响应函数作为研究交通网络局部动力学的新概念
Response functions as a new concept to study local dynamics in traffic networks
AI总结：
本文将金融中的响应函数引入交通系统，揭示速度响应的瞬态与长期两阶段及其与拥堵相关量的线性关系，并用受SIR启发的模型刻画拥堵传播。
摘要：
相邻路段的车辆速度具有相关性，并存在记忆效应。我们探究一系列路段中的速度对给定路段拥堵的响应及其动态特征。为此，我们将响应函数概念从其先前在金融领域的应用迁移到交通系统。动态特征尤其受到关注。我们识别出两个阶段：瞬态响应阶段和长期响应阶段。在考察严重拥堵的向后传播时，瞬态响应十分显著，但对于向前传播则几乎消失。对于每个响应阶段，我们都发现速度响应与拥堵相关量之间存在线性关系，这意味着拥堵相关性极有可能是速度响应的原因。我们还在数学上受流行病学中易感—感染—康复（SIR）模型启发，构建了一个易感—减速—退出模型，用于描述瞬态响应。我们发现，某一路段上的严重拥堵以相近的速率向前和向后传播，但与后方路段相比，前方路段更有可能从严重拥堵的影响中恢复。
英文摘要：
Vehicle velocities in neighbouring road sections are correlated with memory effects. We explore the response of the velocities in the sequence of sections to a congestion in a given section and its dynamic characteristics. To this end, we transfer the concept of response functions from previous applications in finance to traffic systems. The dynamical characteristics are of particular interest. We identify two phases, a phase of transient response and a phase of long-term response. The transient response is pronounced when considering the backward propagation of heavy congestions but almost vanishes for forward propagation. For each response phase, we find a linear relation between the velocity response and the congestion correlator, implying that the correlation of congestion is most likely the cause for the velocity response. We also construct a susceptible-decelerated-withdrawing model mathematically inspired by the susceptible-infectious-recovered (SIR) model in epidemiology to describe the transient response. We find that the heavy congestion on a section propagates forward and backward at a similar rate, but the forward sections are more likely to recover from the effect of heavy congestion than the backward sections.
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