JSIAM Letters
Online ISSN : 1883-0617
Print ISSN : 1883-0609
ISSN-L : 1883-0617
A new compressible fluid model for traffic flow with density-dependent reaction time of drivers
Akiyasu TomoedaDaisuke ShamotoRyosuke NishiKazumichi OhtsukaKatsuhiro Nishinari
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2009 Volume 1 Pages 72-75


In this paper, we have proposed a new compressible fluid model for the one-dimensional traffic flow taking into account a variation of the reaction time of drivers, which is based on the actual measurements. The model is a generalization of the Payne model by introducing a density-dependent function of reaction time. The linear stability analysis of this new model shows the instability of homogeneous flow around a critical density of vehicles, which is observed in real traffic flow. Moreover, the condition of the nonlinear saturation of density against small perturbation is theoretically derived from the reduction perturbation method.

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© 2009 The Japan Society for Industrial and Applied Mathematics
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