Timetable regularity, that is, equability of headways, is an important measure for service quality in high frequency public transit systems, assuring an evenly distributed passenger load as well as improving product attractiveness. However, to be feasible during daily operation a timetable may also have to adhere to other planning requirements, such as departure time coordination with other service providers or deliberately short headways to reduce the passenger load of follow‐up vehicles. In this article, a disjunctive program formulation combining aspects of two previous optimization models is proposed, to generate regular public transit timetables adhering to planning requirements. The modeled requirements not only allow for the consideration of feasibility constraints from daily operations, but also for the consideration of simultaneous departures for transfer connections, an objective traditionally opposed to regularity. To show its applicability the approach is applied to two models of artificial transit networks as well as to models of the public transit network of Cologne, Germany. The results show that the proposed formulation can be used to generate timetables for network instances of realistic size in acceptable time. For networks consisting of multiple connected components it is shown that a decomposition approach can significantly reduce run times.
Operations Design of Modular Vehicles on an Oversaturated Corridor with First-in, First-out Passenger Queueing
Although urban transit systems (UTS) often have fixed vehicle capacity and relatively constant departure headways, they may need to accommodate dramatically fluctuating passenger demands over space and time, resulting in either excessive passenger waiting or vehicle capacity and energy waste. Therefore, on the one hand, optimal operations of UTS rely on accurate modeling of passenger queuing dynamics, which is particularly complex on a multistop transit corridor. On the other hand, capacities of transit vehicles can be made variable and adaptive to time-variant passenger demand so as to minimize energy waste, especially with the emergence of modular vehicle technologies. This paper investigates operations of a multistop transit corridor in which vehicles may have different capacities across dispatches. We specify skewed time coordinates to simplify the problem structure while incorporating traffic congestion. Then, we propose a mixed integer linear programming model that determines the optimal dynamic headways and vehicle capacities over the study time horizon to minimize the overall system cost for the transit corridor. In particular, the proposed model considers a realistic multistop first-in, first-out (MSFIFO) rule that gives the same boarding priority to passengers arriving at a station in the same time interval yet with different destinations. A customized dynamic programming (DP) algorithm is proposed to solve this model efficiently. To circumvent the rapid increase of the state space of a typical DP algorithm, we analyze the theoretical properties of the investigated problem and identify upper and lower bounds to a feasible solution. The bounds largely reduce the state space during the DP iterations and greatly improve the efficiency of the proposed DP algorithm. The state dimensions are also reduced with the MSFIFO rule such that all queues with different destinations at the same origin can be tracked with a single boarding position state variable at each stage. A hypothetical example and a real-world case study show that the proposed DP algorithm greatly outperforms a state-of-the-art commercial solver (Gurobi) in both solution quality and time.
more »
« less
- NSF-PAR ID:
- 10291911
- Date Published:
- Journal Name:
- Transportation Science
- ISSN:
- 0041-1655
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
more » « less
-
null (Ed.)Since passenger demand in urban transit systems is asymmetrically distributed across different periods in a day and different geographic locations across the cities, the tradeoff between vehicle operating costs and service quality has been a persistent problem in transit operational design. The emerging modular vehicle technology offers us a new perspective to solve this problem. Based on this concept, we propose a variable-capacity operation approach with modular transits for shared-use corridors, in which both dispatch headway and vehicle capacity are decision variables. This problem is rigorously formulated as a mixed integer linear programming model that aims to minimize the overall system cost, including passenger waiting time costs and vehicle operating costs. Because the proposed model is linear, the state-of-the-art commercial solvers (e.g., Gurobi) can be used to obtain the optimal solution of the investigated problem. With numerical experiments, we demonstrate the feasibility of the mathematical model, verify the effectiveness of the proposed model in reducing overall system costs in transit systems, as well as the robustness of the proposed model with different parameter settings.more » « less
-
