The advantage of relative priority regimes in multi-class multi-server queueing systems with strategic customers

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