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April 2020 A lower bound on the queueing delay in resource constrained load balancing
David Gamarnik, John N. Tsitsiklis, Martin Zubeldia
Ann. Appl. Probab. 30(2): 870-901 (April 2020). DOI: 10.1214/19-AAP1519


We consider the following distributed service model: jobs with unit mean, general distribution, and independent processing times arrive as a renewal process of rate $\lambda n$, with $0<\lambda <1$, 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 steady-state 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\to \infty $. 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).


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David Gamarnik. John N. Tsitsiklis. Martin Zubeldia. "A lower bound on the queueing delay in resource constrained load balancing." Ann. Appl. Probab. 30 (2) 870 - 901, April 2020.


Received: 1 July 2018; Revised: 1 May 2019; Published: April 2020
First available in Project Euclid: 8 June 2020

zbMATH: 07236137
MathSciNet: MR4108125
Digital Object Identifier: 10.1214/19-AAP1519

Primary: 60G99

Keywords: load balancing , queueing delay , resource constraints

Rights: Copyright © 2020 Institute of Mathematical Statistics


Vol.30 • No. 2 • April 2020
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