Rendezvous Search on the Line with Limited Resources: Maximizing the Probability of Meeting
Steve Alpern, Anatole Beck · Operations Research · 1999
Two players are placed on a line at a distance dwhich is drawn from a known distribution F. The players have no common notion of direction on the line, and each has a resources bound on the total distance he can travel. If Fis bounded and the resources are sufficiently large, then the players can ensure a meeting. The expected time minimization problem in that case has been studied by the authors in a previous paper. Aside from that case the most the players can do is maximize the probability that they meet. This is the problem studied here, for general and specific distributions. This problem generalizes that of Foley et al. (1991), where one of the players is stationary (zero resources).