Multiple metastable network states in urban traffic

Abstract

While abrupt regime shifts between different metastable states have occurred in natural systems from many areas including ecology, biology, and climate, evidence for this phenomenon in transportation systems has been rarely observed so far. This limitation might be rooted in the fact that we lack methods to identify and analyze possible multiple states that could emerge at scales of the entire traffic network. Here, using percolation approaches, we observe such a metastable regime in traffic systems. In particular, we find multiple metastable network states, corresponding to varying levels of traffic performance, which recur over different days. Based on high-resolution global positioning system (GPS) datasets of urban traffic in the megacities of Beijing and Shanghai (each with over 50,000 road segments), we find evidence supporting the existence of tipping points separating three regimes: a global functional regime and a metastable hysteresis-like regime, followed by a global collapsed regime. We can determine the intrinsic critical points where the metastable hysteresis-like regime begins and ends and show that these critical points are very similar across different days. Our findings provide a better understanding of traffic resilience patterns and could be useful for designing early warning signals for traffic resilience management and, potentially, other complex systems.

Empirical evidence for a jamming transition in urban traffic

“…However, we did not find these meta-stable states and each measure of the size of the GC as a function of occupancy is close to the average relation displayed in figure 3b. The most likely explanation for this discrepancy is that our measures are averaged over an hour, which is a long period of time compared with the typical stability duration of the metastable states found in [20], which is of order 10 minutes. This suggests that our measure thus only reflects the average of the systems oscillations between the two states.…”

“…We find that the congestion percolates during rush hours and the dependence of the average giant component size on the average occupancy rate displays a typical shape of percolation in a finite size system, as displayed in figure 3a. Zeng et al [20] have shown that during rush hours the network oscillates between multiple meta-stable states: for a given fraction of congested links, they found that there could either be a giant functional cluster or several small functional clusters. We tried to reproduce these results for our case of the cluster of congestion rather than functional clusters.…”

“…Using a similar approach, Zhang et al [19] studied the size distribution and recovery times of clusters of congested links and in particular the power-law dependence of the recovery time on the cluster size. Furthermore, Zeng et al [20] have shown that the randomness in the traffic demand and the emergence of local congestion means that the transition between the giant functional cluster and several small clusters is not monotonous, but displays switches between multiple metastable states. Cogani & Busonera [21,22] studied the spatial distribution of the clusters and found in agreement with Zhang et al [19] that, once formed, the clusters are stable in time, from day to day, indicating that their existence is determined by the traffic patterns (origins and destinations of the road users) and by the network itself.…”

Self-Organized Criticality of Traffic Flow: There is Nothing Sweet about the Sweet Spot

“…There is mounting empirical evidence suggesting the hypotheses that urban networks exhibit self-organized criticality (SOC) (Zeng et al, 2019, Zhang et al, 2019, Zeng et al, 2020, Bak et al, 1987, a celebrated paradigm in the 90's that has proved very useful in countless areas of science, from earthquakes to stock prices to forest fires to astrophysics (Dȃnilȃ et al, 2015, Aschwanden, 2014. Despite being around for 2 or 3 decades now, the theory and control consequences of SOC have not permeated the transportation literature.…”

Dynamical Recovery of Complex Networks under a Localised Attack

“…Most research on the network assumes that the network is static, while many real systems dynamically evolve. For example, traffic networks with flow changes over time [16], while friendship networks decreased in size with time increasing [17]. For some systems in real-world scenarios, after the collapse, they can spontaneously recover.…”