車流模式遲滯現象之尖點型突變模型

Abstract

根據實際道路偵測器得到的車流速度、密度和流量資料，發現車流在遇到路段瓶頸時，會有減速的過程，當瓶頸通過時，會有加速的過程，而減速與加速的過程在速度與密度的關係圖上會顯示不同路徑，形成迴圈，即為車流遲滯現象，此與傳統車流理論假定速度與密度關係圖為線性且ㄧ對一的關係不相符，並且資料顯示車流在未壅塞車流與擁擠車流兩種不同的狀態下呈現不同車流型態，而且從一車流狀態進入另一車流狀態時，車速會有跳躍的情形發生，尤其在多車道道路突變現象會更為明顯。然而，一般傳統巨觀車流模式並無法解釋車流速度在車流流量和密度微量變動下產生跳躍的行為。 因此本研究運用具有的突跳性、雙重性與遲滯性等特性的尖點型突變模型，構建可說明車流遲滯與突變的尖點車流模式。模式最終可在考量車流的遲滯與突變現象的情形下，依據輸入之佔有率與流量資料估計車流速度。本文透過高速公路單、二、三和四車道路段之車流資料進行驗證並探討模式之適用性，結果顯示，本研究建立之完全延遲尖點車流模式在存有明顯突變與遲滯現象之高速公路車流資料中，對速度估計有90%以上的解釋能力。

According to real traffic data of speed, occupancy and flow, we found the two traffic phenomenon. One is hysteresis phenomenon, it means the difference in pattern between acceleration and deceleration of traffic steam. We can obtain a loop when the two pattern are drew in speed-occupancy diagram, Another is catastrophe phenomenon which means the large speed jumps occur at the transition from uncongested to congested regime. Such transitions are characterized by the gentle change in occupancy and flow, but a sudden, sharp, change in speed. The hysteresis and catastrophe phenomenon are more obvious for the more lane. This study use the cusp catastrophe model to develop a traffic flow model that can estimated traffic speed in the case of hysteresis and catastrophe phenomenon. Data of freeway segments with different lanes are used to test statistically how well the model fits. The results show that the data with hysteresis and obvious catastrophe phenomenon can be explained by the perfect delay model above 90%.