Delay, Memory, and Messaging Tradeoffs in Distributed Service Systems
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Gamarnik_Delay, memory.pdf
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Author(s)
Gamarnik, David
Tsitsiklis, John N
Zubeldia Suarez, Martin
Date Issued
June 2016
Journal
Proceedings of the 2016 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Science - SIGMETRICS '16
Publisher
Association for Computing Machinery (ACM)
Citation
Gamarnik, David; Tsitsiklis, John N. and Zubeldia, Martin. “Delay, Memory, and Messaging Tradeoffs in Distributed Service Systems.” Proceedings of the 2016 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Science, June 14-18 2016, Antibes Juan-les-Pins, France, Association for Computing Machinery, June 2016. © 2016 The Authors
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Author's final manuscript
Abstract
We consider the following distributed service model: jobs with unit mean, exponentially distributed, and independent processing times arrive as a Poisson process of rate λ N, with 0<λ<1, and are immediately dispatched to one of several queues associated with N identical servers with unit processing rate. We assume that the dispatching decisions are made by a central dispatcher endowed with a finite memory, and with the ability to exchange messages with the servers. We study the fundamental resource requirements (memory bits and message exchange rate), in order to drive the expected steady-state queueing delay of a typical job to zero, as N increases. We propose a certain policy and establish (using a fluid limit approach) that it drives the delay to zero when either (i) the message rate grows superlinearly with N, or (ii) the memory grows superlogarithmically with N. Moreover, we show that any policy that has a certain symmetry property, and for which neither condition (i) or (ii) holds, results in an expected queueing delay which is bounded away from zero.
Finally, using the fluid limit approach once more, we show that for any given α>0 (no matter how small), if the policy only uses a linear message rate α N, the resulting asymptotic (as N->∞) expected queueing delay is positive but upper bounded, uniformly over all λ>1. This is a significant improvement over the popular "power-of-d-choices" policy, which has a limiting expected delay that grows as log ←(1/(1-λ)→) when λ↑ 1.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Sloan School of Management
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DOI of Published Version
https://doi.org/10.1145/2896377.2901478
