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2016 A note on non-existence of diffusion limits for serve-the-longest-queue when the buffers are equal in size
Rami Atar, Subhamay Saha
Electron. Commun. Probab. 21: 1-10 (2016). DOI: 10.1214/16-ECP4370

Abstract

We consider the serve-the-longest-queue discipline for a multiclass queue with buffers of equal size, operating under (i) the conventional and (ii) the Halfin-Whitt heavy traffic regimes, and show that while the queue length process’ scaling limits are fully determined by the first and second order data in case (i), they depend on finer properties in case (ii). The proof of the latter relies on the construction of a deterministic arrival pattern.

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Rami Atar. Subhamay Saha. "A note on non-existence of diffusion limits for serve-the-longest-queue when the buffers are equal in size." Electron. Commun. Probab. 21 1 - 10, 2016. https://doi.org/10.1214/16-ECP4370

Information

Received: 16 June 2015; Accepted: 4 January 2016; Published: 2016
First available in Project Euclid: 3 February 2016

zbMATH: 1338.60096
MathSciNet: MR3485371
Digital Object Identifier: 10.1214/16-ECP4370

Subjects:
Primary: 60F17, 60J60, 60K25

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