Greedy Walk on the Real Line

Sergey Foss, Leonardo T. Rolla, Vladas Sidoravicius

Published 2011-11-21, updated 2015-03-23Version 4

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 towards 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.