A real-time mathematical programming model of buses operating on a transit corridor that incorporates vehicle-capacity constraints is proposed. The objective for the model is to minimize the total times experienced by all passengers in the system, from the moment they arrive at a stop to the moment they reach their destination. Two control policies are considered: (a) vehicle holding, which is applicable at any stop, and (b) boarding limits that constrain the number of passengers entering a vehicle even when the vehicle is at less than physical capacity, to increase operating speed. The objective function is quadratic, but not convex with linear constraints. This problem is solved by using MINOS in a reasonable amount of computation time. A case study in a high-demand scenario shows that the proposed control achieves reductions in the objective function of more than 22% and 12% compared with no control and only holding strategies, respectively.
The location and number of bus stops are key to the operational efficiency of the services that use them; these criteria affect commercial speed, reliability, and passenger access times. In the defining of the number of stops, a trade-off arises between reduced access time, which widens a route's coverage area, and both the operational speed of the route and the users’ in-vehicle travel time. In this study, a model for optimally locating stops was developed, and the model was applied to the Grecia Avenue public transport corridor in the city of Santiago, Chile. The proposed model uses a continuous and multiperiod approximation of corridor demand; this approximation allows for the determination of the density of stops, which minimizes the sum of operator costs and total costs to passengers. The model simultaneously solves for the optimal stop density and the headway between successive buses. The actual stop locations of the Grecia Avenue corridor were compared with the optimal locations suggested by the model, and many similarities were found.
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