Electronic Communications in Probability

A note on non-existence of diffusion limits for serve-the-longest-queue when the buffers are equal in size

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.

Article information

Source
Electron. Commun. Probab., Volume 21 (2016), paper no. 2, 10 pp.

Dates
Accepted: 4 January 2016
First available in Project Euclid: 3 February 2016

https://projecteuclid.org/euclid.ecp/1454514622

Digital Object Identifier
doi:10.1214/16-ECP4370

Mathematical Reviews number (MathSciNet)
MR3485371

Zentralblatt MATH identifier
1338.60096

Citation

Atar, Rami; Saha, Subhamay. A note on non-existence of diffusion limits for serve-the-longest-queue when the buffers are equal in size. Electron. Commun. Probab. 21 (2016), paper no. 2, 10 pp. doi:10.1214/16-ECP4370. https://projecteuclid.org/euclid.ecp/1454514622

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