Waiting time based routing policies to parallel queues with percentiles objectives

We develop a method to obtain near-optimal routing policies to parallel queues with decisions based on customers' wait and performance objectives which include percentiles of the waiting time. We formulate and explicitly derive a value function where the waiting time is used as a decision variable. This allows us to apply a one-step policy improvement method to obtain an efficient routing solution. Numerical illustrations reveal that classical monotone policies are not always optimal.