]. D. Références1, D. Anick, M. M. Mitra, and . Sondhi, Stochastic theory of a data-handling system with multiple sources, Bell Syst. Techn. J, issue.8, pp.611871-1894, 1982.

D. Artiges and P. Nain, Upper and lower bound for the multiplexing of multiclass Markovian on/off sources, Performance Evaluation, vol.27, issue.28, pp.673-698, 1996.

S. Asmussen, C. Klüppelberg, and K. Sigman, Sampling at subexponential times, with queueing applications, Stochastic Processes and their Applications, vol.79, issue.2, 1998.
DOI : 10.1016/S0304-4149(98)00064-7
URL : http://doi.org/10.1016/s0304-4149(98)00064-7

N. H. Bingham, C. M. Goldie, and J. L. , Teugels, Regular Variation, 1987.

O. J. Boxma, Fluid queues and regular variation, Performance Evaluation, vol.27, issue.28, pp.699-712, 1996.
DOI : 10.1016/0166-5316(96)00014-4
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.34.6831

O. J. Boxma and V. Dumas, Fluid queues with long-tailed activity period distributions To appear in a Special Issue of Computer Communications on " Stochastic Analysis and Optimizstion of Communication Systems, 1997.

G. L. Choudhury and W. Whitt, Long-tail buffer-content distributions in broadband networks, Performance Evaluation, vol.30, issue.3, pp.177-190, 1997.
DOI : 10.1016/S0166-5316(96)00059-4
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.132.5153

D. B. Cline, Convolution tails, product tails and domains of attraction, Probability Theory and Related Fields, vol.3, issue.4, pp.529-557, 1986.
DOI : 10.1007/BF00344720

D. B. Cline, Intermediate Regular and ?? Variation, Proc. London Math. Soc, pp.594-616, 1994.
DOI : 10.1112/plms/s3-68.3.594
URL : http://plms.oxfordjournals.org/cgi/content/short/s3-68/3/594

V. Dumas and A. Simonian, Bounds for the tail-analysis of multiplexed on/off sources, 1998.

A. I. Elwalid and D. Mitra, Effective bandwidth of general Markovian traffic sources and admission control of high speed networks, pp.329-343, 1993.

P. Embrechts and C. M. Goldie, On closure and factorization properties of subexponential and related distributions, Journal of the Australian Mathematical Society, vol.27, issue.02, pp.243-256, 1980.
DOI : 10.1214/aop/1176996893

P. Embrechts, C. Klüppelberg, and T. Mikosch, Modelling Extremal Events, 1997.
DOI : 10.1007/978-3-642-33483-2

A. Gut, Stopped Random Walks. Limit Theorems and Applications, 1988.
DOI : 10.1007/978-1-4757-1992-5

L. De-haan, On Regular Variation and Its Application to Weak Convergence of Sample Extremes, CWI Tract, vol.32, 1970.

D. Heath, S. Resnick, and G. Samorodnitsky, Patterns of buffer overflow in a class of queues with long memory in the input stream, The Annals of Applied Probability, vol.7, issue.4, pp.1021-1057, 1997.
DOI : 10.1214/aoap/1043862423

P. R. Jelenkovic and A. A. Lazar, Asymptotic results for multiplexing subexponential on-off sources

A. N. Kolmogorov and S. V. Fomin, Introductory Real Analysis, 1970.

L. Kosten, Stochastic theory of a multi-entry buffer (1), Delft Progress Report, vol.1, pp.10-19, 1974.

W. Leland, M. Taqqu, W. Willinger, and D. Wilson, On the self-similar nature of Ethernet traffic (extended version), IEEE/ACM Transactions on Networking, vol.2, issue.1, pp.1-15, 1994.
DOI : 10.1109/90.282603

R. M. Loynes, The stability of a queue with non-independent inter-arrival and service times, Proc. Cambridge Philos. Soc, pp.497-520
DOI : 10.2307/1992945

D. Mitra, Stochastic theory of a fluid model of producers and consumers coupled by a buffer, Advances in Applied Probability, vol.11, issue.03, pp.646-676, 1988.
DOI : 10.1145/321941.321952

A. G. Pakes, On the tails of waiting-time distributions, Journal of Applied Probability, vol.34, issue.03, pp.555-564, 1975.
DOI : 10.1137/1109088

S. I. Resnick, Extreme Values, regular Variation and Point Processes, 1987.
DOI : 10.1007/978-0-387-75953-1

R. T. Rockafellar, Convex Analysis, 1970.
DOI : 10.1515/9781400873173

T. E. Stern and A. I. Elwalid, Analysis of separable Markov-modulated rate models for information-handling systems, Advances in Applied Probability, vol.34, issue.01, pp.105-139, 1991.
DOI : 10.2307/1427040

N. Veraverbeke, Asymptotic behaviour of Wiener-Hopf factors of a random walk, Stochastic Processes and their Applications, pp.27-37, 1977.
DOI : 10.1016/0304-4149(77)90047-3

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