車流動力學模式

Kinetic Theory of Traffic Models

卓訓榮(Hsun-Jung Cho) ； 傅昱瑄(Yu-Hsuan Fu) ； 陳豐榮(Feng-Jung Chen)

《運輸計劃季刊》 37卷1期 (2008/03) Pp. 109-137

https://doi.org/10.6402/TPJ.200803.0109

摘要

微觀車流模式具有行為基礎，但資料不易取得，尤其在大樣本時更為困難；相反，巨觀車流模式容易取得資料，但是缺乏行為基礎；而介觀車流理論兼具以上兩種車流行為之優點，可藉由行為基礎建立速度分配函數，經過積分後得到巨觀車流資訊。介觀車流基本模式最早由Prigogine與Herman建構，本研究建構一新的車流動力學模式，以此新模式修改Prigogine與Herman模式在空間與速度瞬時變化的假設，使得可以描述減速時速度的連續變化，並且考慮到煞車的空間影響，最後推導出以連續減速模式對速度積分後，滿足流量守衡。為了使模式更容易被了解，本研究補充其有關之基本車流模式、車流速度分配模式、期望速度分配模式、駕駛者交互影響模式、駕駛者跟車行為之速度分配模式、鬆弛時間和奇異點特性分析等研究所需數學定義與模式推導之不足，並且針對Prigogine與Herman建構的介觀模式做模擬，以期可使對此理論有興趣者易於了解，甚而基於此有更深入之研究。

關鍵字

動力學理論 ； 微觀車流 ； 介觀車流 ； 巨觀車流

並列摘要

Microscopic traffic models show the basis for driver behavior. The behavior data is quite difficult to collect, especially when large samples are required. Macroscopic traffic models manipulate the data that is easy to collect but lack of the behavior basis of drivers. Mesoscopic traffic models take advantage of the above models; mesoscopic models can build the velocity distribution function from the behavior basis and obtain the macroscopic parameters through integration of the distribution function. Mesoscopic models are first proposed by Prigogine and Herman. We construct a new model to relax some poor assumptions of Prigogine and Herman's–lack of consideration of finite space and instantaneous velocity-changing. Therefore, our model considers a successive slowing-down process and finite baking space. This study also provides the required mathematical definition and the deduction in the proof of model from basic traffic patterns, traffic velocity distribution model, expected velocity distribution model, driver interactive impact model, driver following behavior velocity distribution model, relaxation time and singularity analysis, etc. studies. And we simulate the Prigogine and Hermann model. With these, we might assist researchers to have a better understanding of the model and thus have the ability of further research.

並列關鍵字

Kinetic theory ； Microscopic traffic ； Mesoscopic traffic ； Macroscopic traffic

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