Continuity Equation Validation for Nonhomogeneous Traffic

The continuity equation involving traffic flow expresses the relationship between density, flow, and speed. Density equals the flow divided by space mean speed. The formulation of this equation in the year 1952 has two important assumptions. One assumption is that spacing and speed are constant, i.e., uncongested conditions with moderate to slightly high volumes. The other assumption is that homogeneous traffic prevails, vehicle composition is uniform and vehicles behave within strict lane discipline rules. To determine if the continuity equation is valid under nonhomogeneous traffic conditions, one performs an experiment involving data collection of density, flow, and speed at three midblock sites in India. Data collection occurred when uncongested conditions prevailed with moderate to slightly high volumes. Comparing the average density derived from observed densities in the field to the density derived from the continuity equation reveals whether or not the continuity equation accurately predicts average density under nonhomogeneous traffic conditions. Similar traffic operating characteristics served as the basis for grouping vehicles into five traffic entity types. The association between average density based on observed densities of nonhomogeneous traffic and density derived from the continuity equation had a correlation coefficient of $+0.88$ for light, four-wheeler type, $+0.85$ for heavy vehicle type, $+0.90$ for motorized, three-wheeler type, $+0.83$ for motorized, two-wheeler type, and $+0.50$ for nonmotorized, two- and three-wheeler type. Additionally, a nonparametric test, i.e., Wilcoxon signed-rank test, compared observed and derived densities. At a 95% confidence level, no significant difference existed between observed and derived densities of light four-wheeler type, heavy vehicle type, motorized two-wheeler type, nonmotorized two- and three-wheeler type, and between cumulative observed and cumulative derived density. Only in the case of the motorized three-wheeler type, the observed, and derived densities are significantly different. These moderate to strong correlations coupled with the results of the nonparametric test validate the application of the continuity equation when traffic is nonhomogeneous.