改良多路徑最大綠寬帶模式演算法

Abstract

號誌控制是有效且低成本的增加路口使用效率的方式，其概念為透過對時差及號誌週期、時相長度等變數的控制，最大化通過路口的車流量、或者最小化路口的延誤。最大化綠寬帶模式(MAXBAND model)為號誌控制的常見方法，以一組連鎖路口為對象，目標為最大化通過連鎖路口的車流續進寬帶長度，求出連鎖號誌時差的最佳解，常用於主幹道上的雙向路徑續進問題。然而，傳統的幹道最大綠寬帶續進模式，面對高速公路下匝道與平面道路相接的路型時，由於無法將匝道轉入主道的高轉向車流量納入模式考量，從而使模型解犧牲路網上重要路徑的效率。針對上述問題，Yang et al.(2015)提出多路徑最大綠寬帶模式，在最大綠寬帶模式中加入支道的轉向車流因素，並最佳化時相順序。 本研究以Yang et al.(2015)研究中提出的模式為基礎，進一步擴充多路徑最大綠寬帶模式的功能，可最佳化時相的長度；並將道路的車流行為加入模型限制當中，使路段上的車輛旅行時間符合車流擴散模型；且引入衝擊波理論構建的路口最大停等車隊長度限制式，使模式中的車隊消散時間變數與時差、週期與時相長度形成關聯。研究中以竹北下匝道地區為實際案例，使用模式進行求解，並以CORSIM模擬求解結果績效。結果顯示本研究的模型可改善40%以上的路網效率，對選擇的關鍵路徑效率亦提高60%。此外，本研究亦提供了以Gurobi求解模型的程式代碼，做為未來研究參考之用。

Signal control is one of the effective methods to enhance the utility of intersections. The concept is that vary the signal variables such as offsets, cycle length and phases length to maximize the throughput or minimize delays of synchronized intersections. MAXBAND model is a common mathematical programming of signal control researches, which solves the optimized offsets solution in order to maximize the progression bandwidth through a suite of synchronized intersections, and it is often applied in the two-way path progression problems. However, the traditional MAXBAND model cannot consider the effect of left-turn traffic flows discharged in ramps when it comes to the network problem of the surface approaches freeway ramps, such that the model solution sacrifices the efficiency of critical paths. To solve this issue as mentioned above, Yang et al.(2015) provided a multi-path progression MAXBAND model to consider the progression problems that include more than two large-volume paths, and make the model able to optimize the phase sequences. Based on the model Yang et al. (2015) proposed, this work extends the ability of the multi-path MAXBAND model, includes that (a) optimizing the phase length/ratio; (b) considering the traffic dispersion effects; (c) using the shockwave theory to formulate the constraints of maximum queue length in the intersections so that the variables of queue clearance time, offsets and cycle length are related in the model. The research takes the network in Chubei, Hsinchu as the experimental case, and use CORSIM simulator to measure the performances between the on-going timing plan and the solution of the revised multi-path MAXBAND model. The results show that the revised model provided by this work can improve over 40% efficiency of the synchronized intersections, and also improve at most 60% efficiency of each important path. Apart from this, this research provides the code programming in Gurobi C++ interface for the future researches.