運輸走廊瓶頸路段擁擠收費與捷運補貼之研究

Abstract

都會區私人運具使用率逐年攀升，但道路容量受限稀少土地與政府財政負擔而無法隨之增加，故當尖峰時段，CBD與周邊衛星城市之跨區通勤旅次常發生擁擠排隊情形。而當前交通擁擠管理傾向以擁擠定價，輔以完善大眾捷運系統路網，以有效移轉小汽車旅次、提高大眾運輸系統使用率，但亦產生擁擠定價是否為民眾接受，及該擁擠費收入用途之正當性等課題。有關擁擠定價之文獻，多討論單一起迄對、以小汽車道路系統為主之單運具模式，其中亦有應用「最適控制理論」構建單一起迄對之動態道路定價模式，而有關大眾運輸系統排班營運文獻大多僅討論營運者如何滿足乘客之需求，其目標是使派車更有效率且讓乘客於車站等候時間最小。 本研究以單一瓶頸道路擁擠定價模式為基礎，加入替代之捷運路線，以系統通勤者有關之依時性成本為目標函數，並考量兩運具運行特性、短期通勤者通勤行為特性，模式中所有變數皆為時間之函數，因此以最適控制理論分析本研究動態問題，其優點為可經乘數的經濟意義來表現邊際成本的狀態，而不需經由定義複雜之成本函數分析其間的關係；此外，本研究將時間視為橫軸、兩運具選擇人數變化為縱軸，當使用者均衡達成時，每個時間點亦對應一兩運具之均衡使用人數；進一步，本研究擬對小汽車收取動態擁擠費，並擬以擁擠費收入用於補貼捷運營運成本，捷運營運單位可配合增加發車班次數，舒緩瓶頸路段小汽車旅次而轉移至捷運系統；由於每車次補貼水準不可能高於現有每車次營運成本，且當補貼過度雖使列車發車次數增多，對乘客時間成本之減少呈現正面效益，但亦有可能因列車使用頻繁使得營運成本不減反增，系統均衡成本亦隨之增加，因此可預先觀察每車次補貼額對系統均衡成本之敏感度，並進一步反推一最適擁擠費移轉比率。 實務上擁擠費用途不僅用於補貼大眾運輸，執行動態擁擠收費所耗之各項軟硬體建置、維護成本，亦由擁擠費收入支應，範例分析結果顯示中最適補貼比率約為49.3%即可大幅改善系統均衡成本，而剩餘收入便可用於非補貼用途；本範例中班距因補貼而縮短，最短可達4.8分鐘，與目前台北捷運尖峰時段班距4~7分鐘內相比尚屬合理，且可供捷運營運單位一最低調整之依據；此外，亦可依即時之擁擠狀況，調整本研究瓶頸路段紓解率函數，代表瓶頸路段幾何設計、號誌設置等影響最大紓解量之綜合調整參數，因此當擁擠趨於嚴重時，可調整釋出可用紓解量影響系統均衡，由範例分析中可發現當釋出可用容量，雖能刺激潛在小汽車使用者，造成小汽車旅次微幅增加、降低系統均衡成本，但其敏感度不如直接補貼捷運顯著，綜上所述，交通管理單位不但可以利用動態擁擠收費與補貼策略外，尚可視實際路況調整瓶頸紓解率，藉此讓兩運具使用率達到最適配置。

Car usage increases rapidly while road capacity usually couldn’t accommodate such a heavy traffic. Especially, in morning peak period, commuters frequently confront congestion at corridors connecting CBD and satellite cities. Transportation authority may either adopt congestion pricing policy or construct the mass transit system. Both of strategies aim to encourage transit usage and shift commuters from private cars to the transit system. The public, however, regards congestion toll as coercive and suspects the purpose of using collected tolls. Much work on static models has focused on single O-D pair bottleneck congestion pricing with a single mode of automobile-highway system. Besides, previous studies have applied the Optimal Control Theory to construct dynamic models on single bottleneck highway congestion pricing. On another line of research, mass transportation system scheduling, dispatching problems have been commonly analyzed by satisfying passenger demands from the perspective of the operator. This study considers the competitive transit line which parallels the highway bottleneck and serves the same corridor. Then, this study applies the Optimal Control Theory to formulate a dynamic traffic assignment model by minimizing commuters’ time-dependent travel cost. If there exists a set of solution in the Optimal Control Problem (OCP), the first-order necessary conditions should be sufficient to this OCP. Meanwhile, the multiplier analysis reveals the system marginal cost fluctuation caused by commuters’ dynamic mode choice decisions. Furthermore, an optimal time-varying toll is derived and an iterative algorithm is proposed for solving this OCP which shows the two-mode assignment evolutions in each time interval of the study period. The study further proposes a strategy that transportation authority collects the toll revenue from car users to subsidize transit operating cost so as to increase the frequency of transit dispatching runs and shift car trips to transit trips. As a result, an optimal subsidy, which minimizes system equilibrium cost could be determined. Practically, toll revenue could be used on subsidizing transit or supporting the facilities of Electronic Road Pricing (ERP). In the case study, we determine an optimal ratio of 49.3% of toll revenue to subsidize transit operating cost, while use the remainder of toll revenue to maintain the ERP’s facilities. Due to the subsidy, transit dispatching headway could be shortened to 4.8 minutes from the initial 6.3 minutes. Compared with the headway of 4-7 minutes of Taipei Metro System during the peak period, the optimal headway of 4.8 minutes obtained in our case study is reasonable. Finally, transportation authority could also release a latent capacity which is considered to be reserved for the adaptive management of high-level congestion.