English

The geometry of big queues

Probability 2019-06-17 v2

Abstract

We use Hamilton equations to find optimal paths to big queues in Jackson networks. They are shown to be given by fluid trajectories of the dual network. The fluid equations are shown to be dual to the Hamilton equations. Thus, a version of the extended Onzager-Machlup principle is proved: a fluctuation trajectory is the time reversal of a relaxation trajectory of the dual dynamic. The case of a two-node network is given a geometric treatment.

Keywords

Cite

@article{arxiv.1811.09764,
  title  = {The geometry of big queues},
  author = {Anatolii Puhalskii},
  journal= {arXiv preprint arXiv:1811.09764},
  year   = {2019}
}

Comments

11 figures, in Russian

R2 v1 2026-06-23T05:26:16.880Z