Self-Similar Characteristics of Vehicle Arrival Pattern on Highways

Abstract

This paper investigates the quantitative characteristics of the vehicle arrival pattern on highways. Inspired from a remarkable finding on data network traffic that most data packet arrival patterns follow the self-similar process as opposed to the classical Poisson process, this paper aims to explore whether the vehicle arrival pattern on highways exhibit the self-similarity property and the corresponding time headway distribution it obeys. By using real highway traffic data provided by the Texas Department of Transportation, United States, this paper examines the existence of self-similarity characteristics on these vehicle arrival data. This is done by estimating the Hurst parameter, which is an index for self-similarity testing. Hypothesis testing for the Hurst parameter estimation shows that the highway vehicle arrival pattern under moderate to heavy traffic conditions exhibit the self-similarity behavior. Then, using the headway data recorded from the Federal Highway situated in Kuala Lumpur of Malaysia, this paper further demonstrates that the time headway of vehicles on the highways follows the heavy-tailed distribution rather than the classical exponential distribution. These two novel findings not only shed some light on the existence of a new distribution to describe the vehicle arrival pattern but also enrich the studies on traffic flow theory.