Stability of the Greedy Algorithm on the Circle
Probability
2018-09-10 v3
Abstract
We consider a single-server system with service stations in each point of the circle. Customers arrive after exponential times at uniformly-distributed locations. The server moves at finite speed and adopts a greedy routing mechanism. It was conjectured by Coffman and Gilbert in~1987 that the service rate exceeding the arrival rate is a sufficient condition for the system to be positive recurrent, for any value of the speed. In this paper we show that the conjecture holds true.
Cite
@article{arxiv.1112.2389,
title = {Stability of the Greedy Algorithm on the Circle},
author = {Leonardo T. Rolla and Vladas Sidoravicius},
journal= {arXiv preprint arXiv:1112.2389},
year = {2018}
}