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, 112 (3), 669-72

Percolation Transition in Dynamical Traffic Network With Evolving Critical Bottlenecks

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Percolation Transition in Dynamical Traffic Network With Evolving Critical Bottlenecks

Daqing Li et al. Proc Natl Acad Sci U S A.

Abstract

A critical phenomenon is an intrinsic feature of traffic dynamics, during which transition between isolated local flows and global flows occurs. However, very little attention has been given to the question of how the local flows in the roads are organized collectively into a global city flow. Here we characterize this organization process of traffic as "traffic percolation," where the giant cluster of local flows disintegrates when the second largest cluster reaches its maximum. We find in real-time data of city road traffic that global traffic is dynamically composed of clusters of local flows, which are connected by bottleneck links. This organization evolves during a day with different bottleneck links appearing in different hours, but similar in the same hours in different days. A small improvement of critical bottleneck roads is found to benefit significantly the global traffic, providing a method to improve city traffic with low cost. Our results may provide insights on the relation between traffic dynamics and percolation, which can be useful for efficient transportation, epidemic control, and emergency evacuation.

Keywords: emergence; percolation; traffic.

Conflict of interest statement

The authors declare no conflict of interest.

Figures

Fig. 1.
Fig. 1.
Road network of the observed district. (A) Map of the investigated district. (B) Road network of the investigated district. Road network at 9:00 AM on March 29, 2013 is shown, where links are classified into three categories according to their velocity ratio rij: velocity ratio below 0.4 (red), between 0.4 and 0.7 (yellow), and above 0.7 (green). Note the clustering of each color.
Fig. 2.
Fig. 2.
Percolation of traffic networks: Traffic networks during the noon period (at 11:50 AM on March 27) for three q values corresponding to different connectivity states. A, B, and C exhibit the traffic networks under different q values with 0.69, 0.38, and 0.19 representing the states of high-, medium-, and low-velocity thresholds, respectively. For clarity, only the largest three clusters are plotted, which are marked in green (largest cluster), blue (second-largest cluster), and strawberry (third-largest cluster). Here the clusters are strongly connected components, considering road direction (more details in SI Appendix). (D) Size of the largest cluster (G) and the second-largest cluster (SG) of traffic networks as a function of q (more examples in SI Appendix). Critical value, qc, is determined as the q value when SG becomes maximal. (E) qc as a function of time, averaged separately over nine weekdays and two weekends.
Fig. 3.
Fig. 3.
Bottleneck links of a traffic network. (A) A typical example of a traffic network just below criticality, where two links (in red within red or black circles) are removed at criticality. Removal of them will disintegrate the giant functional network. (B) Same traffic network after removal of the two links, where the giant functional cluster is disintegrated into five clusters. We find all strongly connected clusters of the traffic network for each q and identify the links removed at threshold qc when the second-largest strongly connected cluster reaches a maximum. Although some of these links are removed by chance, a few links do play a critical role of bridging different traffic clusters of higher velocities. These bridging links are identified as bottleneck links, because when increasing their velocity large clusters can join together to become the largest component (more details in SI Appendix, Fig. S7). (C) The improvement of qc by increasing separately the ratio (rij = rij(1 + α)) of two links marked in A, within which improvement of qc can be achieved only with one (marked with red circle) of them. This link is considered a bottleneck link for global traffic. This is compared with the improvement of one link randomly chosen and the link with highest betweenness. (D) Zipf plot of occurrence times of links as bottlenecks during morning rush hours. It is compared with occurrence times of bottlenecks in the same network with shuffled values of rij during morning rush hours. For the shuffled case, we shuffle the rij values 100,000 times at each instant and find the bottleneck links with the same method.
Fig. 4.
Fig. 4.
Evolving bottlenecks in different periods in 1 d. (A) Bottleneck links with high occurrence in different periods are marked: morning (red), noon (green), and evening (blue). (B) The occurrence times of links (marked in A) as bottlenecks in different periods are plotted: morning (red), noon (green), and evening (blue). (C and D) The network breaks into several clusters after removal of bottlenecks with highest occurrence (top 10 in the morning in C or top 8 at noon in D). Red arrows in C and D are paths bridging different clusters, which are fragmented by the removal of bottleneck links.

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