Greedy walk on the real line

Serguei Foss, Leonardo T. Rolla, Vladas Sidoravicius

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We consider a self-interacting process described in terms of a singleserver 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.

Original languageEnglish
Pages (from-to)1399-1418
Number of pages20
JournalAnnals of Probability
Volume43
Issue number3
DOIs
Publication statusPublished - 2015

Keywords

  • Greedy policy
  • Long-term behavior
  • Self-interaction
  • Stability

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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    Foss, S., Rolla, L. T., & Sidoravicius, V. (2015). Greedy walk on the real line. Annals of Probability, 43(3), 1399-1418. https://doi.org/10.1214/13-AOP898