A Mathematical Model of Joint Congestion Control and Routing in Multisource Networks
Fern Y. Hunt, Vladimir V. Marbukh, Yi Wang
In this paper we study a model of joint congestion control and routing in a ring of network sources with a single destination at the center. A utility maximization problem subject to routing constraints is posed and nist-equations for its solution are presented. In the very symmetric situation where all sources have the same route allocation probabilities and the same link capacities we find conditions for convergence of a continuous approximation to these nist-equations and confirm convergence for the original nist-equations numerically. Despite the symmetry the sources do not always behave identically.
Proceedings of the 2011 IEEE Multiconference on Systems and Control