Greedy walk on the real line
Probability
2015-05-25 v5
Abstract
We consider a self-interacting process described in terms of a single-server system with service stations at each point of the real line. The customer arrivals are given by a Poisson point processes on the space-time half plane. The server adopts a greedy routing mechanism, traveling toward the nearest customer, and ignoring new arrivals while in transit. We study the trajectories of the server and show that its asymptotic position diverges logarithmically in time.
Keywords
Cite
@article{arxiv.1111.4846,
title = {Greedy walk on the real line},
author = {Sergey Foss and Leonardo T. Rolla and Vladas Sidoravicius},
journal= {arXiv preprint arXiv:1111.4846},
year = {2015}
}
Comments
Published at http://dx.doi.org/10.1214/13-AOP898 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)