Solving convex optimization with side constraints in a multi-class queue by adaptive cμ rule
We study convex optimization problems with side constraints in a multi-class M/G/1M/G/1 queue with controllable service rates. In the simplest problem of optimizing linear costs with fixed service rate, the cμ rule is known to be optimal. A natural question to ask is whether such simple policies e...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer US
2016
|
| Online Access: | http://hdl.handle.net/1721.1/104074 |
| _version_ | 1826204133430919168 |
|---|---|
| author | Li, Chih-ping Neely, Michael J. |
| author2 | Massachusetts Institute of Technology. Laboratory for Information and Decision Systems |
| author_facet | Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Li, Chih-ping Neely, Michael J. |
| author_sort | Li, Chih-ping |
| collection | MIT |
| description | We study convex optimization problems with side constraints in a multi-class M/G/1M/G/1 queue with controllable service rates. In the simplest problem of optimizing linear costs with fixed service rate, the cμ rule is known to be optimal. A natural question to ask is whether such simple policies exist for more complex control objectives. In this paper, combining the achievable region approach in queueing systems and the Lyapunov drift theory suitable to optimize renewal systems with time-average constraints, we show that convex optimization problems can be solved by variants of adaptive cμcμ rules. These policies greedily re-prioritize job classes at the end of busy periods in response to past observed delays in each job class. Our method transforms the original problems into a new set of queue stability problems, and the adaptive cμ rules are queue stable policies. An attractive feature of the adaptive cμ rules is that they use limited statistics of the queue, where no statistics are required for the problem of satisfying average queueing delay in each job class. |
| first_indexed | 2024-09-23T12:49:25Z |
| format | Article |
| id | mit-1721.1/104074 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T12:49:25Z |
| publishDate | 2016 |
| publisher | Springer US |
| record_format | dspace |
| spelling | mit-1721.1/1040742022-10-01T11:21:11Z Solving convex optimization with side constraints in a multi-class queue by adaptive cμ rule Li, Chih-ping Neely, Michael J. Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Li, Chih-ping We study convex optimization problems with side constraints in a multi-class M/G/1M/G/1 queue with controllable service rates. In the simplest problem of optimizing linear costs with fixed service rate, the cμ rule is known to be optimal. A natural question to ask is whether such simple policies exist for more complex control objectives. In this paper, combining the achievable region approach in queueing systems and the Lyapunov drift theory suitable to optimize renewal systems with time-average constraints, we show that convex optimization problems can be solved by variants of adaptive cμcμ rules. These policies greedily re-prioritize job classes at the end of busy periods in response to past observed delays in each job class. Our method transforms the original problems into a new set of queue stability problems, and the adaptive cμ rules are queue stable policies. An attractive feature of the adaptive cμ rules is that they use limited statistics of the queue, where no statistics are required for the problem of satisfying average queueing delay in each job class. Network Science Collaborative Technology Alliance (United States. Army Research Laboratory W911NF-09-2-0053) National Science Foundation (U.S.). (Career grant CCF-0747525) 2016-08-30T19:45:26Z 2016-08-30T19:45:26Z 2013-10 2012-11 2016-05-23T12:16:02Z Article http://purl.org/eprint/type/JournalArticle 0257-0130 1572-9443 http://hdl.handle.net/1721.1/104074 Li, Chih-ping, and Michael J. Neely. “Solving Convex Optimization with Side Constraints in a Multi-Class Queue by Adaptive $$c\mu $$ c μ Rule.” Queueing Systems 77.3 (2014): 331–372. en http://dx.doi.org/10.1007/s11134-013-9377-3 Queueing Systems Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Springer Science+Business Media New York application/pdf Springer US Springer US |
| spellingShingle | Li, Chih-ping Neely, Michael J. Solving convex optimization with side constraints in a multi-class queue by adaptive cμ rule |
| title | Solving convex optimization with side constraints in a multi-class queue by adaptive cμ rule |
| title_full | Solving convex optimization with side constraints in a multi-class queue by adaptive cμ rule |
| title_fullStr | Solving convex optimization with side constraints in a multi-class queue by adaptive cμ rule |
| title_full_unstemmed | Solving convex optimization with side constraints in a multi-class queue by adaptive cμ rule |
| title_short | Solving convex optimization with side constraints in a multi-class queue by adaptive cμ rule |
| title_sort | solving convex optimization with side constraints in a multi class queue by adaptive cμ rule |
| url | http://hdl.handle.net/1721.1/104074 |
| work_keys_str_mv | AT lichihping solvingconvexoptimizationwithsideconstraintsinamulticlassqueuebyadaptivecmrule AT neelymichaelj solvingconvexoptimizationwithsideconstraintsinamulticlassqueuebyadaptivecmrule |