Abstract: Differentiated service is typically provided to customers by offering different grades of service at diﬀerent prices. We ﬁrst consider a simple system with heterogeneous customers that are type indexed by $v$. In this system, a customer chooses one of a continuum of service grades that the server provides. Higher service grades are priced higher by the server. Different customers value paying this price differently, which is described by an arbitrary weighting function that is decreasing in $v$. We show that at Nash equilibrium, the revenue to the service provider is independent of how the server chooses to price different service grades.
Next we consider a complex system where a customer has to choose two priority parameters instead of one in simple systems. The service provider uses complex scheduling to provide a grade of service that is a function of the two parameters; higher values of the parameters provide better service grades. The two priority parameters have different cost functions that are increasing in the value of the parameter. Further, the two parameters are weighted differently by different types of customers with one of them having weights increasing while the other decreasing in v. We analyze the Nash equilibrium when customers are selﬁsh in such a complex system and characterize the QoS for each customer type at Nash equilibrium. We then consider pricing the services to maximize the revenue for the service provider in an example system. Examples from diverse domains will show that the results are very general.