Two dimensional extension of the optimal velocity model

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An optimal velocity (OV) model is extended to a 2-dimensional model and properties of the model are investigated analytically and numerically. We clarify a relation among the property of traffic flow and those of granular flow, pedstrian flow, and collective biological motion.In the first year, a 1-dimensional OV model with many variables is investigated. We found that the property of the model can be interpreted within a framework of the OV model with single variable.We extended the OV model straightforwardly to a 2-dimensional model. In the model an ordered state and a disorderd (congested) state exit at relatively low densities. The model can also reproduce lane formation in mixed flow and counter flowWe have also analyzed real traffic data in Japanese highwaysIn the second year, we modified the 2-dimensional OV model and made the model applicable to the case at very high density. In order to investigate the varidity of the model, we have observed the motion of marathon runners and found the existence of lane formation and density fluctuation. The observations are consistent with the result of simulation in the 2-dimensional OV model. We have analyzed the model and found the stability condition of uniform flowThe 2-dimensional model have been applied to the collective biological motion, especially the formation of groups. We have shown that groups is formed from a homogeneous state spontaneously and this phenomenon can be explained by the OV modelWe have also shown that so-called syncronized flow can be reproduced by the OV model