Extreme Events and Congestion Phenomenon on Urban Street Networks

Abstract

Complex networks provide a common framework to study and understand dynamics on them, for instance, on internet, transportation networks, and protein interaction networks of biological systems. Though work on network science can be traced back to almost 200 years ago, there is considerable interest in the last two decades due to many interesting applications. Transport dynamics on complex networks, such as traffic on roads or information packets on network of routers, show many emergent phenomena, one of which is an extreme event, a rare event whose probability of occurrence is very low. An extreme event is said to occur if flux through a certain node goes beyond the prescribed threshold (may be related to its flux handling capacity). We use non-interacting degree-biased random walk routing (in real-time) on urban road transportation networks of four cities, namely, Mumbai, Delhi, Ahmedabad and New York. These are planar networks. We confirm the validity of a previously known result for planar networks as well -- that small degree node are more prone to extreme events than hubs.

Another emergent phenomenon of interest is congestion arising due to walker interaction and finite handling capacity in the system. For example, road junctions can accommodate only a finite and small number of vehicles. We adopted a interacting random walk model for dynamics on city road transportation networks and studied the collective behaviour through phase transition. The congestion phase transition of real planar network shows similarity with that of 2D lattice network (a homogenous network), in spite of the fact that degree distribution of planar network is quite different from a 2D lattice network. Finally, we studied the extreme events using the generalized random walk model, a realistic transport model and showed that nodes with lower degree are more susceptible to encountering extreme events than the hubs.