The Annals of Probability

Greedy walk on the real line

Sergey Foss, Leonardo T. Rolla, and 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.

Article information

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

Dates
First available in Project Euclid: 5 May 2015

Permanent link to this document
https://projecteuclid.org/euclid.aop/1430830285

Digital Object Identifier
doi:10.1214/13-AOP898

Mathematical Reviews number (MathSciNet)
MR3342666

Zentralblatt MATH identifier
1327.60176

Subjects
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]

Keywords
Greedy policy self-interaction long-term behavior stability

Citation

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. https://projecteuclid.org/euclid.aop/1430830285


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