# Large Deviations Of Max-Weight Scheduling Policies

## Speaker:

Vijay Subramanian Hamilton Institute NUI Maynooth Co Kildare Ireland http://www.hamilton.ie/vsubramanian/

## Time:

Monday, 21 December 2009 (All day)

## Venue:

• A-212 (STCS Seminar Room)

We consider a single-server discrete-time system with $K$ users where the server picks operating points from a compact, convex and coordinate convex set in $\\Re_+^K$. For this system we analyse the performance of a stablising policy that at any given time picks operating points from the allowed rate region that maximise a weighted sum of rate, where the weights depend upon the workloads of the users. In particular, we are interested in a Large Deviations based analysis of this policy, and under both the large-buffer and many-sources regimes. The unifying theme of this work is to prove a Large Deviations Principle (LDP) for the queueing process using an appropriate generalization of the contraction principle, namely, Puhalskii's extended contraction principle and Garcia's extended contraction principle.