A tight bound on the speed-up through storage for quickest multi-commodity flows

TL;DR

This paper investigates the maximum possible speed-up in multi-commodity flows over time due to storage, establishing that the speed-up factor can approach the previously known upper bound of 2.

Contribution

The authors construct a family of instances demonstrating that the speed-up factor through storage can asymptotically reach the upper bound of 2, closing the gap in prior bounds.

Findings

Speed-up factor can approach 2 in multi-commodity flows over time.

Previous bounds of 2 are tight, as shown by constructed instances.

Storage can significantly improve flow efficiency in specific scenarios.

Abstract

Multi-commodity flows over time exhibit the non-intuitive property that letting flow wait can allow us to send flow faster overall. Fleischer and Skutella (IPCO~2002) show that the speed-up through storage is at most a factor of~$2$, and that there are instances where the speed-up is as large as a factor of~$4/3$. We close this gap by presenting a family of instances for which the speed-up factor through storage converges to~$2$.