A lower bound on the queueing delay in resource constrained load balancing
Name
1807.02882.pdf
Description
Submitted version
Size
357.72 KB
Format
Adobe PDF
Checksum (MD5)
2a5ad6cfcd5778f3b51dd4c9eafa1749
Author(s)
Gamarnik, David
Tsitsiklis, John N
Zubeldia, Martin
Date Issued
2020
Journal
Annals of Applied Probability
Publisher
Institute of Mathematical Statistics
Version
Original manuscript
Abstract
© 2020 Institute of Mathematical Statistics. All rights reserved. We consider the following distributed service model: Jobs with unit mean, general distribution, and independent processing times arrive as a renewal process of rate λn, 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 queueing delay in steadystate of a typical job to zero, as n increases. We develop a novel approach to show that, within a certain broad class of "symmetric" policies, every dispatching policy with a message rate of the order of n, and with a memory of the order of log n bits, results in an expected queueing delay which is bounded away from zero, uniformly as n→∞. This complements existing results which show that, in the absence of such limitations on the memory or the message rate, there exist policies with vanishing queueing delay (at least with Poisson arrivals and exponential service times).
MIT Department
Sloan School of Management
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1214/19-AAP1519
