The Annals of Probability

Greedy walk on the real line

Sergey Foss, Leonardo T. Rolla, and Vladas Sidoravicius

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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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Ann. Probab., Volume 43, Number 3 (2015), 1399-1418.

First available in Project Euclid: 5 May 2015

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Zentralblatt MATH identifier

Primary: 60K25: Queueing theory [See also 68M20, 90B22] 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 90B22: Queues and service [See also 60K25, 68M20]

Greedy policy self-interaction long-term behavior stability


Foss, Sergey; Rolla, Leonardo T.; Sidoravicius, Vladas. Greedy walk on the real line. Ann. Probab. 43 (2015), no. 3, 1399--1418. doi:10.1214/13-AOP898.

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