# Dynamic Flows with Adaptive Route Choice

arXiv: https://arxiv.org/abs/1811.07381 · HTML: https://mlsanity.com/paper/1811.07381/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Nov 2018.

## Built on by (most cited first, 1 of 1)

- [Machine-Learned Prediction Equilibrium for Dynamic Traffic Assignment](https://mlsanity.com/paper/2109.06713/) (2021)

## Abstract (arXiv)

We study dynamic network flows and introduce a notion of instantaneous dynamic equilibrium (IDE) requiring that for any positive inflow into an edge, this edge must lie on a currently shortest path towards the respective sink. We measure current shortest path length by current waiting times in queues plus physical travel times. As our main results, we show: 1. existence and constructive computation of IDE flows for single-source single-sink networks assuming constant network inflow rates, 2. finite termination of IDE flows for multi-source single-sink networks assuming bounded and finitely lasting inflow rates, 3. the existence of IDE flows for multi-source multi-sink instances assuming general measurable network inflow rates, 4. the existence of a complex single-source multi-sink instance in which any IDE flow is caught in cycles and flow remains forever in the network.