Data networks
Optimal incentive-compatible priority pricing for the M/M/1 queue
Operations Research
Competitive routing in multiuser communication networks
IEEE/ACM Transactions on Networking (TON)
Paris metro pricing for the internet
Proceedings of the 1st ACM conference on Electronic commerce
Proportional differentiated services: delay differentiation and packet scheduling
IEEE/ACM Transactions on Networking (TON)
Convex Optimization
Theory, Volume 1, Queueing Systems
Theory, Volume 1, Queueing Systems
Pricing Communication Networks: Economics, Technology and Modelling (Wiley Interscience Series in Systems and Optimization)
Recent developments in equilibria algorithms
WINE'05 Proceedings of the First international conference on Internet and Network Economics
Proportional differentiation: a scalable QoS approach
IEEE Communications Magazine
Architecting noncooperative networks
IEEE Journal on Selected Areas in Communications
IEEE Network: The Magazine of Global Internetworking
A survey of uniqueness results for selfish routing
NET-COOP'07 Proceedings of the 1st EuroFGI international conference on Network control and optimization
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Differentiated services architectures are scalable solutions for providing class-based Quality of Service (QoS) over packet switched networks. While qualitative attributes of the offered service classes are often well defined, the actual differentiation between classes is left as an open issue. We address here the proportional QoS model, which aims at maintaining pre-defined ratios between the service class delays (or related congestion measures). In particular, we consider capacity assignment among service classes as the means for attaining this design objective. Starting with a detailed analysis for the single hop model, we first obtain the required capacity assignment for fixed flow rates. We then analyze the scheme under a reactive scenario, in which self-optimizing users may choose their service class in response to capacity modifications. We demonstrate the existence and uniqueness of the equilibrium in which the required ratios are maintained, and address the efficient computation of the optimal capacities. We further provide dynamic schemes for capacity adjustment, and consider the incorporation of pricing and congestion control to enforce absolute performance bounds on top of the proportional ones. Finally, we extend our basic results to networks with general topology.