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Volumn 116, Issue 5, 2006, Pages 724-756

Worst-case large-deviation asymptotics with application to queueing and information theory

Author keywords

Bayesian inference; Entropy; Large deviations; Queueing; Simulation

Indexed keywords

APPROXIMATION THEORY; ASYMPTOTIC STABILITY; FUNCTION EVALUATION; PHASE SPACE METHODS; QUEUEING THEORY; RANDOM PROCESSES;

EID: 33747217583     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2005.11.003     Document Type: Article
Times cited : (24)

References (45)
  • 1
    • 0001917727 scopus 로고
    • Probability inequalities for the sum of independent random variables
    • Bennett G. Probability inequalities for the sum of independent random variables. J. Amer. Statist. Assoc. 57 (1962) 33-45
    • (1962) J. Amer. Statist. Assoc. , vol.57 , pp. 33-45
    • Bennett, G.1
  • 2
    • 0042594684 scopus 로고    scopus 로고
    • Atena Scientific, Cambridge, MA (with Angelia Nedic and Asuman E. Ozdaglar)
    • Bertsekas D.P. Convex Analysis and Optimization (2003), Atena Scientific, Cambridge, MA (with Angelia Nedic and Asuman E. Ozdaglar)
    • (2003) Convex Analysis and Optimization
    • Bertsekas, D.P.1
  • 3
    • 0013419904 scopus 로고    scopus 로고
    • Moment problems and semidefinite optimization
    • Handbook of Semidefinite Programming, Kluwer Acad. Publ., Boston, MA
    • Bertsimas D., and Sethuraman J. Moment problems and semidefinite optimization. Handbook of Semidefinite Programming. Internat. Ser. Oper. Res. Management Sci. vol. 27 (2000), Kluwer Acad. Publ., Boston, MA 469-509
    • (2000) Internat. Ser. Oper. Res. Management Sci. , vol.27 , pp. 469-509
    • Bertsimas, D.1    Sethuraman, J.2
  • 5
    • 85027105114 scopus 로고    scopus 로고
    • F. Brichet, A. Simonian, Conservative Gaussian models applied to measurement-based admission control, in: Proceedings of IWQoS, Napa, CA, May 1998, pp. 68-71
  • 6
    • 10744227892 scopus 로고    scopus 로고
    • Geometric programming duals of channel capacity and rate distortion
    • Chiang M., and Boyd S. Geometric programming duals of channel capacity and rate distortion. IEEE Trans. Inform. Theory 50 2 (2004) 245-258
    • (2004) IEEE Trans. Inform. Theory , vol.50 , Issue.2 , pp. 245-258
    • Chiang, M.1    Boyd, S.2
  • 8
    • 0001851198 scopus 로고
    • Application of the method of moments in probability and statistics
    • Moments in Mathematics (San Antonio, TX, 1987), Amer. Math. Soc., Providence, RI
    • Diaconis P. Application of the method of moments in probability and statistics. Moments in Mathematics (San Antonio, TX, 1987). Proc. Sympos. Appl. Math. vol. 37 (1987), Amer. Math. Soc., Providence, RI 125-142
    • (1987) Proc. Sympos. Appl. Math. , vol.37 , pp. 125-142
    • Diaconis, P.1
  • 10
    • 33747590838 scopus 로고    scopus 로고
    • R. Gibbens, F. Kelly, Measurement-based connection admission control, 1997, in: International Teletraffic Congress 15, June 1997
  • 12
    • 0037289503 scopus 로고    scopus 로고
    • Performance evaluation and policy selection in multiclass networks
    • Learning, Optimization and Decision Making (special issue) (invited)
    • Henderson S.G., Meyn S.P., and Tadić V.B. Performance evaluation and policy selection in multiclass networks. Learning, Optimization and Decision Making. Discrete Event Dyn. Sys. 13 1-2 (2003) 149-189 (special issue) (invited)
    • (2003) Discrete Event Dyn. Sys. , vol.13 , Issue.1-2 , pp. 149-189
    • Henderson, S.G.1    Meyn, S.P.2    Tadić, V.B.3
  • 13
