A probabilistic constrained nonlinear optimization framework to optimize RED parameters

The random early detection (RED) technique has seen a lot of research over the years. However, the functional relationship between RED performance and its parameters viz., queue weight (wq), marking probability (maxp), minimum threshold (minth) and maximum threshold (maxth) is not analytically available. Moreover, the precise dependence between the RED average queue length and its parameters is not well understood. In this paper, we formulate a probabilistic constrained optimization problem by assuming a nonlinear relationship between the RED average queue length and its parameters. This problem involves all the RED-parameters as the variables of the optimization problem. We use the barrier and the penalty function approaches for its solution. However (as above), the exact functional relationship between the barrier and penalty objective functions and the optimization variable is not known but noisy samples of these are available for different parameter values. Thus, for obtaining the gradient and Hessian of the objective, we use certain recently developed simultaneous perturbation stochastic approximation (SPSA) based estimates of these. We propose two four-timescale stochastic approximation algorithms based on certain modified second order SPSA updates for finding the optimum RED parameters. We present the results of detailed simulation experiments conducted over different network topologies and network/traffic conditions/settings, comparing the performance of our algorithms with variants of RED and a few other well known adaptive queue management (AQM) techniques discussed in the literature.