This paper studies the quality of service (QoS) provision problem in noncooperative networks where applications or users are selfish and routers implement generalized processor sharing based packet scheduling. We formulate a model of QoS provision in noncooperative networks where users are given the freedom to choose both the service classes and traffic volume allocated, and heterogenous QoS preferences are captured by a user's utility function. We present a comprehensive analysis of the noncooperative multi-class QoS provision game, giving a complete characterization of Nash equilibria and their existence criteria, and show under what conditions they are Pareto and system optimal. We show that, in general, Nash equilibria need not exist, and when they do exist, they need not be Pareto nor system optimal. For certain "resource-plentiful" systems, however, we show that the world indeed can be nice with Nash equilibria, Pareto optima, and system optima collapsing into a single class. We study the problem of facilitating effective QoS in systems with multi-dimensional QoS vectors containing both mean-and burstiness-related QoS measures. We extend the game-theoretic analysis to multi-dimensional QoS vector games and show under what conditions the aforementioned results carry over.
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