Vehicular traffic models for speed-density-flow relationship

The relationship among vehicles on the road is  modeled using fundamental traffic equations. In traffic modeling, a   particular speed-density equation  usually fits a peculiar dataset. The study seeks to parameterize some existing fundamental models so that a given equation could match different  dataset. The new  equations are surmisal offshoots from existing equations.    The parameterized equations are  used in the LWR model and  solved  using the Lax-Friedrichs differencing scheme. The simulation results illustrate different scenarios of acceleration and deceleration traffic  wave profiles.  The proposed  models appropriately explain the varying transitions of  different traffic regimes.