  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.
