What can perimeter control do to improve mobility in cities?

When demand conditions are steady, traffic flow streams on long homogeneous roads exhibit reproducible relations between their average flows and densities that engineers call “fundamental diagrams”. It has been recently proposed that entire city neighborhoods must also exhibit similar macroscopic fundamental diagrams (MFD) connecting the total number of cars on the road at any given time (the accumulation) with the rate at which trips reach their destinations (the output). It has also been proposed that the MFD of neighborhoods that are not too big should be independent of where people are going (the neighborhoods “origin-destination table”); i.e., the MFD should be a property only of the network infrastructure. Daganzo (2007) explains why.

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).

Note: (i) the output and accumulation values closely follow a curve; (ii) there is an ideal mid-range accumulation that maximizes output; (ii) the system gridlocks (outflow drops toward zero) when accumulation is allowed to exceed this ideal amount; and (iv) 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 and Daganzo, 2007b).

Since the MFD is independent of demand, the MFD can be used (e.g., with perimeter control strategies) to ensure that a neighborhood’s vehicular accumulation never enters the gridlock regime; and that it is in fact maintained as closely as possible to its sweet-spot value. This simple strategy (a refined version of those used in London and other cities) turns out to maximize the number of cars and buses that complete their trips at any given time. It can improve everyone’s accessibility.

The animation above (taken from Geroliminis and Daganzo, 2007) shows how, by using the traffic signals in the periphery of the SFBD to prevent too many vehicles from crowding the SFBD beyond its sweet-spot, total output is increased. The pane on left side (and the top graph) display the original simulation; and the pane on right side (bottom graph) the one with control.  Note how the right side “keeps on ticking” when the left side has collapsed and how it serves many more trips. This result is promising for society because something simple and cheap (adjusting the timing of some signals) can have a significant and verifiable benefit.


  1. Daganzo, C.F. (2007) "Urban gridlock: macroscopic modeling and mitigation approaches" Transportation Research B 41, 49-62; "corrigendum" Transportation Research B 41, 379.
  2. Geroliminis N., Daganzo C.F. (2007a) "Macroscopic modeling of traffic in cities" 86th Annual Meeting Transportation Research Board, Washington D.C.