    • 84947403595 scopus 로고
    • Probability inequalities for sums of bounded random variables
    • Hoeffding W. Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58 (1963) 13-30
    • (1963) J. Amer. Statist. Assoc. , vol.58 , pp. 13-30
    • Hoeffding, W.1
  • 14
    • 0001613029 scopus 로고
    • Asymptotically optimal tests for multinomial distributions
    • Hoeffding W. Asymptotically optimal tests for multinomial distributions. Ann. Math. Statist. 36 (1965) 369-408
    • (1965) Ann. Math. Statist. , vol.36 , pp. 369-408
    • Hoeffding, W.1
  • 15
    • 33747603077 scopus 로고    scopus 로고
    • J. Huang, S. Meyn, M. Medard, Error exponents for channel coding and signal constellation design, in: Nonlinear Optimization of Communication Systems, Journal of Selected Areas in Comm. (2005) (special issue) (submitted for publication)
  • 16
    • 23744504171 scopus 로고    scopus 로고
    • Characterization and computation of optimal distribution for channel coding
    • Huang J., and Meyn S.P. Characterization and computation of optimal distribution for channel coding. IEEE Trans. Inform. Theory 51 7 (2005) 1-16
    • (2005) IEEE Trans. Inform. Theory , vol.51 , Issue.7 , pp. 1-16
    • Huang, J.1    Meyn, S.P.2
  • 17
    • 33747596752 scopus 로고    scopus 로고
    • J. Huang, C. Pandit, S. Meyn, M. Medard, V. Veeravalli, Entropy, inference, and channel coding. in: P. Agrawal, M. Andrews, P.J. Fleming, G. Yin, L. Zhang, (Eds.), Proceedings of the Summer Workshop on Wireless Networks, in: IMA volumes in Mathematics and its Applications, Springer-Verlag, New York, 2005 (in press)
  • 18
    • 0001151052 scopus 로고
    • Minimax tests and the Neyman-Pearson lemma for capacities
    • Huber P.J., and Strassen V. Minimax tests and the Neyman-Pearson lemma for capacities. Ann. Statist. 1 (1973) 251-263
    • (1973) Ann. Statist. , vol.1 , pp. 251-263
    • Huber, P.J.1    Strassen, V.2
  • 19
    • 84959945140 scopus 로고
    • Matching moments to phase distributions: nonlinear programming approaches
    • Johnson M.A., and Taaffe M.R. Matching moments to phase distributions: nonlinear programming approaches. Comm. Statist. Stochastic Models 6 2 (1990) 259-281
    • (1990) Comm. Statist. Stochastic Models , vol.6 , Issue.2 , pp. 259-281
    • Johnson, M.A.1    Taaffe, M.R.2
  • 20
    • 0001332637 scopus 로고
    • An investigation of phase-distribution moment-matching algorithms for use in queueing models
    • Johnson M.A., and Taaffe M.R. An investigation of phase-distribution moment-matching algorithms for use in queueing models. Queueing Syst. Theory Appl. 8 2 (1991) 129-147
    • (1991) Queueing Syst. Theory Appl. , vol.8 , Issue.2 , pp. 129-147
    • Johnson, M.A.1    Taaffe, M.R.2
  • 21
    • 0003319243 scopus 로고
    • Tchebycheff systems: With applications in analysis and statistics
    • Interscience Publishers John Wiley and Sons, New York, London, Sydney
    • Karlin S., and Studden W.J. Tchebycheff systems: With applications in analysis and statistics. Pure and Applied Mathematics vol. XV (1966), Interscience Publishers John Wiley and Sons, New York, London, Sydney
    • (1966) Pure and Applied Mathematics , vol.XV
    • Karlin, S.1    Studden, W.J.2
  • 22
    • 0002515295 scopus 로고
    • The general moment problem, a geometric approach
    • Kemperman J.M.B. The general moment problem, a geometric approach. Ann. Math. Statist. 39 (1968) 93-122
    • (1968) Ann. Math. Statist. , vol.39 , pp. 93-122
    • Kemperman, J.M.B.1
  • 23
    • 33749435449 scopus 로고    scopus 로고
