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.
- Greedy policy
- Long-term behavior
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty