# Fluctuation Bounds for the Max-Weight Policy, with Applications to State Space Collapse

arXiv: https://arxiv.org/abs/1810.09180 · HTML: https://mlsanity.com/paper/1810.09180/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2018.

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

- [Learning and Information in Stochastic Networks and Queues](https://mlsanity.com/paper/2105.08769/) (2021)

## Abstract (arXiv)

We consider a multi-hop switched network operating under a Max-Weight (MW) scheduling policy, and show that the distance between the queue length process and a fluid solution remains bounded by a constant multiple of the deviation of the cumulative arrival process from its average. We then exploit this result to prove matching upper and lower bounds for the time scale over which additive state space collapse (SSC) takes place. This implies, as two special cases, an additive SSC result in diffusion scaling under non-Markovian arrivals and, for the case of i.i.d. arrivals, an additive SSC result over an exponential time scale.