Measuring the Utility/Path Diversity Trade off in Multipath Protocols

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 loca- tions, each source s is assigned a route according to an allo- cation scheme where the degree of randomness and therefore path diversity is controlled by hs, the entropy of the distribu- tion defned 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 desti- nation 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.