Stochastic Trip Planning in High Dimensional Public Transit Network

TL;DR

This paper introduces a Gaussian Process-based framework for stochastic trip planning in large, high-dimensional public transit networks, enabling real-time, probabilistic shortest path estimation that improves travel time reliability.

Contribution

The study develops a scalable, online Gaussian Process model for density estimation of edge weights, significantly enhancing stochastic shortest path computation in large transit networks.

Findings

Achieves 30x faster algorithm runtime with maintained accuracy.

Demonstrates up to 40% travel time savings using stochastic paths.

Provides a real-time trip planning system for Delhi's transit network.

Abstract

This paper proposes a generalised framework for density estimation in large networks with measurable spatiotemporal variance in edge weights. We solve the stochastic shortest path problem for a large network by estimating the density of the edge weights in the network and analytically finding the distribution of a path. In this study, we employ Gaussian Processes to model the edge weights. This approach not only reduces the analytical complexity associated with computing the stochastic shortest path but also yields satisfactory performance. We also provide an online version of the model that yields a 30 times speedup in the algorithm's runtime while retaining equivalent performance. As an application of the model, we design a real-time trip planning system to find the stochastic shortest path between locations in the public transit network of Delhi. Our observations show that different paths have different likelihoods of being the shortest path at any given time in a public transit network. We demonstrate that choosing the stochastic shortest path over a deterministic shortest path leads to savings in travel time of up to 40\%. Thus, our model takes a significant step towards creating a reliable trip planner and increase the confidence of the general public in developing countries to take up public transit as a primary mode of transportation.