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Randomized longest-queue-first scheduling for large-scale buffered systems

Part of: Operations research and management science

Published online by Cambridge University Press:  21 March 2016

A. B. Dieker  and
T. Suk
A. B. Dieker*
Affiliation:
Georgia Institute of Technology
T. Suk*
Affiliation:
Georgia Institute of Technology
*
∗ Postal address: H. Milton Stewart School of Industrial and System Engineering, Georgia Institute of Technology, 755 Ferst Drive, NW, Atlanta, GA 30332-0205, USA.
∗ Postal address: H. Milton Stewart School of Industrial and System Engineering, Georgia Institute of Technology, 755 Ferst Drive, NW, Atlanta, GA 30332-0205, USA.
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Abstract

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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.

Keywords

Queueingmean-fieldfluid limitdiffusion limit

MSC classification

Primary: 90B22: Queues and service
Secondary: 90B36: Scheduling theory, stochastic
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 47 , Issue 4 , December 2015 , pp. 1015 - 1038
Copyright
Copyright © Applied Probability Trust 2015 

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