Capacity-Constrained Bus Bridging Optimization Framework

Abstract

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.

Assessing the Bus Bridging Effectiveness on the Operational Resilience of the Subway Service in Toronto

“…Optimal Bus Bridging Data. The optimal bus bridging plans for each of the incidents are obtained using the methodology and tools developed by Itani and colleagues (7,9). The tools use genetic algorithm and queueing analysis for the assessment and optimization of the bus bridging strategy.…”

“…These performance results are compared with those of the This analysis is done using the five incidents described in Table 1, where each incident belongs to one category and is placed on the severity scale. The blue line in Figure 12 shows the TUD of the optimal plans generated using the bus bridging optimization tool developed by Itani et al (7) at different durations, while the orange line presents the TUD of the non-optimal plan estimated using the bus bridging assessment tool presented in Aboudina et al (9). The closure between Sheppard-Yonge and Don Mills Station (Line 4) belongs to the least severe category since the line serves an uncongested corridor.…”

“…A handful of research studies have investigated the optimal bus bridging service. One recent study proposed a genetic algorithm model that determines the optimal deployment and allocation of shuttle buses, considering the subway passenger delays and the impact on bus riders ( 7 ). The optimal number of shuttle buses is subject to bus-bay capacity constraints and the method is applied to a case study in Toronto.…”

“…Data-driven analysis of bus bridging operations is key to understanding how this strategy affects the resilience of the subway service. A decision support tool was developed recently to help agencies manage unplanned service interruptions using optimized bus bridging strategies (7)(8)(9).…”

“…Two types of analyses, namely clustering and classification and regression tree (CART), are used to categorize incidents of the subway network in Toronto based on two major metrics: the total user delay (TUD) and the required number of shuttle buses under an optimal bus bridging strategy. The optimization framework developed by Itani et al ( 7 ) is adopted in this paper to determine the optimal bus bridging plan for the selected incidents. The data used for the analysis include a total of 205 unplanned disruptions affecting the subway network and where shuttle buses were deployed.…”