This study proposes three mathematical programming models with distinct optimization objectives for transfer optimization in a bi-modal public transport network. To improve the applicability of the models and expedite the solution process, some acceleration techniques, including eliminating redundant constraints and incorporating valid inequalities, are suggested. The models and solution methods are applied to a small toy network and a real-life bi-modal public transport network. The results indicate that compared to the third model, the second model can reduce the total transfer waiting time by 12.29% to 30.31%, while the longest transfer waiting time may increase by 4.35% to 22.22%. Furthermore, the third model, which prioritizes minimizing the longest transfer waiting time, may increase the total or average transfer waiting time. The results suggest that decision-makers need to make a trade-off between reducing total passenger transfer waiting time (for efficiency) and reducing the longest passenger transfer waiting time (for fairness). .

To facilitate the shift from conventional to electric buses, the required charging infrastructure must be deployed. This study models the charging station location selection problem for fixed-line public transport services consisting of electric buses. The model considers the deadheading time of electric buses between the final stop of their trip and the locations of the potential charging stations with the objective of minimizing vehicle running costs. The problem is solved at a strategic level; therefore, several parameters of day-to-day operations, such as deadheading distances, are included as aggregate data considering their average values. In addition, it considers different charger types (slow and fast), which are subject to a day-ahead scheduling of the charging sessions of the buses. The developed model is a mixed-integer nonlinear program, which is reformulated as a mixed-integer linear program and can be solved efficiently for large networks with more than 1940 bus trips and 336 charging installation options. The model is applied in the Athens metropolitan area, demonstrating its potential as a decision support tool for selecting charging station locations and charger types in large public transport networks.

Transfer optimization in public transport (PT) networks can be achieved through coordinated timetabling and vehicle scheduling. Traditionally, the coordinated timetabling problem is solved first before proceeding to the vehicle scheduling problem. The integration of these two problems can help further reduce the total operation cost and improve the level of service, especially when timetables of different PT lines are well-coordinated at transfer stations. This work addresses the integrated PT timetable coordination and vehicle scheduling problem while ensuring that each PT line is dispatched with an even headway. We first separately formulate two integer linear programming models for the timetable coordination and vehicle scheduling problems. Next, the two models are integrated into a bi-objective integer linear programming model for the integrated timetable coordination and vehicle scheduling problem. For small size PT networks, the model can be solved by using an ɛ-constraint method, together with off-the-shelf optimization solvers. For large-size problems, two constraint-reduction procedures are developed to reduce the number of redundant constraints so as to reduce the computation complexity and improve the solution process. Finally, the models and solution method are applied to a numerical example and a real-world bus rapid transit (BRT) network in Chengdu, China. Computation results show that the solution generated by the sequential optimization approach is usually dominated by the Pareto-optimal solutions generated by the integrated optimization approach. Our findings suggest that it is not a wise decision to use the solution generated by the sequential optimization approach or the solution with the minimum fleet size generated by the integrated optimization approach. For practical implementation, it is recommended to choose the solution that has a fleet size of one more vehicle than the minimum fleet size.

The trips of a high-frequency urban rail line are typically planned with the aim of achieving even time headways. This results in reliable services for each urban rail line, where successive trips have the same time headway. Maintaining even time headways for each service line has significant advantages for the passengers of the line, but it might result in safety issues, vehicle bunching, and increased transfer times at a common corridor served by multiple urban rail lines. This study investigates the problem of urban rail corridor coordination and develops an exact optimization method for coordinating the vehicle trips of different lines that serve stations along a joint corridor. The proposed formulation is a non-convex mathematical program which is reformulated as a mixed-integer quadratic program with a convex objective function. A branch-and-bound algorithm coupled with the Active-set method is proposed for solving the model to global optimality. Results from a toy network and a case study of the light rail service in The Hague, The Netherlands, demonstrate the improvement potential of time headways at a common corridor, while accounting for the effect on the variation of time headways at isolated segments of the individual service lines.

A transit network design frequency setting model is proposed to cope with the postpandemic passenger demand. The multiobjective transit network design and frequency setting problem (TNDFSP) seeks to find optimal routes and their associated frequencies to operate public transport services in an urban area. The objective is to redesign the public transport network to minimize passenger costs without incurring massive changes to its former composition. The proposed TNDFSP model includes a route generation algorithm (RGA) that generates newlines in addition to the existing lines to serve the most demanding trips, and passenger assignment (PA) and frequency setting (FS) mixed-integer programming models that distribute the demand through the modified bus network and set the optimal number of buses for each line. Computational experiments were conducted on a test network and the network comprising the Royal Borough of Kensington and Chelsea in London.

