Bittihn Stefan, Schadschneider Andreas
Institute for Theoretical Physics, Universität zu Köln, 50937 Köln, Germany.
Phys Rev E. 2016 Dec;94(6-1):062312. doi: 10.1103/PhysRevE.94.062312. Epub 2016 Dec 21.
We study the Braess paradox in the transport network as originally proposed by Braess with totally asymmetric exclusion processes (TASEPs) on the edges. The Braess paradox describes the counterintuitive situation in which adding an edge to a road network leads to a user optimum with higher travel times for all network users. Travel times on the TASEPs are nonlinear in the density, and jammed states can occur due to the microscopic exclusion principle, leading to a more realistic description of trafficlike transport on the network than in previously studied linear macroscopic mathematical models. Furthermore, the stochastic dynamics allows us to explore the effects of fluctuations on network performance. We observe that for low densities, the added edge leads to lower travel times. For slightly higher densities, the Braess paradox occurs in its classical sense. At intermediate densities, strong fluctuations in the travel times dominate the system's behavior due to links that are in a domain-wall state. At high densities, the added link leads to lower travel times. We present a phase diagram that predicts the system's state depending on the global density and crucial path-length ratios.
我们利用边上的完全非对称排斥过程（TASEPs），研究了最初由布雷斯提出的交通网络中的布雷斯悖论。布雷斯悖论描述了一种违反直觉的情况，即在道路网络中增加一条边会导致所有网络用户的出行时间达到更高的用户最优值。TASEPs上的出行时间在密度上是非线性的，并且由于微观排斥原理会出现拥堵状态，这导致对网络上类似交通的运输的描述比之前研究的线性宏观数学模型更现实。此外，随机动力学使我们能够探索波动对网络性能的影响。我们观察到，对于低密度情况，增加的边会导致出行时间降低。对于略高的密度，布雷斯悖论以其经典形式出现。在中等密度时，由于处于畴壁状态的链路，出行时间的强烈波动主导了系统的行为。在高密度时，增加的链路会导致出行时间降低。我们给出了一个相图，它根据全局密度和关键路径长度比预测系统的状态。
