Di Meco Lorenzo, Degli Esposti Mirko, Bellisardi Federico, Bazzani Armando
Department of Physics and Astronomy, University of Bologna, 40126 Bologna, Italy.
INFN Sezione di Bologna, 40127 Bologna, Italy.
Entropy (Basel). 2024 Jul 26;26(8):632. doi: 10.3390/e26080632.
The formation of congestion on an urban road network is a key issue for the development of sustainable mobility in future smart cities. In this work, we propose a reductionist approach by studying the stationary states of a simple transport model using a random process on a graph, where each node represents a location and the link weights give the transition rates to move from one node to another, representing the mobility demand. Each node has a maximum flow rate and a maximum load capacity, and we assume that the average incoming flow equals the outgoing flow. In the approximation of the single-step process, we are able to analytically characterize the traffic load distribution on the single nodes using a local maximum entropy principle. Our results explain how congested nodes emerge as the total traffic load increases, analogous to a percolation transition where the appearance of a congested node is an independent random event. However, using numerical simulations, we show that in the more realistic case of synchronous dynamics for the nodes, entropic forces introduce correlations among the node states and favor the clustering of empty and congested nodes. Our aim is to highlight the universal properties of congestion formation and, in particular, to understand the role of traffic load fluctuations as a possible precursor of congestion in a transport network.
城市道路网络拥堵的形成是未来智慧城市可持续交通发展的关键问题。在这项工作中，我们提出一种简化方法，通过在图上使用随机过程研究一个简单交通模型的稳态，其中每个节点代表一个位置，链路权重给出从一个节点移动到另一个节点的转移速率，代表出行需求。每个节点有一个最大流量速率和一个最大负载容量，并且我们假设平均入流等于出流。在单步过程的近似中，我们能够使用局部最大熵原理解析地表征单个节点上的交通负载分布。我们的结果解释了随着总交通负载增加拥堵节点是如何出现的，类似于渗流转变，其中拥堵节点的出现是一个独立随机事件。然而，通过数值模拟，我们表明在节点同步动态的更现实情况下，熵力在节点状态之间引入相关性，并有利于空节点和拥堵节点的聚类。我们的目标是突出拥堵形成的普遍特性，特别是理解交通负载波动作为交通网络中拥堵可能先兆的作用。
