尖點型突變理論在混合車流上的適用性與模式之研究

Abstract

經由實際錄影調查的車流資料顯示，車流於自由車流與擁擠車流兩種不 同的狀態下呈現不同的車流型態，而且從一車流狀態進入另一車流狀態時 ，車流速率有跳躍的情形發生。然而，一般傳統的巨觀交通車流模式，不 論是單一階段或是多階段的交通車流模式，當車流跨越自由車流階段與擁 擠車流階段等兩種車流狀態時，在車流流量及車流密度微量變動下，均無 法解釋車流速率發生跳躍的行為。 因此，近年來國外學者嘗試利用尖 點型突變理論的突然跳動性及雙重模態性等基本特性來構建交通車流模式 ，並預測交通車流速率特性的變化。過去在國內探討突變理論應用於交通 車流上的文獻極為少數，並且未有混合車流之研究，故本研究除了引用尖 點突變數學模式來構建交通混合車流模式外，並應用該車流模式進行國內 混合車流特性的分析，探討不同機車混合比例在該模式的應用下，所適用 之機車小客車當量值。 本研究車流模式的構建基礎，係根據Hall等學 者於近幾年（1987至1995）在交通車流模式上應用突變理論之觀念及模式 構建架構，再配合國內混合車流特性調查資料，以迴歸分析最小平方法對 尖點型突變曲面作曲線擬合求取模式係數，建立一包含車流速率、流量及 密度等三個變數的尖點型突變交通混合車流模式，並根據車流速率觀測 值-預估值的標準差及判定係數來判斷該模式對混合車流要素預測的準確 性。由實例分析第一部份得知，尖點型突變交通車流模式不僅可以一個數 學模式表現出兩種不同型態的交通混合車流，並可以呈現出車流速率發生 跳躍的特性，而且在車流速率值方面有不錯的預測能力。由實例分析第二 部份得知，不同機車混合比例將 影響機車小客車當量值的選用，且 機車小客車當量值會隨著機車混合比例的增加有下降的傾向。 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.