Optimal admission, routing and service assignment control: the case of single buffer queues

We consider the problem of optimal routing of arriving packets into N servers having no waiting room. Packets that are routed to a busy server are lost. We consider two problems where the objective is to maximize the expected throughput (or equivalently, minimize the loss rate). We assume that the controller has no information on the state of the server. We establish the optimality of the so called "balanced" policies, for exponential service times and general stationary arrival processes, which include, in particular, the interrupted Poisson process, Markov modulated Poisson Process and Markov arrival process. Based on this solution, we solve the dual problem of optimal assignment of a single server to several single server queues to which packets arrive according to Poisson processes. This general model is then applied to solve an optimal scheduling problem for robots of Web search engines.