Stochastic on-time arrival problem in transit networks

This article considers the stochastic on-time arrival problem in transit networks where both the travel time and the waiting time for transit services are stochastic. A specific challenge of this problem is the combinatorial solution space due to the unknown ordering of transit line arrivals. We propose a network structure appropriate to the online decision-making of a passenger, including boarding, waiting and transferring. In this framework, we design a dynamic programming algorithm that is pseudo-polynomial in the number of transit stations and travel time budget, and exponential in the number of transit lines at a station, which is a small number in practice. To reduce the search space, we propose a definition of transit line dominance, and techniques to identify dominance, which decrease the computation time by up to 90% in numerical experiments. Extensive numerical experiments are conducted on both a synthetic network and the Chicago transit network.Comment: 29 pages; 12 figures. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0

Shareability Network Based Decomposition Approach for Solving Large-scale Multi-modal School Bus Routing Problems

We consider the classic School Bus Routing Problem (SBRP) with a multi modal generalization, where students are either picked up by a fleet of school buses or transported by an alternate transportation mode, subject to a set of constraints. The constraints that are typically imposed for school buses are a maximum fleet size, a maximum walking distance to a pickup point and a maximum commute time for each student. This is a special case of the Vehicle Routing Problem (VRP) with a common destination. We propose a decomposition approach for solving this problem based on the existing notion of a shareability network, which has been used recently in the context of dynamic ridepooling problems. Moreover, we simplify the problem by introducing the connection between the SBRP and the weighted set covering problem (WSCP). To scale this method to large-scale problem instances, we propose i) a node compression method for the shareability network based decomposition approach, and ii) heuristic-based edge compression techniques that perform well in practice. We show that the compressed problem leads to an Integer Linear Programming (ILP) of reduced dimensionality that can be solved efficiently using off-the-shelf ILP solvers. Numerical experiments on small-scale, large-scale and benchmark networks are used to evaluate the performance of our approach and compare it to existing large-scale SBRP solving techniques.Comment: 41 pages, 27 figure

Impacts of Covid-19 mode shift on road traffic

This article is driven by the following question: as the communities reopen after the COVID-19 pandemic, will changing transportation mode share lead to worse traffic than before? This question could be critical especially if many people rush to single occupancy vehicles. To this end, we estimate how congestion will increases as the number of cars increase on the road, and identify the most sensitive cites to drop in transit usage. Travel time and mode share data from the American Community Survey of the US Census Bureau, for metro areas across the US. A BPR model is used to relate average travel times to the estimated number of commuters traveling by car. We then evaluate increased vehicle volumes on the road if different portions of transit and car pool users switch to single-occupancy vehicles, and report the resulting travel time from the BPR model. The scenarios predict that cities with large transit ridership are at risk for extreme traffic unless transit systems can resume safe, high throughput operations quickly.Comment: 14 pages, 11 figure

Approximation Algorithms for Capacitated Assignment with Budget Constraints and Applications in Transportation Systems

In this article, we propose algorithms to address two critical transportation system problems: the Generalized Real-Time Line Planning Problem (GRLPP) and the Generalized Budgeted Multi-Visit Team Orienteering Problem (GBMTOP). The GRLPP aims to optimize high-capacity line plans for multimodal transportation networks to enhance connectivity between passengers and lines. The GBMTOP focuses on finding optimal routes for a team of heterogeneous vehicles within budget constraints to maximize the reward collected. We present two randomized approximation algorithms for the generalized budgeted multi-assignment problem (GBMAP), which arises when items need to be assigned to bins subject to capacity constraints, budget constraints, and other feasibility constraints. Each item can be assigned to at most a specified number of bins, and the goal is to maximize the total reward. GBMAP serves as the foundation for solving GRLPP and GBMTOP. In addition to these two algorithms, our contributions include the application of our framework to GRLPP and GBMTOP, along with corresponding models, numerical experiments, and improvements on prior work