Self-Similar Behavior of Highway Road Traffic and Performance Analysis at Toll Plazas

Abstract

Until recently, the Poisson process has been used to model internet and road traffic queues. It has been established that internet traffic exhibits self-similarity, which is very different from the Poisson process. Motivated by this, efforts have been made to examine whether road traffic is also self-similar. Earlier efforts in this direction indicate that road traffic is indeed self-similar. To substantiate this, this paper examines, by various methods, whether real time traffic on a busy national highway in India is self-similar. The results from this examination prove that the traffic observed on the highway is self-similar. This paper also presents a novel method based on percentiles for computing the Hurst parameter, which is an indicator for the intensity of self-similarity. The paper also validates the percentile method with two other existing methods. Additionally, the traffic at a toll plaza on the highway has been modelled as queueing system, and performance measures have also been computed, namely, mean queue length and busy period distribution. The numerical results clearly demonstrate that the analysis presented in this paper can be useful for improved designs of toll plazas.