Transience of a Server with Greedy Strategy on the Real Line

Details Transience of a Server with Greedy Strategy on the Real Line Transience of a Server with Greedy Strategy on the Real Line

2011-11-21

arxiv.org/abs/1111.4846v3

Mathematics

Probability

Scientific paper

We consider a single-server system with 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 towards 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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