Queueing system topologies with limited flexibility
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Tsitsiklis_Queueing system.pdf
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500.79 KB
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Author(s)
Tsitsiklis, John N.
Xu, Kuang
Date Issued
June 2013
Journal
ACM SIGMETRICS Performance Evaluation Review
Publisher
Association for Computing Machinery (ACM)
Citation
John N. Tsitsiklis and Kuang Xu. 2013. Queueing system topologies with limited flexibility. SIGMETRICS Perform. Eval. Rev. 41, 1 (June 2013), 167-178.
Version
Author's final manuscript
Abstract
We study a multi-server model with n flexible servers and rn queues, connected through a fixed bipartite graph, where the level of flexibility is captured by the average degree, d(n), of the queues. Applications in content replication in data centers, skill-based routing in call centers, and flexible supply chains are among our main motivations. We focus on the scaling regime where the system size n tends to infinity, while the overall traffic intensity stays fixed. We show that a large capacity region (robustness) and diminishing queueing delay (performance) are jointly achievable even under very limited flexibility (d(n) l n). In particular, when d(n) gg ln n , a family of random-graph-based interconnection topologies is (with high probability) capable of stabilizing all admissible arrival rate vectors (under a bounded support assumption), while simultaneously ensuring a diminishing queueing delay, of order ln n/ d(n), as n-> ∞. Our analysis is centered around a new class of virtual-queue-based scheduling policies that rely on dynamically constructed partial matchings on the connectivity graph.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1145/2494232.2465757