    • I. Kontoyiannis, L.A. Lastras-Montaño, S.P. Meyn, Relative entropy and exponential deviation bounds for general Markov chains, in: Proceedings of the IEEE International Symposium on Information Theory, Adelaide, Australia, 4-9 September, 2005
  • 24
    • 0037279497 scopus 로고    scopus 로고
    • Spectral theory and limit theorems for geometrically ergodic Markov processes
    • Presented at the INFORMS Applied Probability Conference, NYC, July, 2001
    • Kontoyiannis I., and Meyn S.P. Spectral theory and limit theorems for geometrically ergodic Markov processes. Ann. Appl. Probab. 13 (2003) 304-362 Presented at the INFORMS Applied Probability Conference, NYC, July, 2001
    • (2003) Ann. Appl. Probab. , vol.13 , pp. 304-362
    • Kontoyiannis, I.1    Meyn, S.P.2
  • 25
    • 15944385310 scopus 로고    scopus 로고
    • Large deviations asymptotics and the spectral theory of multiplicatively regular Markov processes
    • (electronic)
    • Kontoyiannis I., and Meyn S.P. Large deviations asymptotics and the spectral theory of multiplicatively regular Markov processes. Electron. J. Probab. 10 3 (2005) 61-123 (electronic)
    • (2005) Electron. J. Probab. , vol.10 , Issue.3 , pp. 61-123
    • Kontoyiannis, I.1    Meyn, S.P.2
  • 26
    • 0008300452 scopus 로고
    • The ideas of P. L. Čebyšev and A. A. Markov in the theory of limiting values of integrals and their future developments
    • Kreǐn M.G. The ideas of P. L. Čebyšev and A. A. Markov in the theory of limiting values of integrals and their future developments. Transl. Amer. Math. Soc. 12 (1959) 1-121
    • (1959) Transl. Amer. Math. Soc. , vol.12 , pp. 1-121
    • Kreǐn, M.G.1
  • 29
    • 0003256486 scopus 로고
    • Inequalities: theory of majorization and its applications
    • Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York
    • Marshall A.W., and Olkin I. Inequalities: theory of majorization and its applications. Mathematics in Science and Engineering vol. 143 (1979), Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York
    • (1979) Mathematics in Science and Engineering , vol.143
    • Marshall, A.W.1    Olkin, I.2
  • 30
    • 23944507769 scopus 로고    scopus 로고
    • Dynamic safety-stocks for asymptotic optimality in stochastic networks
    • Meyn S.P. Dynamic safety-stocks for asymptotic optimality in stochastic networks. Queueing Syst. Theory Appl. 50 (2005) 255-297
    • (2005) Queueing Syst. Theory Appl. , vol.50 , pp. 255-297
    • Meyn, S.P.1
  • 31
    • 33747604005 scopus 로고    scopus 로고
    • C. Pandit, Robust statistical modeling based on moment classes with applications to admission control, large deviations and hypothesis testing, Ph.D. Thesis, University of Illinois at Urbana Champaign, University of Illinois, Urbana, IL, USA, 2004
  • 32
    • 33747595055 scopus 로고    scopus 로고
    • C. Pandit, S.P. Meyn, Robust measurement-based admission control using Markov's theory of canonical distributions, in: Conference version presented at the Conference on Information Sciences and Systems, 2003, IEEE Trans. Inform. Theory (2003) (submitted for publication)
  • 33
    • 33747621931 scopus 로고    scopus 로고
    • C. Pandit, S.P. Meyn, V.V. Veeravalli, Asymptotic robust Neyman-Pearson hypothesis testing based on moment classes, 2005 (in preparation)
  • 34
    • 0007296694 scopus 로고
    • Convex functions, partial orderings, and statistical applications
    • Academic Press Inc., Boston, MA
    • Pečarić J.E., Proschan F., and Tong Y.L. Convex functions, partial orderings, and statistical applications. Mathematics in Science and Engineering vol. 187 (1992), Academic Press Inc., Boston, MA
