We consider in this paper a set of connections sharing a common bottleneck link. We assume first that we have data transfer using TCP congestion control protocol and real-time traffic using some TCP-friendly transport protocol that satisfies the same square-root formula for throughput. The performance measures are determined according to the operational parameters of a RED buffer management. Those parameters are assumed to be able to give differentiated services to the applications according to their choice of service class. In terms of loss probabilities and of throughputs, we consider a best effort type of service differentiation where the QoS of connections is not guaranteed, but by choosing a better (more expensive) service class, the QoS parameters of a session can be improved (as long as that session is the only one to change its service class). We assume however, that the system is dimensioned so as to satisfy some average delay requirement. The choice of a service class of an application will depend both on the utility as well as on the cost it has to pay. We first study the performance of each traffic source as a function of the connections' parameters and the pricing policy of the network. We then study the Stackelberg equilibrium, i.e. the service provider's problem of how to choose the pricing so as to maximize its utility, taking into account the reaction of the users.