The mathematics of nonlinear programming
The mathematics of nonlinear programming
Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Optimization flow control—I: basic algorithm and convergence
IEEE/ACM Transactions on Networking (TON)
Convex Optimization
Stability of end-to-end algorithms for joint routing and rate control
ACM SIGCOMM Computer Communication Review
Cross-layer optimization in TCP/IP networks
IEEE/ACM Transactions on Networking (TON)
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
On the Connection-Level Stability of Congestion-Controlled Communication Networks
IEEE Transactions on Information Theory
Towards Robust Multi-Layer Traffic Engineering: Optimization of Congestion Control and Routing
IEEE Journal on Selected Areas in Communications
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We derive a model of congestion control where the trade-off between utility and path diversity can be investigated. In a network where there can be multiple routes between locations, each source s is assigned a route according to an allocation scheme where the degree of randomness and therefore path diversity is controlled by hs, the entropy of the distribution defined by the allocation. Model equations are derived from a network utility maximization problem and the results of the analysis of two networks with a single source destination are presented. We conclude for each such network there is a critical value of hs for which stable equilibrium solutions of the model equations exist and using the results of [9] it can be shown that they are also solutions of the original optimization problem. Treating hs as a parameter, the trade-off is discussed in terms of the behavior of the time averaged utility as a function of hs.