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Via the data analysis of earlier studies, the traffic flow has two different regimes─the free-flow regime (the uncongested regime), and the congested regime─as if there is a jump between two regimes. When the traffic flow jump from one regime to the other, the conventional macroscopic traffic flow models, neither single-regime nor multiregime models, can provide a good explanation for the occurrence of speed change by flow and density.In recent year, the foreign researchers have tried to use the Cusp Catastrophe Theory''''s "sudden jump" and "bimodality" properties to model traffic flow, and to predict the change of traffic speed. But the traffic flow model in Taiwan still follow the tradition framework, and there has no research on traffic mix flow. Therefore, this study tries to apply Cusp Catastrophe Theory not only to discuss the domestic traffic mix flow characteristics, but also to discuss distinct motorcycle mix ratio under the applying of traffic mix flow model motorcycle''''s suitable passenger car equivalent(PCE)The base of this study is the conceptual framework of Catastrophe Theory applied to traffic stream model described by Hall etc. From 1987 to 1994, and we use the domestic traffic flow data with parameters calibrates by regression analysis least square method for curve fitting. Then, we get the Cusp Catastrophe Traffic flow Model with the traffic flow, the speed, and the density variables. We apply a series of statistical analysis for the model, including the standard deviation of error and the coefficient of standard deviation between the observed and predicted values for speed, as well as indicators of the goodness of fit of the models. The first part of result shows the Cusp Catastrophe Traffic Flow Model not only can express two different traffic flow regimes in one mathematics formula, but also has good prediction in traffic speed value and realizes the flow feature of speed jump. The second part of result shows motorcycle''''s mix ratio will affect its passenger car equivalent, and motorcycle''''s passenger car equivalent has the trend of falling with its changeable mix ratio.
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