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February 2015 Necessary condition for null controllability in many-server heavy traffic
Gennady Shaikhet
Ann. Appl. Probab. 25(1): 406-428 (February 2015). DOI: 10.1214/13-AAP1001

Abstract

Throughput sub-optimality (TSO), introduced in Atar and Shaikhet [Ann. Appl. Probab. 19 (2009) 521–555] for static fluid models of parallel queueing networks, corresponds to the existence of a resource allocation, under which the total service rate becomes greater than the total arrival rate. As shown in Atar, Mandelbaum and Shaikhet [Ann. Appl. Probab. 16 (2006) 1764–1804] and Atar and Shaikhet (2009), in the many server Halfin–Whitt regime, TSO implies null controllability (NC), the existence of a routing policy under which, for every finite $T$, the measure of the set of times prior to $T$, at which at least one customer is in the buffer, converges to zero in probability at the scaling limit. The present paper investigates the question whether the converse relation is also true and TSO is both sufficient and necessary for the NC behavior.

In what follows we do get the affirmation for systems with either two customer classes (and possibly more service pools) or vice-versa and state a condition on the underlying static fluid model that allows the extension of the result to general structures.

Citation

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Gennady Shaikhet. "Necessary condition for null controllability in many-server heavy traffic." Ann. Appl. Probab. 25 (1) 406 - 428, February 2015. https://doi.org/10.1214/13-AAP1001

Information

Published: February 2015
First available in Project Euclid: 16 December 2014

zbMATH: 1311.60108
MathSciNet: MR3297777
Digital Object Identifier: 10.1214/13-AAP1001

Subjects:
Primary: 60F05, 60K25, 68M20, 90B22, 90B36

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.25 • No. 1 • February 2015
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