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Original Articles

Large deviations for multi-dimensional reflected fractional Brownian motion

Pages 233-257 | Accepted 25 Nov 2002, Published online: 17 Oct 2011

References

  • Chang Cheng-Shang Yao David D. Zajic Tim 1996 Moderate deviations for queues with long-range dependent input Glasserman Paul Sigman Karl Yao David D. Stochastic Networks: Stability and Rare Events Lecture Notes in Statistics, Springer Verlag Berlin 117 275 298
  • Chang Cheng-Shang Yao David D. Zajic Tim 1999 Large deviations, moderate deviations and queues with long-range dependent input Advances in Applied Probability 31 254 278
  • Chang Cheng-Shang Yao David D. Zajic Tim 2001 Large deviations, moderate deviations and queues with long-range dependent input Preprint 1712 IMA
  • Cottle Richad W. Pang Jong-Shi Stone Richard E. 1992 The Linear Complementarity Problem Academic Press New York
  • Dembo Amir Zeitouni Ofer 1993 Large Deviations Techniques and Applications Jones and Bartlett London
  • Duffield N.G. O'Connell Neil 1995 Large deviations and overflow probabilities for the general single-server queue, with applications Mathematical Proceedings of the Cambridge Philosophical Society 118 2 363 374
  • Dupuis Paul Ishii Hitoshi 1991 On Lipschitz continuity of the solution mapping to the Skorokhod problem, with applications Stochastics and Stochastic Reports 35 31 62
  • Dupuis Paul Ramanan Kavita 1999 Convex duality and the Skorokhod problem. I. Probability Theory and Related Fields 115 2 153 195
  • Paul Dupuis and Kavita Ramanan (2002) “A time-reversed representation for the tail probabilities of stationary reflecteds Brownian motion”, Stochastic Processes and Their Applications 98
  • Ganesh A.J. O'Connell Neil 2002 A large deviation principle with queueing applications Stochastics and Stochastics Reports 73 1–2 25 35
  • Harrison Michael Viên Nguyen J. 1993 Brownian models of multiclass queueing networks: Current status and open problems Queueing Systems 13 5 40
  • Harrison Michael Martin J. Reiman I. 1981 Reflected Brownian motion on an orthant The Annals of Probability 9 2 302 308
  • Konstantopoulos Takis Lin Si-Jian 1996 Fractional Brownian motion approximations of queueing networks Glasserman Paul Sigman Karl Yao David D. Stochastic Networks: Stability and Rare Events Lecture Notes in Statistics, Springer Verlag Berlin 117 257 274
  • Kozachenksy Vasytyk, O. Sottinen T. 2002 Path space large deviations of a large buffer with Gaussian input traffic Queueing Systems 42 113 129
  • Will E. Leland Murad Taqqu S. Willinger Walter Wilson Daniel V. 1994 On the self-similar nature of Ethernet traffic (extended version) IEEE/ACM Transactions on Networking 2 1 1 15
  • Majewski Kurt Large Deviations of Feedforward Queueing Networks Ph.D. thesis, Ludwig-Maximilians-Universität München München
  • Majewski Kurt 1996 Large deviations of stationary reflected Brownian motions Kelly F.P. Zachary S. Ziedins I. Stochastic Networks: Theory and Applications, Number 4 Royal Statistical Society, Lecture Note Series, Oxford Science Publications New York, NY 105 118
  • Majewski Kurt 1998 Large deviations of the steady-state distribution of reflected processes with applications to queueing systems Queueing Systems 29 2–4 351 381
  • Majewski Kurt 2000 Single class queueing networks with discrete and fluid customers on the time interval R Queueing Systems 36 4 405 435
  • Majewski, Kurt (2003) Path-wise heavy traffic convergence of open single class queueing networks and large deviations. In preparation.
  • Avi Mandelbaum (1989) The dynamic complementarity problem. Unpublished.
  • Norros Ilkka 1995 On the use of fractional Brownian motions in the theory of connectionless networks IEEE Journal on Selected Areas in Communications 13 6 953 962
  • Revuz Daniel Yor Marc 1991 Continuous Martingales and Brownian Motion Springer-Verlag Berlin
  • Rockafellar Tyrrell Roger R. Wets J-B. 1998 Variational Analysis Springer-Verlag Berlin
  • Samorodnitsky Gennady Taqqu Murad S. 1994 Stable Non-Gaussian Random Processes Chapman and Hall New York
  • Veinott A.F. Jr 1969 Discrete dynamic programming with sensitive discount optimality criteria The Annals of Mathematical Statistics 40 1635 1660
  • Weidmann Joachim 1976 Lineare Operatoren in Hilberträumen B.G. Teubner Stuttgart
  • Williams Ruth 1996 On the approximation of queueing networks in heavy traffic Kelly F.P. Zachary S. Ziedins I. Stochastic Networks: Theory and Applications, Number 4 Royal Statistical Society, Lecture Note Series, Oxford Science Publications New York 35 56
  • Willinger Walter Taqqu Murad S. Sherman Robert Wilson Daniel V. 1997 Self-similarity through high-variability: Statistical analysis of ethernet LAN traffic at the source level IEEE/ACM Transactions on Networking 5 1 71 86

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