Linear waste of best fit bin packing on skewed distributions

We prove that best-fit bin packing has linear waste on the discrete distribution U{j,k} (where items are drawn uniformly from the set {1/k, 2/k, ..., j/k}) for sufficiently large k when j=αk and 0.66⩽α<2/3. Our results extend to continuous skewed distributions, where items are drawn uniformly on [0,a], for 0.66⩽a<2/3. This implies that the expected asymptotic performance ratio of best-fit bin packing is strictly greater than 1 for these distributions