Pure strategy asymmetric rendezvous on the line with an unknown initial distance

Suppose two blind agents with unit speed are placed a distance H apart on an infinite line, and faced in random directions. Their initial distance H is picked from a distribution F with finite mean μ. We present a pair of rendezvous strategies which do not depend on the distribution F and ensure a meeting in expected time less than 5.514μ. This improves the bound of 5.74μ given by Baston and Gal. Furthermore, the bound we give is best possible for strategies of our type.