Queueing system topologies with limited flexibility
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 flexibl...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Association for Computing Machinery (ACM)
2014
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| Online Access: | http://hdl.handle.net/1721.1/90978 https://orcid.org/0000-0003-2658-8239 |
| _version_ | 1826209100616171520 |
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| author | Tsitsiklis, John N. Xu, Kuang |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Tsitsiklis, John N. Xu, Kuang |
| author_sort | Tsitsiklis, John N. |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T14:17:16Z |
| format | Article |
| id | mit-1721.1/90978 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:17:16Z |
| publishDate | 2014 |
| publisher | Association for Computing Machinery (ACM) |
| record_format | dspace |
| spelling | mit-1721.1/909782022-09-28T19:46:21Z Queueing system topologies with limited flexibility Tsitsiklis, John N. Xu, Kuang Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Tsitsiklis, John N. Xu, Kuang 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. National Science Foundation (U.S.) (Grant CMMI-1234062) MIT-Xerox Fellowship Program 2014-10-20T13:09:43Z 2014-10-20T13:09:43Z 2013-06 Article http://purl.org/eprint/type/ConferencePaper 01635999 http://hdl.handle.net/1721.1/90978 John N. Tsitsiklis and Kuang Xu. 2013. Queueing system topologies with limited flexibility. SIGMETRICS Perform. Eval. Rev. 41, 1 (June 2013), 167-178. https://orcid.org/0000-0003-2658-8239 en_US http://dx.doi.org/10.1145/2494232.2465757 ACM SIGMETRICS Performance Evaluation Review Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Association for Computing Machinery (ACM) MIT web domain |
| spellingShingle | Tsitsiklis, John N. Xu, Kuang Queueing system topologies with limited flexibility |
| title | Queueing system topologies with limited flexibility |
| title_full | Queueing system topologies with limited flexibility |
| title_fullStr | Queueing system topologies with limited flexibility |
| title_full_unstemmed | Queueing system topologies with limited flexibility |
| title_short | Queueing system topologies with limited flexibility |
| title_sort | queueing system topologies with limited flexibility |
| url | http://hdl.handle.net/1721.1/90978 https://orcid.org/0000-0003-2658-8239 |
| work_keys_str_mv | AT tsitsiklisjohnn queueingsystemtopologieswithlimitedflexibility AT xukuang queueingsystemtopologieswithlimitedflexibility |