REFERENCES
- Addie , R. ; Mannersalo , P. ; Norros , I. Most probable paths and performance formulae for buffers with Gaussian input traffic . European Transactions on Telecommunications 2002 , 13 ( 3 ), 183 – 196 .
- Addie , R.G. ; Neame , T.D. ; Zukerman , M. Performance evaluation of a queue fed by a Poisson Pareto burst process . Computer Networks 2002 , 40 , 377 – 397 .
- Bucklew , J.A Introduction to Rare Event Simulation ; Springer Series in Statistics ; Springer-Verlag : New York , 2004 .
- Crovella , M.E. ; Bestavros , A. Self-similarity in world wide web traffic: evidence and possible causes . IEEE/ACM Transactions on Networking 1997 , 5 ( 6 ), 835 – 846 .
- Dembo , A. ; Zeitouni , O. Large Deviations Techniques and Applications ; Jones and Bartlett : London , 1993 .
- Dieker , A.B. Conditional limit theorems for queues with Gaussian input, a weak convergence approach . Stochastic Processes and Their Applications 2005 , 115 , 849 – 873 .
- Duffield , N.G. Queueing at large resources driven by long-tailed M/G/∞-modulated processes . Queueing Systems 1998 , 28 , 245 – 266 .
- Duffield , N.G. ; O'Connell , N. Large deviations and overflow probabilities for the general single-server queue, with applications . Mathematical Proceedings of the Cambridge Philosophical Society 1995 , 118 ( 2 ), 363 – 374 .
- Ganesh , A.J. ; O'Connell , N. A large deviation principle with queueing applications . Stochastics and Stochastics Reports 2002 , 73 ( 1-2 ), 25 – 35 .
- Ganesh , A. ; O'Connell , N. ; Wischik , D. Big Queues ; Lecture Notes in Mathematics . Vol. 1838 ; Springer-Verlag : Berlin , 2004 .
- Guerin , C.A. ; Nyberg , H. ; Perrin , O. ; Resnick , S. ; Rootzén , H. ; Stărică C. Empirical testing of the infinite source Poisson data traffic model . Stochastic Models 2003 , 19 ( 3 ), 151 – 200 .
- Heidelberger , P. Fast simulation of rare events in queueing and reliability models . ACM Transactions on Modeling and Computer Simulation 1995 , 5 ( 1 ), 43 – 85 .
- Hogg , R.V. ; Klugman , S.A. Loss Distributions ; John Wiley & Sons : New York , 1984 .
- Kaj , I. ; Taqqu , M.S. Convergence to fractional Brownian motion and to the Telecom process: The integral representation approach (Technical Report 2004:16). Uppsala University, Department of Mathematics: July, 2004 .
- Kaj , I. On scaling limits of arrival processes with long-range dependence . Kalashnikov Memorial Seminar 2002 , 2 ( 2 ), 201 – 203 .
- Kozachenko , Y. ; Vasylyk , O. ; Sottinen , T. Path space large deviations of a large buffer with Gaussian input traffic . Queueing Systems 2002 42 , 113 – 129 .
- Leland , W.E. ; Taqqu , M.S. ; Willinger , W. ; Wilson , D.V. On the self-similar nature of ethernet traffic (extended version). IEEE/ACM Transactions on Networking 1994, 2 (1), 1–15.
- Liu , Z. ; Nain , P. ; Towsley , D ,; Zhang , Z. Asymptotic behavior of a multiplexer fed by a long-range dependent process . Journal of Applied Probability 1999 , 36 , 105 – 118 .
- Loynes , R.M. The stability of a queue with non-independent inter-arrivals and service times . Math. Proc. Cambridge Philos. Soc. 1962 , 58 , 497 – 520 .
- Majewski , K. Heavy traffic approximations of large deviations of feedforward queueing networks . Queueing Systems 1998 , 28 ( 1–3 ), 125 – 155 .
- Majewski , K. Single class queueing networks with discrete and fluid customers on the time interval ℝ . Queueing Systems 2000 , 36 ( 4 ), 405 – 435 .
- Majewski , K. Large deviations for multi-dimensional reflected fractional Brownian motion . Stochastics and Stochastics Reports 2003 , 75 ( 4 ), 233 – 257 . Corrigendum 2004 , ( 5 ), 479 .
- Majewski , K. Sample path moderate deviations for a family of long-range dependent traffic and associated queue length processes . Stochastics 2005 , 77 ( 1 ), 81 – 107 .
- Majewski , K. Sample path large deviations for a family of long-range dependent traffic and associated queue length processes . Queueing Systems 2006 , 52 ( 1 ), 105 – 118 .
- Mandjes , M. A note on queues with M/G/∞ input . Operations Research Letters 2001 , 28 , 233 – 242 .
- Mannersalo , P. ; Norros , I. A most probable path approach to queueing systems with general Gaussian input . Computer Networks 2002 , 40 ( 3 ), 399 – 411 .
- Mikosch , T. ; Resnick , S. ; Rootzén , H. ; Stegeman , A. Is network traffic approximated by stable Lévy motion or fractional Brownian motion? The Annals of Applied Probability 2002 , 12 ( 1 ), 23 – 68 .
- Norros , I. On the use of fractional Brownian motions in the theory of connectionless networks . IEEE Journal on Selected Areas in Communications 1995 , 13 ( 6 ), 953 – 962 .
- Norros , I. Busy periods of fractional Brownian storage: a large deviations approach . Advances in Performance Analysis 1999 , 2 ( 1 ), 1 – 19 .
- Parulekar , M. ; Makowski , A.M. Tail probabilities for M/G/∞ input processes (i): preliminary asymptotics . Queueing Systems 1997 , 27 , 271 – 296 .
- Paxson , V. ; Floyd , S. Wide area traffic: the failure of poisson modeling . IEEE/ACM Transactions on Networking 1995 , 3 ( 3 ), 226 – 244 .
- Reich , E. On the integrodifferential equation of Takács. I. Annals of Mathematical Statistics 1958 , 29 , 563 – 570 .
- Rockafellar , R.T. Convex Analysis ; Princeton University Press : Princeton , 1970 .
- Samorodnitsky , G. ; Taqqu , M.S. Stable Non-Gaussian Random Processes ; Chapman and Hall : New York , 1994 .
- Shwartz , A. ; Weiss , A. Large Deviations for Performance Analysis: Queues, Communications and Computing ; Chapman and Hall : New York , 1995 .
- Willinger , W ; Taqqu , M.S. ; Sherman , R ; Wilson , D.V. Self-similarity through high-variability: statistical analysis of ethernet LAN traffic at the source level . IEEE/ACM Transactions on Networking 1997 , 5 ( 1 ), 71 – 86 .