Pricing in multiservice loss networks: Static pricing, asymptotic optimality, and demand substitution effects

We consider a communication network with fixed routing that can accommodate multiple service classes, differing in bandwidth requirements, demand pattern, call duration, and routing. The network charges a fee per call which can depend on the current congestion level, and which affects user's demand. Building on the single-node results of Paschalidis and Tsitsiklis, 2000, we consider both problems of revenue and of welfare maximization, and show that static pricing is asymptotically optimal in a regime of many, relatively small, users. In particular, the performance of an optimal (dynamic) pricing strategy is closely matched by a suitably chosen class-dependent static price, which does not depend on instantaneous congestion. This result holds even when we incorporate demand substitution effects into the demand model. More specifically, we model the situation where price increases for a class of service might lead users to use another class as an imperfect substitute. For both revenue and welfare maximization objectives we characterize the structure of the asymptotically optimal static prices, expressing them as a function of a parsimonious number of parameters. We employ a simulation-based approach to tune those parameters and to efficiently compute an effective policy away from the limiting regime. Our approach can handle large, realistic, instances of the problem.