Traffic Equations

If you are like me, during a long drive you'll drift into thinking about traffic. Seems to me there is an important function that relates speed and density of the cars, this is the minimum_safe_distance( s ) for a speed s. Below this distance you cannot stop in time. The average distance between cars is >= min_safe_dist(s). If we think of density as the reciprocal of average distance then

• (1/traffic density) >= min_safe_dist(s)

  We can add a few other rules of thumb:

• higher density lanes tend to merge into lower density ones
• as many cars enter an interchange as leave it. 
• people usually drive as fast as they can