Electronic Communications in Probability

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

Rami Atar and Subhamay Saha

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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

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

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

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Zentralblatt MATH identifier

Primary: 60F17: Functional limit theorems; invariance principles 60J60: Diffusion processes [See also 58J65] 60K25: Queueing theory [See also 68M20, 90B22]

diffusion limits Halfin-Whitt regime serve-the-longest queue heavy-traffic

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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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