Stochastic approximations for the macroscopic fundamental diagram of urban networks

• The network MFD depends mainly on the mean block length to green ratio and the mean red to green ratio.
• It is symmetric, whereby it exhibits identical probability distributions in free-flow and congestion.
• The effect of buses can be approximated with the proposed theory by accounting for their effect in the red to green ratio parameter.

This paper proposes a theory for estimating the Macroscopic Fundamental Diagram (MFD) on inhomogeneous corridors and networks using probabilistic methods. By exploiting a symmetry property of the stochastic MFD, whereby it exhibits identical probability distributions in free-flow and congestion, it is found that the network MFD depends mainly on two dimensionless parameters: the mean block length to green ratio and the mean red to green ratio. The theory is validated with an exact traffic simulation and with the empirical data from the city of Yokohama. It is also shown that the effect of buses can be approximated with the proposed theory by accounting for their effect in the red to green ratio parameter.