25-07-2017 11:00  Graduate Seminar

Control, Optimization, and Diffusion Limits for Queuing Systems

This work is concerned with control and optimization problems for queuing systems in heavy traffic. First we study a multiclass G/G/1 queue with reneging. We formulate a control problem where cost is associated with holding and reneging, present a Brownian Control Problem that arises in the diffusion limit, its reduction to a 1-dimensional problem and its connection to a one-dimensional Bellman equation. We show how a policy is derived from the Bellman equation, and that it is asymptotically optimal. This policy is based on dynamic priority. It performs better than the well-known c rule as well as the c/? rule. The second system consists of a G/G/1 queue with finite buffer and retrials. We present two results on this model. The first is the identification of a degenerate diffusion with oblique reflection, that corresponds to the weak scaling limit. The second is an optimization over the buffer size, to minimize a natural cost. The main observation here is a reduction to a one dimensional problem when the retrial parameter goes to zero or infinity. This is accompanied by a corresponding asymptotic optimality result.

Location: 861
Speaker: Anat Lev-Ari
Affiliation: Dept. of Electrical Engineering Technion Back