Capacity-Constrained Bus Bridging Optimization Framework

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Urban rail systems frequently suffer from unexpected service disruptions, which can result in severe delays and user dissatisfaction. “Bus bridging” is the strategy most commonly applied in responding to rail service interruptions in North America and Europe. Buses are pulled from regular routes and dispatched to serve as shuttles along the disrupted rail segment until regular train service is restored. In determining the required number of buses and source routes, most transit agencies rely on ad hoc approaches based on operational experience and constraints, which do not necessarily alleviate the extensive delays and queue build-ups at affected stations, nor do they minimize system-wide impacts in an optimal manner. This paper proposes a genetic algorithm-based optimization model to determine the optimal number of shuttle buses and route allocation to minimize overall subway- and bus rider delay for any given rail disruption incident. The generated optimal solutions were sensitive to bus-bay capacity constraints along the shuttle service corridor of any given disrupted subway segment, utilizing methods found in the Transit Capacity and Quality of Service Manual. The model was used in an analysis of real-world incident data obtained from the Toronto Transit Commission and supplemented by other passenger and travel time data. The bus bridging toolkit showed strong potential to produce efficient shuttle response plans that reduced the transit user delays by more than 50% while ensuring minimum queue formation at disrupted stations and maximizing the utilization of shuttle buses.