|
|
MIT Electrical Engineering and Computer Science
EECS Event |
Thursday, November 1, 2001
4:00 PM (reception following)
Room 35-225
LIDS Colloquium
Abstract
Although variability in a queueing system may have significant impact on performance, variability often plays a minor role in relative performance in network models, when comparing two candidate policies for network control. In this seminar we explores this idea, and provide some answers to the following related questions:
(i) It is known that an understanding of variability is important in the determination of safety stocks to prevent unwanted idleness. Is this the only use of high-order statistical information in policy synthesis?
(ii) Will a translation of an optimal policy for the deterministic fluid model (in which there is no variability) lead in general to an allocation which is approximately optimal for the stochastic network? If so, what is the 'regret'?
(iii) Where are the highest sources of sensitivity in network control?
The approach taken is based on the analyisis of various 'workload relaxations' of the network model of interest. This provides a tool for comparing stochastic network models, and models that include no variability.
Provided the optimal solution for the deterministic model is unique, and has pointwise-minimal workload-trajectories, there is nearly perfect solidarity between the deterministic and stochastic optimal control solutions.
If the optimal deterministic solution is not non-idling, then the discrepency between the control solutions is significant. The optimal policies are defined by switching curves in either model, The gap between these curves grows exactly linearly with increasing variability. However, second-order sensitivity to policy structure vanishes with increased variability, so computation of the precise policy in a stochastic model has vanishing practical significance.
Many of these results together with background material may be found at
http://black1.csl.uiuc.edu/~meyn/pages/ColumbiaLectures.pdf