Traffic density estimation using dimensional analysis

Traffic density, defined as the number of vehicles per unit length, is the primary measure used for quantifying road congestion. However, the direct measurement of this variable is difficult due to its spatial nature and the only method to directly measure it from field is aerial photography. Hence, it is usually estimated from other easily measurable variables such as speed or flow. Some of the reported approaches to obtain density include the input output analysis, fundamental traffic flow relation, and occupancy-based measurements in addition to those based on statistics, machine learning or model-based approaches. However, for better performance, all these methods require the careful selection of the relevant input variables/parameters and their relationships. One way of obtaining these relationships is to perform a dimensional analysis of the variables/parameters involved, identifying the non-dimensional variables/parameters and then obtaining a relationship between them using experimental data. This approach has been attempted for estimating road traffic density in this paper. The appropriate non-dimensional variables/parameters that characterize road traffic flow were first determined and the relation between them was then found out using simulated data. This relationship was subsequently used to estimate density for other datasets and the results were found to be promising.