The movie above (taken from Geroliminis and Daganzo, 2007) is a 4-hour simulation of the San Francisco business district (SFBD) morning rush hour to test these conjectures. The right side pane shows the street network. Green and red dots are the traffic signals and the moving dots are vehicles. The demand is 3-4 times larger than in reality to ensure that the network is subjected to severe loads. The diagram on the top left side shows the accumulation and output values that arise during the simulation. The diagram on the bottom shows that there is a stable proportional relationship between output (which is difficult to observe in real life) and the vehicle-kilometers traveled per unit time (which is easy to observe).
- the output and accumulation values closely follow a curve;
- there is an ideal mid-range accumulation that maximizes output;
- the system gridlocks (outflow drops toward zero) when accumulation is allowed to exceed this ideal amount;
- and the multi-colored dots that appear when the simulation ends (corresponding to simulations with vastly different origin-destination tables) follow the same curves.
Thus, it appears that the MFD does indeed exist independent of the demand. This has been recently confirmed in the field with a test that used a combination of fixed detectors and floating vehicle probes.
Geroliminis N., Daganzo C.F., (2007), Macroscopic modeling of traffic in cities, 86th Annual Meeting Transportation Research Board, Washington D.C.