Rendezvous Search on the Line With Distinguishable Players

Authors:
Steve Alpern;Shmuel Gal
Affiliations:
-;-
Venue:
SIAM Journal on Control and Optimization
Year:
1995

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Abstract

Two players are placed on the real line at a distance $d$ with a distribution $F$ known to both. Neither knows the direction of the other, nor do they have a common notion of a positive direction on the line. We seek the least expected rendezvous time $R=R\left(F\right)$ in which they can meet, given maximum speeds of one. We consider the cases where $F$ is a bounded, point, discrete, or finite mean distribution. We obtain upper bounds or exact values for $R$ and in one case an optimality condition for search strategies. A connection with Beck's linear search problem is established.