Evolution of macroscopic models for modeling the heterogeneous traffic: an Indian perspective

The Lighthill-Whitham-Richards (LWR) model and its initial extensions treated traffic as homogenous and thus could only be employed for homogeneous traffic modeling where the entities of traffic, viz. vehicles, differed not much in their vehicle-class. Improvements and extensions were made to the LWR model, thus broadening the discipline of macroscopic traffic flow modeling. Several researchers introduced models that could comprehend the heterogeneity in vehicle classes. However, the traffic streams observed in the Indian subcontinent consists of numerous vehicle classes with complex interactions. Even the recent multiclass models are inadequate to represent these complex interactions. This paper explores various recent models and observes that the tradition through which the evolution of macroscopic modeling of heterogeneous traffic has happened does not account for some of the phenomena observed in the Indian road traffic. One such phenomenon, side-by-side movement of motorized two-wheelers (TW), is explained and an idea of diminishing density is introduced, which would improve the usability of the existing heterogeneous traffic flow models in an Indian perspective.