Self and social optimization in multi-class multi-server queueing systems with relative priorities

In this paper we show how the use of relative priorities can reduce queueing costs in queueing systems that are multi-server and multi-class as long as customers choose their routing policy strategically. This is demonstrated in two basic models with multi-class Poisson arrivals and parallel memoryless servers with linear cost functions of class expected mean waiting times. For each model we investigate the Nash equilibria under a given relative priority rule. Next, we characterize the central planner's optimal policy, which is shown to be of strictly relative priorities in some cases.