Traffic congestion, nothing to gridlock

Three agent based models were studied, the difference being in how the base speed was calculated before, potentially, being clamped by the distance to the vehicle in front. The classical Nagel-Schreckenberg model produced an odd looking fundamental diagram. A constant speed model produced the classic triangle shape seen when real world data is plotted on a fundamental diagram. A multinomial distribution produced a smoothed version of the classic triangle.

The multinomial distribution was chosen since it is approximated by the normal. The effect of congestion was firstly to transform it to the more general Quartic Exponential distribution before turning into the Dirac delta distribution at gridlock as shown above in the animation for the sum of four six-sided dice minus four.

Further details are contained in a pre-print on GitHub.