Travel time estimation by urgent-gentle class traffic flow model

To estimate travel time through a ring road, an urgent-gentle class traffic flow model (UGM) with viscoelastic and ramp effects is developed. Vehicles in traffic flow are divided into urgent and gentle categories, and the urgent class has the demand of arriving at destination in time, while the gentle class hasn't. It is assumed that the urgent and gentle classes have the same instantaneous speed to simply the mathematical modeling. To validate the proposed traffic model, a Navier-Stokes like model (Zhang, 2003) is further extended just for validating the present model. Numerical simulations based on the present model are carried out to calculate the travel time on a ring road with total length of 80  km and four initially assumed jams. It was found that similar to the effect of initially assumed jams, the on/off ramp flows play significant roles in the formation and evolution of traffic flow patterns. Urgent density fraction propagates at local traffic speed, its temporal evolution and spatial distribution curves have different shapes as compared with that of traffic density and speed. The average travel time increases monotonically with the increase of ring road initial density. Rational management of road operation is necessary.