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

Abstract

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 Þnite.

An adaptive framework for addressing fairness issues in wireless networks

“…We describe below a fairly simplified version of a Theorem appearing in Ref. [4] which is sufficient for our discussion and avoids several of the complicating technical issues that may arise in specific applications. In Section 5 we indicate cases where the more general version is needed.…”

“…A fairly general one can be found in Ref. [4,Section 3.2] which we restate in Appendix C so that we can refer to it in the discussion below. In this section we examine some of the assumptions made in the previous sections and discuss the manner that may be weakened.…”

“…For example, in Ref. [4,Section 3.2], it was sufficient to make certain assumptions on the moments of the input parameters for the system under consideration.…”

“…In Ref. [4,Section 3.2], it was shown for the corresponding system that is sufficient to make updates so that no more that 2L regeneration points occur between two updates, where L is any fixed number. The proof of this requires the full power of the theorem in Appendix C, and is using the fact that the policy is of index type.…”

“…The method presented in this paper can address more general utility optimization problems. It has been employed successfully to the solution of specific control problems related to scheduling jobs in multi-class queueing systems [4] and recently to downlink scheduling in wireless communications [19], for the system considered in Ref. [5].…”