On the power of (even a little) flexibility in dynamic resource allocation

We study the role of partial flexibility in large-scale dynamic resource allocationproblems, in which multiple types of processing resources are used to serve multipletypes of incoming demands that arrive stochastically over time. Partial flexibilityrefers to scenarios where (a) only a small fraction of the total processing resourcesis flexible, or (b) each resource is capable of serving only a small number of demandtypes. Two main running themes are architecture and information: the former askshow a flexible system should be structured to fully harness the benefits of flexibility,and the latter looks into how information, across the system or from the future, maycritically influence performance.Overall, our results suggest that, with the right architecture, information, anddecision policies, large-scale systems with partial flexibility can often vastly outper-form their inflexible counterparts in terms of delay and capacity, and sometimes bealmost as good as fully flexible systems. Our main findings are:1. Flexible architectures. We show that, just like in fully flexible systems, a largecapacity region and a small delay can be achieved even with very limited flexi-bility, where each resource is capable of serving only a vanishingly small fractionof all demand types. However, the system architecture and scheduling policy need to be chosen more carefully compared to the case of a fully flexible system.(Chapters 3 and 4.)2. Future information in flexible systems. We show that delay performance in apartially flexible system can be significantly improved by having access to pre-dictive information about future inputs. When future information is sufficient,we provide an optimal scheduling policy under which delay stays bounded inheavy-traffic. Conversely, we show that as soon as future information becomesinsufficient, delay diverges to infinity under any policy. (Chapters 5 and 6.)3. Decentralized partial pooling. For the family of Partial Pooling flexible architec-tures, first proposed and analyzed by [84], we demonstrate that a decentralizedscheduling policy can achieve the same heavy-traffic delay scaling as an optimalcentralized longest-queue-first policy used in prior work. This demonstratesthat asymptotically optimal performance can be achieved in a partially flexiblesystem with little information sharing. Our finding, which makes use of a newtechnical result concerning the limiting distribution of an M/M/1 queue fed bya superposition of input processes, strengthens the result of [84], and providesa simpler line of analysis. (Chapter 7.) Thesis Supervisor: John N. TsitsiklisTitle: Clarence J. Lebel Professor of Electrical Engineering