We perform a systematic review of real-time control strategies for transfer synchronisations in public transport. In particular, we review inter-station and intra-station control measures that can be applied in near real-time, including vehicle holding, stop-skipping, speed control, short-turning, rescheduling, interlining, rerouting, and boarding limits. The topic of public transfer synchronisation at the operational phase is both a technically challenging and timely topic. It is technically challenging because finding optimal control measures is a computationally intensive problem and these measures should be computed in near real-time. It is also timely because of the emerging developments in shared mobility, Mobility-as-a-Service schemes, on-demand public transport, and vehicle automation that pose new opportunities as well as challenges in designing seamless passenger transfers. In our systematic review, we analyse the modelling approaches for real-time transfer synchronisation, including mathematical programmes, heuristics, rule-based approaches, and stochastic optimisation models. We then critically discuss the available literature and provide a future outlook, outlining six research directions.

Public transport is one of the most disrupted sectors of the COVID-19 pandemic with reported ridership drops up to 90% in majorly affected countries. As many government authorities strive to partially resume activities, public transport operators are in an urgent need for models that can evaluate the impact of different social distancing policies on operational and passenger-related costs. In this study, we introduce a mixed-integer quadratic programming model for the redesign of public transport services considering the operational, passenger, and revenue loss-related costs by evaluating the effects of different social distancing policies. Our model is applied at the metro network of Washington DC and provides optimal redistribution of vehicles across lines for different social distancing scenarios. This model can be used as a decision support tool by other policymakers and public transport operators that are in need of evaluating the costs related to the implementation of different social distancing policies.

In this literature review, we systematically review studies on public transit control with a specific focus on at-stop measures. In our synthesis of the relevant literature, we consider three perspectives: (1) the mathematical models of the proposed methodologies; (2) their complexity; (3) their applicability in real-time operations and their advantages and disadvantages considering their practical implications. The reviewed control methods include holding, dynamic dispatching, and stop-skipping. Control methods, that have attracted more attention in recent years due to the advancements in automation and data availability, aim at alleviating the negative effects of service variability because of external disruptions. Following the synthesis of the literature, we propose a research agenda pertaining to the combination of control measures, passenger-oriented decision making, coordinated network control, deployment of electric buses and disturbance management.

This study proposes an exact model for timetable recovery after disturbances in the context of high-frequency public transport services. The objective of our model is the minimization of the deviation between the actual headway and the respective planned value. The resulting mathematical program for the rescheduling problem is nonlinear and non-smooth; thus, it cannot be solved to optimality. To rectify this, we reformulate the model using slack variables. The reformulated model can be solved to global optimality in real-time with quadratic programming. We apply the model to real data from the red metro line in Washington D.C. in a series of experiments. In our experiments, we investigate how many upstream trips should be rescheduled to respond to a service disturbance. Our findings demonstrate an improvement potential of service regularity of up to 30% if we reschedule the five upstream trips of a disturbed train.

The COVID-19 pandemic crisis has greatly impacted public transport ridership and service provision across the world. As many countries start to navigate their return to normality, new public transport planning requirements are devised. These measures imply a major reduction in service capacity compared to the pre-COVID-19 era. At the time of writing, there is a severe lack of knowledge regarding the potential impact of the pandemic on public transport operations and models that can support the service planning given these new challenges. In this literature review, we systematically review and synthesise the literature on the impacts of COVID on public transport to identify the need to adjust planning measures, and, on the other hand, the existing methods for public transport planning at the strategic, tactical and operational level. We identify intervention measures that can support public transport service providers in planning their services in the post-shutdown phase and their respective modelling development requirements. This can support the transition from the initial ad-hoc planning practices to a more evidence-based decision making.

Travel time and demand disturbances lead to unreliable bus operations and missed passenger transfers. This study formulates the multi-line synchronization problem as a robust min(i)max problem that considers the fluctuations of the travel and dwell times of bus trips. Given the infeasibility of the multi-line synchronization problem in extreme cases of travel/dwell time disturbances, we introduce a flexible problem formulation that incorporates the constraint violations into the objective function. To produce a robust schedule, the dispatching times of trips are our design variables and the travel and dwell time fluctuations are the environmental variables which have an adversarial role in our minimax problem. We validate our approach in the bus network of The Hague using 1 month of actual vehicle location and passenger counting data. There, we demonstrate the potential improvement in terms of service regularity and increased synchronizations in common case and extreme case conditions.

This work proposes a periodic bus holding control method where the bus holding times of all running trips are computed simultaneously within each optimization time period; thus, increasing the coordination among running buses for avoiding bus bunching. This paper considers the adverse effects of the bus holding control in the in-vehicle travel times of on-board passengers and performs holistic bus holding decisions by modelling the bus holding problem as a discrete, nonlinear, constrained optimization problem. Given the computational complexity of the bus holding problem, an alternating minimization approach is introduced for computing the optimal holding times at each optimization instance. The performance of the periodic control method is evaluated against the performance of event-based control methods using 5-month automated vehicle location and automated passenger count data from bus line 1 in Stockholm for contacting simulation-based experiments.