|Abstract:||Public transportation is a sustainable solution to reduce traffic congestion in urban areas by providing shared mobility to its users. However, a good level of service is a crucial performance indicator for transit agencies to ensure sufficient ridership and maintain the benefits of public transportation (e.g. lower CO2 emissions per traveler, lower transit fares). To provide satisfying service, transit should be fast, convenient, and reliable, in order for the passengers to arrive at their destination in a timely fashion, but also cost-effective. More specifically, transit agencies need to ensure availability (temporal and spatial accessibility to the system), punctuality (limited deviations from schedule), and acceptable travel time for all passengers at reasonable costs for providing service.
Many factors can impact the design and schedule of public transit systems (e.g. physical/geographical constraints, socio-economic and environmental conditions, stochastic events). Specifically, as a result from specialization and pursuit of economies of scale, the distribution of passengers origins and destinations with respect to time and space could be largely heterogeneous (e.g. centers of interest such as CBD typically attract a majority of the transit trips). Such heterogeneous settings should be accounted for when designing a transit system to provide good accessibility to its users. In addition, reliability can be severely hindered by real-world disruptions (e.g. traffic congestion, passenger needs, driver vagaries). During transit operations, external disturbances create discrepancies between the schedule and the actual arrival times, which are magnified over time until buses bunch into pairs instead of being evenly spaced. This bus bunching phenomenon is well-known in the industry as an illustration of the instability of uncontrolled transit systems. It creates large temporal gaps in the service, which cause a severe loss in punctuality. As a result, more passengers are served by late buses than by early buses, and the expected waiting time for public transit passengers increases as the variance of the headways increases. This shows the necessity for transit agencies to also implement strategies to stabilize bus schedules.
This Ph.D. research aims at tackling several challenging topics in the field of public transportation, from strategic and tactical decisions to real-time control, including: (i) heterogeneous transit network design, and (ii) bus bunching mitigation. Specifically, we propose several modeling frameworks to design various transit systems to incorporate the settings heterogeneities in transit network design and schedule stochasticity in transit operations.
Under low demand, traditional fixed-route transit systems generally yield large route spacings, which exposes passengers to larger access distances. In such cases, flexible transit is an advantageous alternative as it provides door-to-door service to the users and eliminates the need for walking to and from the stations in addition to the agency investments associated with fixed stations. Transit agencies could provide flexible transit for operating environments such as “paratransit” (e.g., for elderlies and disable people who have trouble accessing the bus stations) or “safe ride”, or in unsafe and inconvenient conditions (e.g., at night, during adverse weather). This research aims at designing a hybrid grand structure for flexible transit, including a heterogeneous central grid and a hub-and-spoke system in the periphery. The model accounts for local demand variations and aims at providing high-level insights using continuum approximation (C.A.) to reduce the number of decision variables. For a hypothetical mono-centric demand distribution, the proposed system is shown to produce lower costs in terms of both agency investments and user costs, as compared to typical fixed- route and flexible-route homogenous grid networks. The proposed framework is also applied to a real-world case.
As reliability remains one of the main challenges of transit agencies, this research also investigates bunching mitigation strategies. Many approaches have been studied to tackle bus bunching. While holding strategies (e.g. slack, speed control) are widely used to mitigate the effects of unreliable bus schedules, most of them impose longer dwell times on the passengers. In this research, an alternative bus substitution strategy to prevent bus bunching is proposed. This strategy is currently implemented by some transit agencies in an ad-hoc manner; it deploys a fleet of standby buses to take over service from any early or late buses so as to contain deviations from schedule. The intention is to impose minimum penalties on the onboard passengers. This bus substitution strategy is appealing to transit agencies because it requires minimal hardware (e.g., GPS units and communications devices are already in place nowadays), it is extremely simple to implement, and it does not affect bus drivers’ driving behavior. It is particularly friendly to the onboard passengers as they do not get disrupted by any extra dwell time or transfers. We develop a discrete-time infinite-horizon approximate dynamic programming approach to find the optimal substitution policy to minimize the overall agency and passenger costs and compare our proposed method with the traditional slack method, and the dynamic speed control methods.
The bus substitution strategy is then extended to multiline systems. More specifically, the proposed strategy is designed under either homogeneous settings or time-varying settings. In the latter scenario, the fleet of standby buses can be dynamically utilized to save on opportunity costs. We model the agency’s substitution decisions and standby bus prepositioning decisions as a stochastic dynamic program so as to obtain the optimal policy that minimizes the system-wide costs. Numerous numerical examples are presented to illustrate the advantage and the applicability of the proposed strategy in the context of multiple bus lines. The substitution strategy not only holds the promise to outperform traditional holding methods in terms of reducing passenger costs, they can also be used to complement other methods to better control very unstable systems.
Finally, we develop a framework to optimize the prepositioning of the standby buses.
Standby buses need to be located near the transit lines so as to most efficiently perform substitutions while considering the costs of holding those resources at several parking locations. Standby locations are typically parking lots or on-street parking, which can potentially be fully occupied by regular vehicles, making those locations unavailable to standby buses. As such, the problem is modeled as a reliability facility location problem, where transit stops represent customers while parking locations are considered as facilities, and embedded into the dynamic substitution framework through an iterative process that successively estimate the need for substitution and the optimal location layout. A Lagrangian relaxation with branch and bound algorithm is used to solve the reliability location problem. A real-world example is presented to show the applicability of the proposed approach in realistic settings and provide insights to the local agency for the planning of its resources. Extensive sensitivity analysis are also conducted to examine several important problem parameters and to help reveal useful insights and facilitate decision-makings.