Infinitesimal Perturbation Analysis for Active Queue Management
Adams, Richelle Vive-Anne
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Active queue management (AQM) techniques for congestion control in Internet Protocol (IP) networks have been designed using both heuristic and analytical methods. But so far, there has been found no AQM scheme designed in the realm of stochastic optimization. Of the many options available in this arena, the gradient-based stochastic approximation method using Infintesimal Perturbation Analysis (IPA) gradient estimators within the Stochastic Fluid Model (SFM) framework is very promising. The research outlined in this thesis provides the theoretical basis and foundational layer for the development of IPA-based AQM schemes. Algorithms for computing the IPA gradient estimators for loss volume and queue workload were derived for the following cases: a single-stage queue with instantaneous, additive loss-feedback, a single-stage queue with instantaneous, additive loss-feedback and an unresponsive competing flow, a single-stage queue with delayed, additive loss-feedback, and a multi-stage tandem network of $m$ queues with instantaneous, additive loss-feedback. For all cases, the IPA gradient estimators were derived with the control parameter, $ heta$, being the buffer-limits of the queue(s). For the single-stage case and the multi-stage case with instantaneous, additive loss-feedback, the IPA gradient estimators for when the control parameter, $ heta$, is the loss-feedback constant, were also derived. Sensitivity analyses and optimizations were performed with control parameter, $ heta$, being the buffer-limits of the queue(s), as well as the loss-feedback constant.