Bertrand games between multi-class queues

We develop a framework to study differentiated services when there are competing network providers. We adopt a multi-class queueing model, where providers post prices for various service classes. Traffic is elastic and users are Quality of Service (QoS)-sensitive, and choose a queue and a class with one of the providers. We model the relationship between capacity, QoS and prices offered by service providers in a competitive network services market. We establish sufficient conditions for existence of Nash equilibrium in the multi-class queueing game.