A field experiment in Yokohama (Japan) reveals that a macroscopic fundamental diagram (MFD) linking space-mean flow, density and speed exists on a large urban area. The experiment used a combination of fixed detectors and floating vehicle probes as sensors. It was observed that when the somewhat chaotic scatter-plots of speed vs. density from individual fixed detectors were aggregated the scatter nearly disappeared and points grouped neatly along a smoothly declining curve. This evidence suggests, but does not prove, that an MFD exists for the complete network because the fixed detectors only measure conditions in their proximity, which may not represent the whole network. Therefore, the analysis was enriched with data from GPS-equipped taxis, which covered the entire network. The new data were filtered to ensure that only full-taxi trips (i.e., representative of automobile trips) were retained in the sample. The space-mean speeds and densities at different times-of-day were then estimated for the whole study area using relevant parts of the detector and taxi data sets. These estimates were still found to lie close to a smoothly declining curve with deviations smaller than those of individual links -and entirely explained by experimental error. The analysis also revealed a fixed relation between the space-mean flows on the whole network, which are easy to estimate given the existence of an MFD, and the trip completion rates, which dynamically measure accessibility.

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Abstract-Recent analysis of empirical data from cities showed that a macroscopic fundamental diagram (MFD) of urban traffic provides for homogenous network regions a unimodal lowscatter relationship between network vehicle density and network space-mean flow. In this paper, the optimal perimeter control for two-region urban cities is formulated with the use of MFDs

a b s t r a c tIt has been recently shown that a macroscopic fundamental diagram (MFD) linking spacemean network flow, density and speed exists in the urban transportation networks under some conditions. An MFD is further well defined if the network is homogeneous with links of similar properties. This collective behavior concept can also be utilized to introduce simple control strategies to improve mobility in homogeneous city centers without the need for details in individual links. However many real urban transportation networks are heterogeneous with different levels of congestion. In order to study the existence of MFD and the feasibility of simple control strategies to improve network performance in heterogeneously congested networks, this paper focuses on the clustering of transportation networks based on the spatial features of congestion during a specific time period. Insights are provided on how to extend this framework in the dynamic case. The objectives of partitioning are to obtain (i) small variance of link densities within a cluster which increases the network flow for the same average density and (ii) spatial compactness of each cluster which makes feasible the application of perimeter control strategies. Therefore, a partitioning mechanism which consists of three consecutive algorithms, is designed to minimize the variance of link densities while maintaining the spatial compactness of the clusters. Firstly, an over segmenting of the network is provided by a sophisticated algorithm (Normalized Cut). Secondly, a merging algorithm is developed based on initial segmenting and a rough partitioning of the network is obtained. Finally, a boundary adjustment algorithm is designed to further improve the quality of partitioning by decreasing the variance of link densities while keeping the spatial compactness of the clusters. In addition, both density variance and shape smoothness metrics are introduced to identify the desired number of clusters and evaluate the partitioning results. These results show that both the objectives of small variance and spatial compactness can be achieved with this partitioning mechanism. A simulation in a real urban transportation network further demonstrates the superiority of the proposed method in effectiveness and robustness compared with other clustering algorithms.

a b s t r a c tA field experiment in Yokohama (Japan) revealed that a macroscopic fundamental diagram (MFD) linking space-mean flow, density and speed exists on a large urban area. It was observed that when the highly scattered plots of flow vs. density from individual fixed detectors were aggregated the scatter nearly disappeared and points grouped along a well defined curve. Despite these and other recent findings for the existence of well-defined MFDs for urban areas, these MFDs should not be universally expected. In this paper we investigate what are the properties that a network should satisfy, so that an MFD with low scatter exists. We show that the spatial distribution of vehicle density in the network is one of the key components that affect the scatter of an MFD and its shape. We also propose an analytical derivation of the spatial distribution of congestion that considers correlation between adjacent links. We investigate the scatter of an MFD in terms of errors in the probability density function of spatial link occupancy and errors of individual links' fundamental diagram (FD). Later, using real data from detectors for an urban arterial and a freeway network we validate the proposed derivations and we show that an MFD is not well defined in freeway networks as hysteresis effects are present. The datasets in this paper consist of flow and occupancy measures from 500 fixed sensors in the Yokohama downtown area in Japan and 600 loop detectors in the Twin Cities Metropolitan Area Freeway network in Minnesota, USA.