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May 2015 Greedy walk on the real line
Sergey Foss, Leonardo T. Rolla, Vladas Sidoravicius
Ann. Probab. 43(3): 1399-1418 (May 2015). DOI: 10.1214/13-AOP898

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.

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Sergey Foss. Leonardo T. Rolla. Vladas Sidoravicius. "Greedy walk on the real line." Ann. Probab. 43 (3) 1399 - 1418, May 2015. https://doi.org/10.1214/13-AOP898

Information

Published: May 2015
First available in Project Euclid: 5 May 2015

zbMATH: 1327.60176
MathSciNet: MR3342666
Digital Object Identifier: 10.1214/13-AOP898

Subjects:
Primary: 60K25, 60K35, 90B22

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 3 • May 2015
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