That may have been done in the underlying paper by Mitzenmacher et al., but I haven't checked.
I'm more confident that that paper established that firing n requests at n servers will result in a max server load proportional to log(log(n)) with high probability, vs. proportional to log(n) for random -- IOW an exponential improvement in max server load over random.
I'm more confident that that paper established that firing n requests at n servers will result in a max server load proportional to log(log(n)) with high probability, vs. proportional to log(n) for random -- IOW an exponential improvement in max server load over random.