The macroscopic fundamental diagram in urban network: analytical theory and simulation
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The Macroscopic Fundamental Diagram (MFD) is a diagram that presents a relationship between the average flow (production) and the average density in an urban network. Ever since the existence of low scatter MFD in urban road network was verified, significant efforts have been made to describe the MFD quantitatively. Due to the complexity of the traffic environment in urban networks, an accurate and explicit expression for the MFD is not yet developed and many recent research efforts for MFD rely on computer simulations. On a single corridor, an analytical approximation model for the MFD exists. However, this thesis expanded this theory in two directions. First, we specialize the method for models with equal road length on the corridor, which greatly reduces the complexity of the method. We introduce the adoption of seven straight cuts in approximation. Computer simulations are conducted and show a high compatibility with the approximated results. However the analytical approximation can only be applied with the assumption of constant circulating vehicles in the system without turnings and endogenous traffics. Secondly, we show that turnings and endogenous traffic can bring various impact on the shape of the MFD, the capacity, the critical density, the variance in density and cause a phenomenon of clustered traffic status along the MFD curve. Furthermore, the simulation using stochastic variables reveals that the variance in turning rates and endogenous traffic don’t have significant impact on the MFD. This discovery enables studies to focus on scenarios with deterministic parameters for those factors. While traditional objective of engineering for network is to maximize capacity and widen the range for the maximum capacity, our results indicate that traffic stability at the maximum performance is poor if the system does not stay constantly in equilibrium status. This thesis provides insights into the factors that affect the shape of the MFD by analytical approximation and simulation.