User equilibria in heterogeneous discriminatory processor sharing queues

We consider a strategic routing game for a two-class discriminatory processor-sharing queue with an additional cost for joining the premium class. We show that, depending on the specific parameters of the system, various equilibria can coexist, including equilibria where the queueing system is not ergodic for the equilibrium traffic split. We also investigate how the server can select the priority of the classes and the fees charged to the customers to maximise its revenue. We then investigate learning strategies that converge to particular equilibria. Finally, we study how the elasticity of the traffic demand affects the equilibrium solutions.