Solving convex optimization with side constraints in a multi-class queue by adaptive cμ rule
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11134_2013_9377_ReferencePDF.pdf
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Author(s)
Li, Chih-ping
Neely, Michael J.
Date Issued
October 2013
Journal
Queueing Systems
Publisher
Springer US
Citation
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.
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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DOI of Published Version
https://doi.org/10.1007/s11134-013-9377-3
