Multiplicative feedback control in communication networks using stochastic flow models

We use stochastic flow models (SFMs) of communication networks with multiplicative feedback for the purpose of control and optimization (rather than performance analysis). Using infinitesimal perturbation analysis (IPA), we derive gradient estimators for loss and throughput related performance metrics with respect to a threshold (feedback range) parameter, i.e., feedback only takes place when the value of the state is above the threshold. The unbiasedness of these IPA estimators is also established. Combining this work with earlier results on the feedback gain parameter in H. Yu and C.G. Cassandras (2004), we consider an optimization problem to jointly determine the values of feedback gain and range parameters. We use a gradient-based stochastic approximation algorithm to solve the problem, where the gradient estimates are provided by IPA, and demonstrate the effectiveness of the algorithm through simulations.