Statistics of stop-and-go traffic: Emergent properties of congestion behavior arising from collective vehicular dynamics in an urban environment

The movement of large numbers of vehicles along the complex network of roads in a city result in interactions between them that become stronger as the traffic density increases. The non-trivial behavior arising from the collective dynamics of vehicles include the occurrence of persistent congestion at different points of the transport network that typically reduce the efficiency of overall traffic flow. In order to understand the mechanisms responsible for the characteristic spatio-temporal patterns of urban traffic, we first need to identify statistically robust features from empirical observations, which one can then try to recreate in computational models of traffic dynamics. In this article, we have analyzed the GPS traces collected round the clock for more than a hundred taxis operating in a major Indian city over a period of 1 month. The available information allows us to precisely measure the periods during which the vehicle is static and when it is moving. We focus on the intermittent patterns of rest and motion that a car exhibits during its passage through city traffic, which provides a window into key aspects of collective dynamics resulting from congestion. We show that the distribution of waiting time, i.e., the period during which a car is static between two successive epochs of movement, has a highly skewed nature. The bulk of the probability distribution appears to follow power-law scaling with exponent value of 1.78. As city traffic has very different densities during peak hours and off-peak hours, we have also investigated this distribution at different times of the day. While the power-law scaling is found to be robust, the exact value of the exponent does change slightly.We have also considered the active time distribution, i.e., the period of movement between two epochs when the car is static, which does not exhibit a power-law signature but rather resembles a inverse Gaussian or a log-logistic distribution. We also look at the recurrence relation between the durations of successive waiting times, as well as, that between active time duration and the duration of the preceding waiting time. Our results can be used to help understand how the statistical properties of large-scale traffic movement over complex road networks which characterize cities deviate from that of other types of collective dynamics, e.g., the diffusion of random walkers.