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arXiv · 1111.4846

Greedy walk on the real line

Sergey Foss·Leonardo T. Rolla·Vladas Sidoravicius
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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. 2015-05-22. Greedy walk on the real line. https://doi.org/10.1214/13-aop898

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