Steady state traffic flow, entropy production rate, temporal fluctuations and fuel consumption

We obtain an approximated expression for steady state distance headway that takes into account all the physical processes involved in real braking. This simple approximated formula gives a good description of the empirical data. The peculiarity of this approximation is that at small vehicle speed the gap increases with an increase in speed sharper than a linear function, whereas in most models this function gap vs. speed is a linear function or weaker than the linear function. A new concept of the production rate of entropy due to traffic flow has been presented. With the use of such a concept the percentage of increase in the fuel consumption rate due to velocity fluctuations on the traffic flow is easily determined. The same percentage of increase in the fuel consumption rate could be obtained as a function of the fluctuations on the CO2 production rate due to the traffic flow. The practical applications of such analysis are obvious. It is possible that the use of the simple model developed here could be very useful in the conceptual scheme of the three-phase traffic theory.