Abnormal dynamics in cascading models for time-weighted path optimization

Abstract

In real traffic networks, route choice preferences tend to prioritize the shortest travel time over the shortest distance. To address this, we propose a cascading failure model that incorporates time dynamics. By introducing the BPR function, our model quantifies edge transmission time, identifies time-optimal paths, and distributes loads proportionally based on edge time weights. Three parameters are introduced to redefine cascading dynamics and evaluate network robustness.Simulations on both artificial and real-world networks reveal several key findings: First, increasing node weights leads to an uneven load distribution, thereby weakening the network’s robustness. Second, the network exhibits both the “capacity paradox” and the “expansion paradox.” The capacity paradox indicates that increasing the capacity of edges can actually reduce network robustness. In networks with loop structures, enlarging edge capacities redirects traffic to critical edges, creating bottlenecks that amplify cascading failures. Similarly, the expansion paradox shows that increasing maximum capacity can destabilize the network by concentrating loads on key edges, which, if overloaded, can trigger widespread failures. These findings challenge the conventional assumptions that enhancing capacity universally improves robustness. Instead, our results emphasize the importance of balancing topological design and load distribution.For practical networks, strategies such as diversifying travel routes and limiting the load on hub nodes prove to be more effective than simply increasing capacity. This work advances cascading failure modeling by integrating time dynamics and provides actionable insights for improving infrastructure resilience.