Rahul Singh
ABSTRACT
The model is a "generalized switch", serving multiple traffic flows in discrete time. The switch uses MaxWeight algorithm to make a service decision (scheduling choice) at each time step, which determines the probability distribution of the amount of service that will be provided. We are primarily motivated by the following question: in the heavy traffic regime, when the switch load approaches critical level, will the service processes provided to each flow remain "smooth" (i.e., without large gaps in service)? Addressing this question reduces to the analysis of the asymptotic behavior of the unscaled queue-differential process in heavy traffic. We prove that the stationary regime of this process converges to that of a positive recurrent Markov chain, whose structure we explicitly describe. This in turn implies asymptotic "smoothness" of the service processes.
- M. Andrews, K. Kumaran, K. Ramanan, A. L. Stolyar, R. Vijayakumar, P. Whiting. Providing Quality of Service over a Shared Wireless Link. IEEE Communications Magazine, 2001, Vol.39, No. 2, pp. 150--154. Google Scholar
Digital Library
- M. Andrews, K. Jung, A. L. Stolyar. Stabilityof the Max-Weight Routing and Scheduling Protocol in Dynamic Networks and at Critical Loads. STOC'07, San Diego, CA, June 11-13, 2007. Google ScholarDigital Library
- A. Eryilmaz and R. Srikant. Asymptotically Tight Steady-State Queue Length Bounds Implied by Drift Conditions. Queueing Systems, 2012, Vol. 72, No.3--4, pp .311--359. Google ScholarDigital Library
- B. Hajek. Hitting-Time and Occupation-Time Bounds Implied by Drift Analysis with Applications. Advances in Applied Probability, 1982, Vol. 14, No. 3, pp. 502--525.Google ScholarCross Ref
- I-H. Hou, V. Borkar and P.R. Kumar. A Theory of QoS for Wireless. INFOCOM 2009.Google ScholarCross Ref
- R. Li, A. Eryilmaz, B. Li. Throughput-Optimal Wireless Scheduling with Regulated Inter-Service Times. INFOCOM 2013.Google Scholar
- B. Li, R. Li, A. Eryilmaz. Heavy-Traffic-Optimal Scheduling with Regular Service Guarantees in Wireless Networks. MobiHoc 2013. Google ScholarDigital Library
- S. P. Meyn and R.L. Tweedie. Stability of Markovian Processes I: Criteria for Discrete-Time chains. Advances in Applied Probability, 1992, Vol. 24, No. 3,pp. 542--574.Google ScholarCross Ref
- A.L. Stolyar.Max Weight Scheduling in a Generalized Switch: State Space Collapse and Workload Minimization in Heavy Traffic. Annals of Applied Probability, 2004, Vol. 14, No. 1, pp. 1--53.Google ScholarCross Ref
- L. Tassiulas, E. Ephremides. Stability properties of constrained queueingsystems and scheduling policies for maximum throughput in multihop radio networks. IEEE Trans. Automat. Control, 1992, Vol. 37, No. 1, pp. 1936-1948.Google ScholarCross Ref
- J. Ni, B. Tan and R. Srikant. Q-CSMA: Queue-Length Based CSMA/CA Algorithms for Achieving Maximum Throughput and Low Delay in Wireless Networks. INFOCOM 2010. Google ScholarDigital Library
- R. Singh and A. Stolyar. MaxWeight Scheduling: Asymptotic Behavior of Unscaled Queue-Differentials in Heavy Traffic. http://arxiv.org/abs/1502.03793Google Scholar
Index Terms
- MaxWeight Scheduling: Asymptotic Behavior of Unscaled Queue-Differentials in Heavy Traffic
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