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Seminar_20230531

Stability Properties of Proportional fairness and the MaxWeight Policy

5/31/23 | 3:30pm | MHL 452

Dr. Neil Walton, Professor

Durham University Business School

Abstract: We present results on the stability of MaxWeight and Proportional Fairness, both of which are policies that are readily employed in the analysis of communications systems. MaxWeight is a greedy policy that does not depend on knowledge of arrival rates and is straightforward to implement. We prove that MaxWeight itself is not in general maximally stable in networks where jobs move between queues. We prove MaxWeight is maximally stable in a more restrictive setting, and that a weighted version of MaxWeight, where the weighting depends on the traffic intensity, is always stable. We introduce a scheduling policy for FIFO networks, the Proportional Scheduler, which is based on the proportional fairness criterion. We show that the Proportional Scheduler has a maximal stability region and does not require explicit knowledge of traffic arrival rates. The Proportional Scheduler has the advantage that information about the network’s route structure is not required for scheduling, which substantially improves the policy’s performance for large networks. Based on joint work with Maury Bramson and Bernardo D’Auria.

Bio: Neil Walton is a Professor in Operations Management at Durham University Business School. He received his undergraduate (’05), Masters (’06) and PhD (’10) in Mathematics at the University of Cambridge. His research is in applied probability and principally concerns the decentralized minimization of congestion in networks. He was a lecturer at University of Amsterdam where he held an NWO Veni Fellowship. He then moved to the University of Manchester where was a Reader in Mathematics. Neil has conducted research visits at Microsoft Research Cambridge, the Basque Centre for Mathematics and the Automatic Control Laboratory ETH Zurich. From 2017 to 2019 Neil was the head of probability and statistics group at the University of Manchester. Neil was a Fellow of the Alan Turing Institute and a guest lecturer at London Business School. He has an honorary position at the Manchester University NHS Foundation Trust. Here he is using queueing theory to reduce the waiting list backlog from the covid pandemic.  In Durham, he is Deputy Head of the Department of Management and Marketing. He is an associate editor at the journal Stochastic Systems. He is an area editor for stochastic models at Operations Research. He has won best papers awards at the ACM Sigmetrics conference and he was awarded the 2018 Erlang Prize by the Informs Applied Probability Society. 

Event Time and Venue: May 31, 2023-3:30pm, MHL 452

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