[Paper Review] A New Formulation of The Shortest Path Problem with On-Time Arrival Reliability

Georgi Andonov, Bin Yang|arXiv (Cornell University)|Apr 20, 2018

Transportation Planning and Optimization12 references3 citations

TL;DR

This paper proposes a novel formulation of the shortest path with on-time arrival reliability (SPOTAR) problem in the path-centric uncertain road network model (PACE), which captures travel time dependencies among edges via path-level uncertainty. The authors develop a generic algorithm with heuristic speed-ups that outperforms baseline methods in runtime and search space size while maintaining accuracy, demonstrating that PACE enables more reliable path selection without sacrificing efficiency on real GPS trajectory data from Aalborg, Denmark.

ABSTRACT

We study stochastic routing in the PAth-CEntric (PACE) uncertain road network model. In the PACE model, uncertain travel times are associated with not only edges but also some paths. The uncertain travel times associated with paths are able to well capture the travel time dependency among different edges. This significantly improves the accuracy of travel time distribution estimations for arbitrary paths, which is a fundamental functionality in stochastic routing, compared to classic uncertain road network models where uncertain travel times are associated with only edges. We investigate a new formulation of the shortest path with on-time arrival reliability (SPOTAR) problem under the PACE model. Given a source, a destination, and a travel time budget, the SPOTAR problem aims at finding a path that maximizes the on-time arrival probability. We develop a generic algorithm with different speed-up strategies to solve the SPOTAR problem under the PACE model. Empirical studies with substantial GPS trajectory data offer insight into the design properties of the proposed algorithm and confirm that the algorithm is effective. This report extends the paper "Stochastic Shortest Path Finding in Path-Centric Uncertain Road Networks", to appear in IEEE MDM 2018, by providing a concrete running example of the studied SPOTAR problem in the PACE model and additional statistics of the used GPS trajectories in the experiments.

Motivation & Objective

• To address the limitations of edge-centric models in capturing travel time dependencies among road segments.
• To formulate the SPOTAR problem within the PACE model, where path-level travel time distributions reflect edge dependencies.
• To design and evaluate a generic algorithm with heuristic speed-ups for solving SPOTAR under the PACE model.
• To empirically validate the algorithm’s efficiency and accuracy using real-world GPS trajectory data from Aalborg, Denmark.
• To demonstrate that PACE enables better on-time arrival reliability than traditional edge-centric models without increased computational cost.

Proposed method

• The PACE model assigns uncertain travel times not only to edges but also to selected paths, enabling joint distributions that capture inter-edge travel time dependencies.
• The SPOTAR problem is formulated as finding a source-destination path that maximizes the probability of arrival within a given time budget.
• A generic search algorithm is proposed, enhanced with two heuristic functions: shortest path tree (SP) and Euclidean distance divided by max speed (BA).
• The SP heuristic computes a lower bound on travel time, while the BA heuristic provides a more optimistic but less accurate estimate.
• The algorithm explores the search space using these heuristics to guide path expansion, with pruning based on time budget constraints.
• Experiments use real GPS trajectories (37M records) to instantiate PACE model, with uncovered edges estimated using speed limits.

Experimental results

Research questions

• RQ1 Can the PACE model improve on-time arrival reliability estimation compared to edge-centric models by capturing inter-edge travel time dependencies?
• RQ2 How does the performance of the SPOTAR algorithm vary under different heuristic functions (SP vs. BA) in the PACE model?
• RQ3 Does the PACE model incur significantly higher computational cost than the edge-centric model despite its enhanced accuracy?
• RQ4 How do path distributions and search space sizes differ between PACE and edge-centric models under varying source-destination distances and time budgets?
• RQ5 To what extent do the paths selected by PACE differ from those selected by edge-centric models in real-world GPS data?

Key findings

• The SP heuristic significantly reduces runtime and search space size compared to the BA heuristic across all settings and models.
• The SP+PACE method achieves the best performance, with substantially smaller search spaces and faster runtimes than BA+PACE and BA+EDGE.
• Runtime growth under the BA heuristic is much steeper than under the SP heuristic as source-destination distance increases.
• The PACE model does not incur higher runtime than the edge-centric model; both models show similar runtime performance under the same heuristic.
• The paths returned by PACE differ from those by the edge-centric model, indicating that path-level uncertainty modeling leads to different and potentially more reliable route choices.
• Visual analysis confirms that SP explores far fewer edges than BA, and the PACE path is distinct from the EDGE path, validating the impact of improved modeling.