Heavy Traffic Queue Length Behavior in a Switch Under the MaxWeight Algorithm
Published Online:14 Nov 2016https://doi.org/10.1287/15-SSY193
References
- , “Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks,” IEEE Transactions on Automatic Control, vol. 37, no. 12, pp. 1936–1948, 1992. MR1200609Google Scholar
- , “Achieving 100% throughput in an input queued switch,” in Proceedings of IEEE INFOCOM, 1996, pp. 296–302.Google Scholar
- , “Maxweight scheduling in a generalized switch: State space collapse and workload minimization in heavy traffic,” Annals of Applied Probability, pp. 1–53, 2004. MR2023015Google Scholar
- , “Stability of the max-weight routing and scheduling protocol in dynamic networks and at critical loads,” in Proceedings of the Thirty-ninth Annual ACM Symposium on Theory of Computing, ser. STOC ’07, 2007, pp. 145–154. MR2402438Google Scholar
- , “Switched networks with maximum weight policies: Fluid approximation and multiplicative state space collapse,” The Annals of Applied Probability, vol. 22, no. 1, pp. 70–127, 2012. MR2932543Google Scholar
- , “Diffusion approximation for an input-queued packet switch operating under a maximum weight algorithm,” Stochastic Systems, 2012.Google Scholar
- , “Asymptotically tight steady-state queue length bounds implied by drift conditions,” Queueing Systems, vol. 72, no. 3–4, pp. 311–359, 2012. MR2989493Google Scholar
- , “Brownian models of open queueing networks with homogeneous customer populations,” Stochastics, vol. 22, no. 2, pp. 77–115, 1987. MR0912049Google Scholar
- , “State space collapse and diffusion approximation for a network operating under a fair bandwidth sharing policy,” The Annals of Applied Probability, pp. 1719–1780, 2009. MR2569806Google Scholar
- , “On optimal scheduling algorithms for small generalized switches,” IEEE/ACM Transactions on Networking, vol. 18, no. 5, pp. 1585–1598, 2010.Google Scholar
- , “Optimal scaling of average queue sizes in an input-queued switch: an open problem,” Queueing Systems, vol. 68, no. 3–4, pp. 375–384, 2011. MR2834209Google Scholar
- , “Logarithmic delay for n × n packet switches under the crossbar constraint,” IEEE/ACM Transactions on Networking, vol. 15, no. 3, pp. 657–668, 2007.Google Scholar
- , “Optimal queue-size scaling in switched networks,” Ann. Appl. Probab., vol. 24, no. 6, pp. 2207–2245, 12 2014. MR3262502Google Scholar
- , “On queue-size scaling for input-queued switches,” 2014, arxiv. MR3161642Google Scholar
- , Communication Networks: An Optimization, Control and Stochastic Networks Perspective. Cambridge University Press, 2014. MR3202391Google Scholar
- , “Polytopes,” Lecture Notes, http://www.ms.uky.edu/~readdy/Papers/readdy_WAM_lectures.pdf.Google Scholar
- , Lectures on Polytopes, ser. Graduate Texts in Mathematics. Springer New York, 1995. MR1311028Google Scholar
- , Convex Optimization & Euclidean Distance Geometry. Meboo Publishing, 2005.Google Scholar
- , “Hitting-time and occupation-time bounds implied by drift analysis with applications,” Advances in Applied Probability, pp. 502–525, 1982. MR0665291Google Scholar
- , “Performance of multiclass Markovian queueing networks via piecewise linear Lyapunov functions,” Ann. Appl. Probab., vol. 11, no. 4, pp. 1384–1428, 11 2001. MR1878302Google Scholar
- , Course project, ECE 567 Communication Network Analysis, Fall 2012, University of Illinois at Urbana Champaign.Google Scholar
- , “Maxweight scheduling: Asymptotic behavior of unscaled queue-differentials in heavy traffic,” arXiv preprint arXiv:1502.03793, 2015.Google Scholar
- , Combinatorial Optimization: Polyhedra and Efficiency, ser. Algorithms and Combinatorics. Springer, 2003, v. 24.Google Scholar
- , “Stable scheduling policies for fading wireless channels,” IEEE/ACM Trans. Network., vol. 13, no. 2, pp. 411–424, 2005.Google Scholar
- , Advanced Combinatorics: The Art of Finite and Infinite Expansions. Springer Netherlands, 1974. MR0460128Google Scholar

