Large deviations of max-weight scheduling policies on convex rate regions

2008 Information Theory and Applications Workshop - Conference Proceedings, ITA

Volumn , Issue , 2008, Pages 535-544

  Subramanian, Vijay G ^a  

^a NATIONAL UNIVERSITY OF IRELAND   (Ireland)

Author keywords

[No Author keywords available]

Indexed keywords

CYBERNETICS; DIGITAL CONTROL SYSTEMS; DISCRETE TIME CONTROL SYSTEMS; INFORMATION THEORY; SET THEORY;

CONVEX SETS; DISCRETE-TIME SYSTEMS; LARGE DEVIATIONS; OPERATING POINTS; RATE FUNCTIONS; SCHEDULING POLICIES; SINGLE SERVERS; WEIGHTED-SUM;

COMPUTATIONAL FLUID DYNAMICS;

EID: 52949143127     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ITA.2008.4601080     Document Type: Conference Paper

References (34)

1. T. M. Cover and J. A. Thomas, Elements of information theory, 2nd ed. Hoboken, NJ: Wiley-Interscience [John Wiley & Sons], 2006.
2. L. Tassiulas and A. Ephremides, "Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks," IEEE Transactions on Automatic Control, vol. 37, pp. 1936-1948, 1992.
3. N. McKeown, A. Mekkittikul, V. Anantharam, and J. Walrand, "Achieving 100% throughput in an input-queued switch," IEEE Trans. on Comm., vol. 47, no. 8, pp. 1260-1267, Aug. 1999.
4. M. Andrews, K. K. Kumaran, K. Ramanan, A. L. Stolyar, R. Vijayakumar, and R Whiting, "Scheduling in a queueing system with asynchronously varying service rates," Probability in Engineering and Informational Sciences, vol. 18, no. 2, pp. 191-217, 2004.
5. H. Chen and D. D. Yao, Fundamentals of Queueing Networks. Springer, New York, 2001.
6. S. Foss and T. Konstantopoulos, "An overview of some stochastic stability methods," Journal of the Operations Research Society of Japan, vol. 47, no. 4, pp. 275-303, 2004.
7. C. Maglaras and J. A. Van Mieghem, "Queueing systems with leadtime constraints: A fluid-model approach for admission and sequencing control," European J. Oper. Res., vol. 167, no. 1, pp. 179-207, 2005.
8. A. L. Stolyar and K. Ramanan, "Largest weighted delay first scheduling: Large deviations and optimality," The Annals of Applied Probability, vol. 11, no. 1, pp. 1-48, 2001.
9. A. L. Stolyar, "Control of end-to-end delay tails in a multiclass network: LWDF discipline optimality," Ann. Appl. Probab., vol. 13, no. 3, pp. 1151-1206, 2003.
10. D. Bertsimas, I. Paschalidis, and J. Tsitsiklis, "Asymptotic buffer overflow probabilities in multi-class multiplexers: An optimal, control approach," IEEE Trans. on Automatic Control, vol. 43, pp. 315-335, March 1998.
11. A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, 2nd Ed. Springer, 1998.
12. P. Billingsley, Convergence of probability measures, 2nd ed., ser. Wiley Series in Probability and Statistics: Probability and Statistics. New York: John Wiley & Sons Inc., 1999, a Wiley-Interscience Publication.
13. S. N. Ethier and T. G. Kurtz, Markov processes: Characterization and convergence, ser. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. New York: John Wiley & Sons Inc., 1986.
14. J. Jacod and A. N. Shiryaev, Limit theorems for stochastic processes, 2nd ed., ser. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Berlin: Springer-Verlag, 2003, vol. 288.
15. A. A. Puhalskii, Large deviations and idempotent probability, ser. Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics. Chapman & Hall/CRC, Boca Raton, FL, 2001, vol. 119.
16. _, "The action functional for the Jackson network," Markov Processes and Related Fields, vol. 13, no. 1, pp. 99-136, 2007.
17. A. A. Puhalskii and A. A. Vladimirov, "A large deviation principle for Join the Shortest Queue," Mathematics of Operations Research, vol. 32, pp. 700-710, 2007.
18. V. G. Subramanian, "Large deviations of max-weight scheduling policies on convex rate regions," Hamilton Institute, National University of Ireland, Maynooth, Co. Kildare, Ireland, Tech. Rep., 2007.
19. J. Garcia, "An extension of the contraction principle," J. Theoret. Probab., vol. 17, no. 2, pp. 403-434, 2004.
20. J. L. Doob, Measure theory, ser. Graduate Texts in Mathematics. New York: Springer-Verlag, 1994, vol. 143.
21. A. Dembo and T. Zajic, "Large deviations: From empirical mean and measure to partial sums process," Stochastic Process. Appl., vol. 57, no. 2, pp. 191-224, 1995.
22. R. M. Dudley, Real analysis and probability, ser. Cambridge Studies in Advanced Mathematics. Cambridge: Cambridge University Press, 2002, vol. 74.
23. A. A. Puhalskii, "Large deviations for stochastic processes," Notes for LMS/EPSRC Short Course: Stochastic Stability, Large Deviations and Coupling Methods, Heriot-Watt University, Edinburgh, Sept. 2006. [Online]. Available: http://www-math.cudenver.edu/~puhalski/ld/ course_1.pdf
24. A. A. Mogul'skiǐ, "Large deviations for the trajectories of multidimensional random walks," Theory Probab. Appl., vol. 21, no. 2, pp. 309-323, 1976.
25. _, "Large deviations for processes with, independent increments," Ann, Probab., vol. 21, no. 1, pp. 202-215, 1993.
26. K. Yosida, Functional analysis, reprint of the sixth (1980) ed., ser. Classics in Mathematics. Berlin: Springer-Verlag, 1995.
27. H. Brézis, Opérateurs maximaux monotones et semigroups de contractions dans les espaces de Hilbert. Amsterdam: North-Holland Publishing Co., 1973, .north-Holland Mathematics Studies, No. 5. Notas de Matemática (50).
28. R. T. Rockafellar and R. J.-B. Wets, Variational analysis, ser. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Berlin: Springer-Verlag, 1998, vol. 317.
29. F. E. Browder, "Nonlinear operators and nonlinear equations of evolution in Banach spaces," in Nonlinear functional analysis (Proc. Sympos. Pure Math., Vol. XVIII, Part2, Chicago, III., 1968). Providence, R.I.: Amer. Math. Soc., 1976, pp. 1-308.
30. R. Rockafellar, Convex analysis, ser. Princeton Mathematical Series, No. 28. Princeton, N.J.: Princeton University Press, 1970.
31. E. Cépa, "Problème de Skorohod multivoque," Ann. Probab., vol. 26, no. 2, pp. 500-532, 1998.
32. D. N. C. Tse and S. V. Hanly, "Multiaccess fading channels. I. Polymatroid structure, optimal resource allocation and throughput capacities," IEEE Trans. Inform. Theory, vol. 44, no. 7, pp. 2796-2815, 1998.
33. D. N. C. Tse, P. Viswanath, and L. Zheng, "Diversity-multiplexing tradeoff in multiple-access channels," IEEE Trans. Information Theory, vol. 50, no. 9, pp. 1859-1874, 2004.
34. S. Kittipiyakul and T. Javidi, "Optimal operating point for MIMO multiple access channel with bursty traffic," accepted to IEEE Transactions on Wireless Communication, 2007.