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December 2015 Randomized longest-queue-first scheduling for large-scale buffered systems
T. Suk
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Adv. in Appl. Probab. 47(4): 1015-1038 (December 2015). DOI: 10.1239/aap/1449859798


We develop diffusion approximations for parallel-queueing systems with the randomized longest-queue-first scheduling (LQF) algorithm by establishing new mean-field limit theorems as the number of buffers n → ∞. We achieve this by allowing the number of sampled buffers d = d(n) to depend on the number of buffers n, which yields an asymptotic 'decoupling' of the queue length processes. We show through simulation experiments that the resulting approximation is accurate even for moderate values of n and d(n). To the best of the authors' knowledge, this is the first derivation of diffusion approximations for a queueing system in the large-buffer mean-field regime. Another noteworthy feature of our scaling idea is that the randomized LQF algorithm emulates the LQF algorithm, yet is computationally more attractive. The analysis of the system performance as a function of d(n) is facilitated by the multi-scale nature in our limit theorems: the various processes we study have different space scalings. This allows us to show the trade-off between performance and complexity of the randomized LQF scheduling algorithm.


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T. Suk. "Randomized longest-queue-first scheduling for large-scale buffered systems." Adv. in Appl. Probab. 47 (4) 1015 - 1038, December 2015.


Published: December 2015
First available in Project Euclid: 11 December 2015

zbMATH: 1335.90015
MathSciNet: MR3433294
Digital Object Identifier: 10.1239/aap/1449859798

Primary: 90B22
Secondary: 90B36

Keywords: diffusion limit , fluid limit , mean-field , Queueing

Rights: Copyright © 2015 Applied Probability Trust


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Vol.47 • No. 4 • December 2015
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