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 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.