Optimal structured feedback control policies for rate-based flow control of available bit rate service in asynchronous transfer mode networks are obtained in the presence of information and propagation delays, using a numerically efficient two-timescale simultaneous perturbation stochastic approximation (SPSA) algorithm. Models comprising both a single bottleneck node and a network with multiple bottleneck nodes are considered. A convergence analysis of the algorithm is presented. Numerical experiments demonstrate fast convergence even in the presence of significant delays. We also illustrate performance comparisons with the well-known explicit rate indication for congestion avoidance (ERICA) algorithm and describe another algorithm (based on ERICA) that does not require estimating available bandwidth (as in ERICA).