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Conventional approach to cross-layer network optimization assumes elastic users adjusting their bandwidth requirements in response to the resource congestion prices. This assumption leads to Network Utility Maximization (NUM) framework with Lagrange multipliers associated with resource capacity constraints playing role of the congestion prices. However, often users can more naturally quantify their preferences in terms of the rate and high-level Quality of Service (QoS) requirements rather thanfatcat:icihcsecujagdhypaoyckjno54