Addie, R., Mannersalo, P., Norros, I.: Most probable paths and performance formulae for buffers with Gaussian input traffic. Eur. Trans. Telecommun. 13(3), 183–196 (2002)
Adler, R.J.: An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes. Lecture Notes-Monographs, vol. 12. Institute of Mathematical Statistics, Bethesda (1990)
Araujo, A., Giné, E.: The Central Limit Theorem for Real and Banach Valued Random Variables. Wiley, New York (1980)
Bahadur, R.R., Zabell, S.L.: Large deviations of the sample mean in general vector spaces. Ann. Probab. 7(4), 587–621 (1979)
Barndorf-Nielsen, O.E., Shepard, N.: Integrated OU processes and non-Gaussian OU-based stochastic volatility models. Scand. J. Stat. 30, 277–295 (2003)
Bauer, H.: Maß- und Integrationstheorie. de Gruyter, Berlin (1990)
Borovkov, A.A.: Asymptotic Methods in Queueing Theory. Wiley, Chichester (1984)
Brandt, A., Brandt, M.: On the distribution of the number of packets in the fluid flow approximation of packet arrival streams. Queueing Syst. 17, 275–315 (1994)
Chen, H., Mandelbaum, A.: Leontief systems, RBV’s and RBM’s. In: Davis, M.H.A., Elliott, R.J. (eds.) Proceedings of the Imperial College Workshop on Applied Stochastic Processes, pp. 1–43. Gordon and Breach, New York (1991)
Xia, C.: Probability of moderate deviations for b-valued independent random vectors. Chin. J. Contemp. Math. 11(4), 381–393 (1990)
Choudhury, G.L., Lucantoni, D.M., Whitt, W.: Squeezing the most out of ATM. IEEE Trans. Commun. 44(2), 203–217 (1996)
Cramér, H.: Sur un nouveaux theorème-limite de la théorie des probabilités. In: Actualités Scientifiques et Industrielles 736, vol. 3, pp. 5–23. Herman, Paris (1938) Colloque consacré à la théorie des probabilités, October 1937
Dębicki, K., Palmowski, Z.: On-off fluid models in heavy traffic environment. Queueing Syst. 33, 327–338 (1999)
Dembo, A., Zajic, T.: Uniform large and moderate deviations for functional empirical processes. Stoch. Process. Appl. 71, 195–211 (1997)
Dembo, A., Zeitouni, O.: Large Deviations Techniques and Applications. Jones and Bartlett, London (1993)
Deuschel, J.-D., Stroock, D.W.: Large Deviations. Academic, Boston (1989)
Dupuis, P., Ishii, H.: On Lipschitz continuity of the solution mapping to the Skorokhod problem, with applications. Stoch. Stoch. Rep. 35, 31–62 (1991)
Ganesh, A.J., O’Connell, N.: A large deviation principle with queueing applications. Stoch. Stoch. Rep. 73(1–2), 25–35 (2002)
Ganesh, A., O’Connell, N., Wischik, D.: Big Queues. Lecture Notes in Mathematics, vol. 1838. Springer, Berlin (2004)
Habib, I.W., Saadawi, T.N.: Multimedia traffic characteristics in broadband networks. IEEE Commun. Mag. 30(7), 48–54 (1992)
Iglehart, D.L.: Limiting diffusion approximations for the many server queue and the repairman problem. J. Appl. Probab. 2, 429–441 (1965)
Kesidis, G., Walrand, J., Chang, C.-S.: Effective bandwidth for multiclass Markov fluids and other ATM sources. IEEE/ACM Trans. Netw. 1(4), 424–427 (1993)
Kulkarni, V., Rolski, T.: Fluid model driven by an Ornstein–Uhlenbeck process. Probab. Eng. Inform. Sci. 8, 403–417 (1994)
Kurtz, T.G.: Strong approximation theorems for density dependent Markov chains. Stoch. Process. Appl. 6, 223–240 (1978)
Ledoux, M.: Sur les déviations modérées des sommes de variables aléatoires vectorielles indépendantes de même loi. Ann. Inst. Henri Poincaré Probab. Stat. 28(2), 267–280 (1992)
Majewski, K.: Single class queueing networks with discrete and fluid customers on the time interval ℝ. Queueing Syst. 36(4), 405–435 (2000)
