Two point one sided rendezvous

In a rendezvous search two or more teams called seekers try to minimize the time needed to find each other. In this paper, we consider two seekers in the plane. This is a one sided problem since Seeker 1 begins at a predetermined point O  . Seeker 2 begins at one of a finite set of points xixi with probability pipi. We first discuss the general situation and then consider the specific case when Seeker 2 can begin from one of two points.