性重构技术，经Sioux Falls等网络实例验证了方法有效性。
AI中文摘要：
受波动出行需求下可靠交通管理需求的驱动，我们研究受需求不确定性影响的多商品交通网络中最坏情况拥塞的确定问题。为此，我们通过识别使拥塞最大化的需求实现及对应的出行者路径选择，对给定网络进行压力测试。假设交通网络的用户遵循Wardrop原理中的一种，即用户均衡或系统最优，因此所得拥塞模型可视为包含单个领导者与多个追随者的双层问题。为应对不确定出行需求，我们考虑椭球不确定集、预算不确定集及hose多面体等不同模型。我们提出拥塞模型的单层混合整数非线性重构，该重构利用二元变量与大M常数，证明最优解的存在性，推导有效的大M值，并提出多种增强技术以进一步强化模型。针对Sioux Falls网络实例及SNDlib实例开展的广泛计算研究，证明了所提技术的计算有效性，并揭示了不同拥塞度量与不确定性模型对最坏情况拥塞的影响。
英文摘要：
Motivated by the need for reliable traffic management under fluctuating travel demand, we study the problem of determining the worst-case congestion in a multi-commodity traffic network subject to demand uncertainty. To this end, we stress-test a given network by identifying demand realizations and corresponding travelers' route choices that maximize congestion. The users of the traffic network are assumed to act according to one of the two Wardrop principles, the user equilibrium or the system optimum, so that the resulting congestion models can be seen as bilevel problems with a single leader and multiple followers. To address uncertain travel demand, we consider different models such as ellipsoidal or budgeted uncertainty sets and the hose polyhedron. We present single-level mixed-integer nonlinear reformulations of the congestion models that exploit binary variables and big-M constants, prove the existence of optimal solutions, derive valid big-Ms, and propose several enhancement techniques to further strengthen the formulations. An extensive computational study on instances of the Sioux Falls network and instances from the SNDlib demonstrates the computational effectiveness of the proposed techniques and provides insight into the impact of different congestion measures and uncertainty models on the resulting worst-case congestion.
