Analysis of energy dissipation in traffic flow with a variable slope

We derive the motion energy dissipation model to investigate the relation between the additional energy loss of vehicles and the slope of a gradient. Simulations are carried out to check the validity of the dissipation model. Analysis of the results shows that the total energy consumption is inversely proportional to the slope in an uphill situation and the opposite conclusion can be drawn in a downhill situation. The energy dissipation rate depends on the density of traffic and the road length in two situations in a rule. It is found that the simulation result is in good agreement with real traffic.