MPI-I-97-1-023

We consider the on-line problem of call admission and routing on trees and meshes. Previous work considered randomized algorithms and analyzed the {\em competitive ratio} of the algorithms. However, these previous algorithms could obtain very low profit with high probability. We investigate the question if it is possible to devise on-line competitive algorithms for these problems that would guarantee a ``good'' solution with ``good'' probability. We give a new family of randomized algorithms with provably optimal (up to constant factors) competitive ratios, and provably good probability to get a profit close to the expectation. We also give lower bounds that show bounds on how high the probability of such algorithms, to get a profit close to the expectation, can be. We also see this work as a first step towards understanding how well can the profit of an competitively-optimal randomized on-line algorithm be concentrated around its expectation.