Problems of Adaptive Optimization In Multiclass M/GI/1 Queues with Bernoulli Feedback

Adaptive algorithms are obtained for the solution of separable optimization problems in multiclass M/GI/1 queues with Bernoulli feedback. Optimality of the algorithms is established by modifying and extending methods of stochastic approximation. These algorithms, can be used as a basis for designing policies for semi-separable and approximate lexicographic optimization problems and in the case of M/GI/1 queues without feedback, they also provide a simple policy for lexicographic optimization. The results obtained on stochastic approximation imply convergence of classical recursions such as Robbins-Monroe in cases where the conditional second moment of their increments is not finite.