Macroscopic Modeling of Traffic in Congested Cities: Empirical Evidence, Analytical Derivations and Control Applications
published: July 10, 2009, recorded: June 2009, views: 7341
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Various theories have been proposed to describe vehicular traffic movement in cities on an aggregate level. They fall short to create a macroscopic model with variable inputs and outputs that could describe a rush hour dynamically. This work shows that a Macroscopic Fundamental Diagram (MFD) relating production (the product of average flow and network length) and accumulation (the product of average density and network length) exists for neighborhoods of cities in the order of 5 − 10 km2. It also demonstrates that conditional on accumulation large networks behave predictably and independently of their Origin-Destination tables. These results are based on analysis using simulation of large scale city networks and real data from urban metropolitan areas. Regularity conditions under which an MFD exists for different types of networks are proposed and tested. Further analysis of real data shows that an MFD is not a universal recipe that can describe any type of large network. For example, MFDs for spatially inhomogeneous networks or non-redundant networks, like freeway traffic systems, are highly scattered. An analytical model based on Variational Theory describes the connection between network structure and a network’s MFD for urban neighborhoods controlled at least in part by traffic signals. The MFD is applied to develop control strategies based on neighborhood accumulation and speeds and improve accessibility without the uncertainty inherent in forecast-based approaches.
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