以先進細胞自動機模式探索高速公路時空交通特性

Abstract

1992年物理學家Nagel及Schreckenberg兩人首度將細胞自動機(Cellular Automaton，CA)應用於公路車流行為研究，透過幾個簡單的加減速規則，利用電腦快速運算，讓車輛進行彼此交互作用與規則疊代，呈現出與實測相當之巨觀車流特性，又能描述微觀車流特性。迄今已有相當數量之改良CA模式，惟多針對小客車為研究對象，且對細胞單元之定義均相當粗糙，亦未探討異質(指同類型車種可具不同之速率、加減速、變換車道行為)混合(指同一道路空間可同時運行不同類型車種，如機車、小型車、大型車)車流課題。為更符合實際車流現象，本研究發展精緻型CA模式，並改良傳統CA模式加減速過大之不合理現象，用以探索異質混合車流之時空交通特性。

本研究首先提出一個基礎的異質混合車流細胞自動機模式，該模式比以往細胞自動機模式研究更為精細的「細胞」及「網格」概念，定義「基本單元」(CU)作為衡量車輛及道路空間之共通單位。並進一步以時空網格被車輛細胞移動軌跡所佔用之比例代表佔有率，以車輛細胞每個時階移動的格位數代表速率，每個時階通過的細胞數代表流量，定義一般化佔有率、速率與流量，以精確描述異質混合車流車輛的總體行為。經發展CA基本模式，模擬不同車流密度情況下純車流之時空交通特性，再構建總體交通流量、速率與佔有率的基本關係。惟模擬結果顯示車輛運行過程車速會驟降停止之情形，模式規則待改進。

接著本研究針對前述規則之缺點提出一個修正CA模式，該模式進一步整合駕駛跟車空間預期效應、採取速度相依之隨機項、啟動延遲規則、變換車道與大小車互動規則等。模擬環境設定在二車道的高速公路中進行，模擬情境為在車流中加入慢速車(如同慢速移動瓶頸)與停止車(如同固定地點瓶頸)，探討混合車流之時空交通特性，並進一步探討車流軌跡、流量密度關係與時空車流型態。模擬結果顯示修正CA模式能夠呈現出真實交通環境重要的車流特性與型態。

研究最後針對模擬過程中以往CA模式均未處理之缺點，即車輛在接近前方為停止車輛或固定物時所出現不合理急煞車之情形，提出一個更精緻的CA模式來改善。模式在規則中引入Forbes的跟車概念，利用多段線性速率修正傳統CA模式加減速過大之不合理現象。經高速公路之驗證與測試發現，確能改正車輛速率驟降之缺失，並能顯示Kerner所提出的三相交通現象及其相變。本研究進一步利用此修正CA模式應用在施工區，探討不同速率控制策略對行車效率及安全之影響。

Cellular automata (CA) model was first proposed by Nagel and Schreckenberg in 1992 to simulate the highway traffic. The core logic was to introduce several simple update rules for vehicle movement in computer programs to efficiently simulate the complicated interactive traffic behaviors. A considerable number of revised or extended CA models have been developed to date, most of which only focused on pure traffic with coarse cell units in the simulations. Very little has devoted to the heterogeneous traffic situations and/or mixed traffic contexts, which comprise different types of vehicle. This research aims to develop advanced CA models to simulate the spatiotemporal behaviors under heterogeneous mixed traffic contexts on freeway.

Firstly, a basic CA model is developed to explore the fundamental traffic features. Generalized definitions of traffic variables, in spatiotemporal sense, and a new concept of common unit (CU) for gauging non-identical vehicle sizes and various lane widths are presented. Pure light vehicle and pure heavy vehicle experiments are tested on a two-lane freeway context. Vehicular trajectories, flow-occupancy diagrams, and spatiotemporal traffic patterns under deterministic and stochastic conditions are displayed. The results show that abrupt speed drops occasionally emerge during the simulations.

To resolve this shortcoming, this study continues to propose a revised CA model, which considers the anticipation effect, velocity-dependent randomization, slow-to-start, lane change, and interaction among vehicles. The effects of both stationary and slow-moving bottlenecks on global traffic are examined using this revised CA model. Vehicular trajectories, flow-occupancy, and spatiotemporal traffic patterns are displayed. The results reveal noticeable traffic patterns with free flow, wide moving jam and synchronized flow phases, suggesting that the revised CA model is capable of capturing the essential features of traffic flows.

Finally, this study further proposes a refined CA model using the rationale of Forbes’ car-following concept with a piecewise-linear movement mechanism, which aims to rectify the common defect of abrupt deceleration existent in most conventional CA models. The proposed CA model is validated in a two-lane freeway mainline context. It shows that this refined CA model can fix the unrealistic deceleration behaviors, thus can reflect the genuine driver behaviors in real world. The model is also capable of revealing Kerner’s three-phase traffic patterns and phase transitions among them. Furthermore, the refined CA model is applied to simulate a highway work zone wherein traffic efficiency (maximum flow rates) and safety (speed deviations) impacted by various control schemes are investigated.