TCP and explicit congestion notification
ACM SIGCOMM Computer Communication Review
The complexity of approximating a nonlinear program
Mathematical Programming: Series A and B
Optimization flow control—I: basic algorithm and convergence
IEEE/ACM Transactions on Networking (TON)
Fair end-to-end window-based congestion control
IEEE/ACM Transactions on Networking (TON)
The Mathematics of Internet Congestion Control (Systems and Control: Foundations and Applications)
The Mathematics of Internet Congestion Control (Systems and Control: Foundations and Applications)
Efficiency Loss in a Network Resource Allocation Game
Mathematics of Operations Research
Congestion control for high performance, stability, and fairness in general networks
IEEE/ACM Transactions on Networking (TON)
Selfish Routing and the Price of Anarchy
Selfish Routing and the Price of Anarchy
Non-convex optimization and rate control for multi-class services in the Internet
IEEE/ACM Transactions on Networking (TON)
Priority Pricing in Utility Fair Networks
ICNP '05 Proceedings of the 13TH IEEE International Conference on Network Protocols
A distributed utility max-min flow control algorithm
Computer Networks: The International Journal of Computer and Telecommunications Networking
Counter-intuitive throughput behaviors in networks under end-to-end control
IEEE/ACM Transactions on Networking (TON)
Delay-independent stability and performance of distributed congestion control
IEEE/ACM Transactions on Networking (TON)
Heterogeneous Congestion Control: Efficiency, Fairness and Design
ICNP '06 Proceedings of the Proceedings of the 2006 IEEE International Conference on Network Protocols
Utility proportional fair bandwidth allocation: an optimization oriented approach
QoS-IP'05 Proceedings of the Third international conference on Quality of Service in Multiservice IP Networks
Fundamental design issues for the future Internet
IEEE Journal on Selected Areas in Communications
IEEE Network: The Magazine of Global Internetworking
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This paper deals with a congestion control framework for elastic and real-time traffic, where the user's application is associated with a utility function. We allow users to have concave as well as non-concave utility functions, and aim at allocating bandwidth such that utility values are shared fairly. To achieve this, we transform all utilities into strictly concave second order utilities and interpret the resource allocation problem as the global optimization problem of maximizing aggregate second order utility. We propose a new fairness criterion, utility proportional fairness, which is characterized by the unique solution to this problem. Our fairness criterion incorporates utility max-min fairness as a limiting case. Based on our analysis, we obtain congestion control laws at links and sources that (i) are linearly stable regardless of the network topology, provided that a bound on round-trip-times is known, (ii) provide a utility proportional fair resource allocation in equilibrium. We further investigate the efficiency of utility fair resource allocations. Our measure of efficiency is defined as the worst case ratio of the total utility of a utility proportional fair rate vector and the maximum possible total utility. We present a generic technique, which allows to obtain upper bounds on the efficiency loss. For special cases, such as linear and concave utility functions, and non-concave utility functions with bounded domain, we explicitly calculate such upper bounds. Then, we study utility fair resource allocations with respect to bandwidth fairness. We derive a fairness metric assessing the aggressiveness of utility functions. This allows us to design fair utility functions for various applications. Finally, we simulate the proposed algorithms using the NS2 simulator.