本研究求解單一路線大眾運輸系統之時變發車頻率問題:在給定路網、車隊規模與動態、隨機乘客抵達率條件下,求解此一大眾運輸系統每單位時間的服務率。於研究中首先以逐點流體基礎近似方法(Point-wise Fluid-Based Approximation Approach)建構單一路線動態大眾運輸等候網路(Dynamic Transit Queuing Network, DTQN)模型,接著將此模型與最佳化數學規劃模型整合,在考慮兩個不同的目標下:最小化總系統成本(營運成本與等候成本)與最小化總系統成本加上碳排放成本,求解這兩個不同的問題模式,而且所求解的時變發車頻率必須介於交通主管機關所訂之最大班距與給定車隊規模所能提供之最小班距間。本研究根據台北市公車路線資料產生接近實際狀況之測試例題,利用GAMS的MINOS求解器求解此測試例題之最佳時變發車頻率,並分析改變乘客抵達率與目標式各成本項權重對發車頻率、等候人數與各成本項目的影響。研究結果發現:時變服務率與各站等候人數都隨著整體抵達率增加而增加;考慮碳排放成本會使得發車頻率降低,等候成本的變化則與營運成本變化成反比。
This study deals with the frequency (the reciprocal of headway) setting problem for a single transit route, given its stops, fleet, and dynamic, stochastic passenger arrival rates. The objective is to obtain optimal time-varying frequencies in terms of the service rate (or number of available seats) per time unit which can be used to derive the multiple headways in the planning horizon. A point-wise fluid-based approximation approach is adopted to construct a single route dynamic transit queuing network (DTQN) that describes the single transit route system. The DTQN is the encapsulated in an optimization model that determines optimal time-varying frequencies with respect to a certain objective and subject to the minimal and maximal headway requirements set by the fleet size and the government agency, respectively. This study considers two different objectives: the first one is to minimize total system cost (including operational and waiting costs), the second being the first plus carbon emission cost. A test problem instance was designed based on a bus route in Taipei city, and the MINOS solver of GAMS was applied to solve for the optimal time-varying frequencies with respect to the above two different objectives. The sensitivity analyses were also conducted to examine the impacts of passenger arrival rates and weights of the cost components in the objective function on the frequency, waiting cost, and operational cost.