# An Experimental Comparison of Uncertainty Sets for Robust Shortest Path Problems

## TL;DR

This paper compares various uncertainty set assumptions for robust shortest path problems using real-world traffic data, evaluating their reasonableness and guiding future algorithmic development.

## Contribution

It empirically tests different uncertainty set models on real traffic data, linking theoretical assumptions to practical applicability.

## Key findings

- Certain uncertainty models better fit real traffic data.
- Some models lead to more conservative but reliable solutions.
- The study guides future research towards more realistic uncertainty modeling.

## Abstract

Through the development of efficient algorithms, data structures and preprocessing techniques, real-world shortest path problems in street networks are now very fast to solve. But in reality, the exact travel times along each arc in the network may not be known. This lead to the development of robust shortest path problems, where all possible arc travel times are contained in a so-called uncertainty set of possible outcomes. Research in robust shortest path problems typically assumes this set to be given, and provides complexity results as well as algorithms depending on its shape. However, what can actually be observed in real-world problems are only discrete raw data points. The shape of the uncertainty is already a modelling assumption. In this paper we test several of the most widely used assumptions on the uncertainty set using real-world traffic measurements provided by the City of Chicago. We calculate the resulting different robust solutions, and evaluate which uncertainty approach is actually reasonable for our data. This anchors theoretical research in a real-world application and allows us to point out which robust models should be the future focus of algorithmic development.