The “asymmetry” between spatiotemporally varying passenger demand and fixed-capacity transportation supply has been a long-standing problem in urban mass transportation (UMT) systems around the world. The emerging modular autonomous vehicle (MAV) technology offers us an opportunity to close the substantial gap between passenger demand and vehicle capacity through station-wise docking and undocking operations. However, there still lacks an appropriate approach that can solve the operational design problem for UMT corridor systems with MAVs efficiently. To bridge this methodological gap, this paper proposes a continuum approximation (CA) model that can offer near-optimal solutions to the operational design for MAV-based transit corridors very efficiently. We investigate the theoretical properties of the optimal solutions to the investigated problem in a certain (yet not uncommon) case. These theoretical properties allow us to estimate the seat demand of each time neighborhood with the arrival demand curves, which recover the “local impact” property of the investigated problem. With the property, a CA model is properly formulated to decompose the original problem into a finite number of subproblems that can be analytically solved. A discretization heuristic is then proposed to convert the analytical solution from the CA model to feasible solutions to the original problem. With two sets of numerical experiments, we show that the proposed CA model can achieve near-optimal solutions (with gaps less than 4% for most cases) to the investigated problem in almost no time (less than 10 ms) for large-scale instances with a wide range of parameter settings (a commercial solver may even not obtain a feasible solution in several hours). The theoretical properties are verified, and managerial insights regarding how input parameters affect system performance are provided through these numerical results. Additionally, results also reveal that, although the CA model does not incorporate vehicle repositioning decisions, the timetabling decisions obtained by solving the CA model can be easily applied to obtain near-optimal repositioning decisions (with gaps less than 5% in most instances) very efficiently (within 10 ms). Thus, the proposed CA model provides a foundation for developing solution approaches for other problems (e.g., MAV repositioning) with more complex system operation constraints whose exact optimal solution can hardly be found with discrete modeling methods.more » « less
-
Extreme heat events induced by climate change present a growing risk to transit passenger comfort and health. To reduce exposure, agencies may consider changes to schedules that reduce headways on heavily trafficked bus routes serving vulnerable populations. This paper develops a schedule optimization model to minimize heat exposure and applies it to local bus services in Phoenix, Arizona, using agent-based simulation to inform travel demand and rider characteristics. Rerouting as little as 10% of a fleet is found to reduce network-wide exposure by as much as 35% when operating at maximum fleet capacity. Outcome improvements are notably characterized by diminishing returns, owing to skewed ridership and the inverse relationship between fleet size and passenger wait time. Access to spare vehicles can also ensure significant reductions in exposure, especially under the most extreme temperatures. Rerouting, therefore, presents a low-cost, adaptable resilience strategy to protect riders from extreme heat exposure.more » « less
-
Gørtz, Inge Li ; Farach-Colton, Martin ; Puglisi, Simon J. ; Herman, Grzegorz (Ed.)In this paper, we study efficient parallel edit distance algorithms, both in theory and in practice. Given two strings A[1..n] and B[1..m], and a set of operations allowed to edit the strings, the edit distance between A and B is the minimum number of operations required to transform A into B. In this paper, we use edit distance to refer to the Levenshtein distance, which allows for unit-cost single-character edits (insertions, deletions, substitutions). Sequentially, a standard Dynamic Programming (DP) algorithm solves edit distance with Θ(nm) cost. In many real-world applications, the strings to be compared are similar to each other and have small edit distances. To achieve highly practical implementations, we focus on output-sensitive parallel edit-distance algorithms, i.e., to achieve asymptotically better cost bounds than the standard Θ(nm) algorithm when the edit distance is small. We study four algorithms in the paper, including three algorithms based on Breadth-First Search (BFS), and one algorithm based on Divide-and-Conquer (DaC). Our BFS-based solution is based on the Landau-Vishkin algorithm. We implement three different data structures for the longest common prefix (LCP) queries needed in the algorithm: the classic solution using parallel suffix array, and two hash-based solutions proposed in this paper. Our DaC-based solution is inspired by the output-insensitive solution proposed by Apostolico et al., and we propose a non-trivial adaption to make it output-sensitive. All of the algorithms studied in this paper have good theoretical guarantees, and they achieve different tradeoffs between work (total number of operations), span (longest dependence chain in the computation), and space. We test and compare our algorithms on both synthetic data and real-world data, including DNA sequences, Wikipedia texts, GitHub repositories, etc. Our BFS-based algorithms outperform the existing parallel edit-distance implementation in ParlayLib in all test cases. On cases with fewer than 10⁵ edits, our algorithm can process input sequences of size 10⁹ in about ten seconds, while ParlayLib can only process sequences of sizes up to 10⁶ in the same amount of time. By comparing our algorithms, we also provide a better understanding of the choice of algorithms for different input patterns. We believe that our paper is the first systematic study in the theory and practice of parallel edit distance.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1287/trsc.2021.1074
