# Flows over time in time-varying networks

arXiv: https://arxiv.org/abs/1401.6053 · HTML: https://mlsanity.com/paper/1401.6053/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2014.

## Built on by (most cited first, 2 of 2)

- [Generalized Schr"odinger Bridge on Graphs](https://mlsanity.com/paper/2602.04675/) (2026)
- [Congestion Reduction in EV Charger Placement Using Traffic Equilibrium Models](https://mlsanity.com/paper/2512.12081/) (2025)

## Abstract (arXiv)

There has been much research on network flows over time due to their important role in real world applications. This has led to many results, but the more challenging continuous time model still lacks some of the key concepts and techniques that are the cornerstones of static network flows. The aim of this paper is to advance the state of the art for dynamic network flows by developing the continuous time analogues of the theory for static network flows. Specifically, we make use of ideas from the static case to establish a reduced cost optimality condition, a negative cycle optimality condition, and a strong duality result for a very general class of network flows over time.