Using estimated entropy in a queueing system with dynamic routing

In this article we consider a discrete time two server queueing system with dynamic routing. We prove logarithmic asymptotics for the liklihood that a message from a source that divides its messages between the two servers in a way that minimizes the message’s waiting time experiences a large waiting time. We demonstrate the merit of this asymptotic by comparing its predictions with experimental data. We illustrate how estimated entropies of the traffic streams can be used to predict the likelihood of long waiting times and demonstrate the method’s accuracy through comparison with simulations.