On the Pathwise Optimal Bernoulli Routing Policy for Homogeneous Parallel Servers

A long-standing conjecture on the optimal Bernoulli routing policy is proven to be true. For the case of equal exponential service times it is shown that splitting equally among the queues minimizes the departure times in a stochastic pathwise sense. A new technique is used, showing that certain distributional properties related to Schur convexity propagate forward in time.