    • (1992) Mathematics in Science and Engineering , vol.187
    • Pečarić, J.E.1    Proschan, F.2    Tong, Y.L.3
  • 35
    • 0003506181 scopus 로고
    • An introduction to signal detection and estimation
    • Springer-Verlag, New York (A Dowden and Culver Book)
    • Poor H.V. An introduction to signal detection and estimation. Springer Texts in Electrical Engineering. 2nd ed. (1994), Springer-Verlag, New York (A Dowden and Culver Book)
    • (1994) Springer Texts in Electrical Engineering. 2nd ed.
    • Poor, H.V.1
  • 37
    • 0009909847 scopus 로고
    • On the probability of large deviations of random magnitudes
    • Sanov I.N. On the probability of large deviations of random magnitudes. Mat. Sb. N. S. 42 84 (1957) 11-44
    • (1957) Mat. Sb. N. S. , vol.42 , Issue.84 , pp. 11-44
    • Sanov, I.N.1
  • 38
    • 33747592917 scopus 로고
    • (Papers from the AMS-IMS-SIAM Joint Summer Research Conference held in Seattle, Washington, July 1991). Shaked M., and Tong Y.L. (Eds), Institute of Mathematical Statistics, Hayward, CA
    • (Papers from the AMS-IMS-SIAM Joint Summer Research Conference held in Seattle, Washington, July 1991). In: Shaked M., and Tong Y.L. (Eds). Stochastic Inequalities. Institute of Mathematical Statistics Lecture Notes-Monograph Series vol. 22 (1992), Institute of Mathematical Statistics, Hayward, CA
    • (1992) Institute of Mathematical Statistics Lecture Notes-Monograph Series , vol.22
  • 39
    • 33747613634 scopus 로고    scopus 로고
    • Duality of linear conic problems
    • (published electronically)
    • Shapiro A., and Nemirovski A. Duality of linear conic problems. Optimization Online (2003) 1-27 (published electronically)
    • (2003) Optimization Online , pp. 1-27
    • Shapiro, A.1    Nemirovski, A.2
  • 40
    • 0004089461 scopus 로고
    • Large deviations for performance analysis
    • Chapman and Hall, London Queues, communications, and computing, With an appendix by Robert J. Vanderbei
    • Shwartz A., and Weiss A. Large deviations for performance analysis. Stochastic Modeling Series (1995), Chapman and Hall, London Queues, communications, and computing, With an appendix by Robert J. Vanderbei
    • (1995) Stochastic Modeling Series
    • Shwartz, A.1    Weiss, A.2
  • 41
    • 0009566044 scopus 로고
    • Generalized Chebychev inequalities: theory and applications in decision analysis
    • Smith J.E. Generalized Chebychev inequalities: theory and applications in decision analysis. Operations Res. 43 5 (1995) 807-825
    • (1995) Operations Res. , vol.43 , Issue.5 , pp. 807-825
    • Smith, J.E.1
  • 42
    • 33747617415 scopus 로고    scopus 로고
    • L. Vandenberghe, S. Boyd, K. Comanor, Generalized Chebyshev bounds via semidefinite programming, SIAM Review, Problems and Techniques Section, January 2004 (in press)
  • 44
    • 0001096846 scopus 로고
    • Bivariate distributions with given marginals
    • Whitt W. Bivariate distributions with given marginals. Ann. Statist. 4 6 (1976) 1280-1289
    • (1976) Ann. Statist. , vol.4 , Issue.6 , pp. 1280-1289
    • Whitt, W.1
  • 45
    • 0026117687 scopus 로고
    • On universal hypotheses testing via large deviations
    • Zeitouni O., and Gutman M. On universal hypotheses testing via large deviations. IEEE Trans. Inform. Theory 37 2 (1991) 285-290
    • (1991) IEEE Trans. Inform. Theory , vol.37 , Issue.2 , pp. 285-290
    • Zeitouni, O.1    Gutman, M.2


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