Majewski, K.: Large deviations for multi-dimensional reflected fractional Brownian motion. Stoch. Stoch. Rep. 75(4), 233–257 (2003). Corrigendum 76(5), 479 (2004)
Majewski, K.: Fractional Brownian heavy traffic approximations of multiclass feedforward queueing networks. Queueing Syst. 50(2–3), 199–230 (2005)
Majewski, K.: Large deviation properties of constant rate data streams sharing a buffer with long-range dependent traffic in critical loading. To appear in Adv. Appl. Probab. 39(2), June 2007
Majewski, K.: Sample path moderate deviations for a family of long-range dependent traffic and associated queue length processes. Stoch. 77(1), 81–107 (2005)
Majewski, K.: Sample path large deviations for multiclass feedforward queueing networks in critical loading. Ann. Appl. Probab. 16(4), 1893–1924 (2006)
Mandjes, M.: Rare event analysis of the state frequencies of a large number of Markov chains. Commun. Stat. Stoch. Models 15(3), 577–592 (1999)
Mandjes, M., Mannersalo, P.: Queueing systems fed by many exponential on-off sources: an infinite-intersection approach. Queueing Syst. 54, 5–20 (2006)
Mandjes, M., Ridder, A.: Optimal trajectory to overflow in a queue fed by a large number of sources. Queueing Syst. 31, 137–170 (1999)
Mannersalo, P., Norros, I.: A most probable path approach to queueing systems with general Gaussian input. Comput. Netw. 40(3), 399–411 (2002)
Martin-Löf, A.: Mixing properties, differentiability of the free energy and the central limit theorem for a pure phase in the Ising model at low temperature. Commun. Math. Phys. 32, 75–92 (1973)
Norros, I.: Busy periods of fractional Brownian storage: A large deviations approach. Adv. Perform. Anal. 2(1), 1–19 (1999)
Norros, I., Roberts, J.W., Simonian, A., Virtamo, J.T.: The superposition of variable bit rate sources in an ATM multiplexer. IEEE J. Sel. Areas Commun. 9(3), 378–387 (1991)
Pollard, D.: Convergence of Stochastic Processes. Springer, New York (1984)
Puhalskii, A.A.: Moderate deviations for queues in critical loading. Queueing Syst. 31, 359–392 (1999)
Ramanan, K., Dupuis, P.: Large deviation properties of data streams that share a buffer. Ann. Appl. Probab. 8(4), 1070–1129 (1998)
Shwartz, A., Weiss, A.: Large Deviations for Performance Analysis: Queues, Communications and Computing. Chapman & Hall, New York (1995)
Simonian, A.: Stationary analysis of a fluid queue with input rate varying as an Ornstein–Uhlenbeck process. SIAM J. Appl. Math. 51(3), 828–842 (1991)
Simonian, A., Guibert, J.: Large deviations approximations for fluid queues fed by a large number of on/off sources. IEEE J. Sel. Areas Commun. 13(6), 1017–1027 (1995)
Sriram, K., Whitt, W.: Characterizing superposition arrival processes in packet multiplexers for voice and data. IEEE J. Sel. Areas Commun. SAC-4(6), 833–846 (1986)
Ward, A.R., Glynn, P.: Properties of the reflected Ornstein–Uhlenbeck process. Queueing Syst. 44(2), 109–123 (2003)
Weidmann, J.: Lineare Operatoren in Hilberträumen. B.G. Teubner, Stuttgart (1976)
Weiss, A.: A new technique for analyzing large traffic systems. Adv. Appl. Probab. 18, 506–532 (1986)
Wentzell, A.D.: Limit Theorems on Large Deviations for Markov Stochastic Processes. Mathematics and Its Applications, vol. 38. Kluwer Academic, Boston (1990). Originally published by Nauka Publishers, Moscow (1986), in Russian
Whitt, W.: Stochastic-Process Limits: An Introduction to Stochastic-Process Limits and their Applications to Queues. Springer, New York (2001)
Williams, R.: An invariance principle for semimartingale reflecting Brownian motions in an orthant. Queueing Syst. 30, 5–25 (1998)