On load balancing equilibria in multiqueue systems with multiclass traffic

We consider a queueing system with two non identical FCFS servers together serving two classes of customers. All customers have i.i.d service requirements. One of the queues may charge an admission price, say c. Arrivals are randomly routed to one of the servers and the routing probabilities are determined centrally to optimise a global objective, or from a local mechanism minimising a local-class or individual-objective. Our interest is to analyse the use of c to achieve a target distribution of loads among the servers. We first analyse the structure of the optimal allocation and then consider (1) a system with a dispatcher for each class, (2) a non atomic system, and (3) a system where one of the classes has a dispatcher.