H. Takagi, Application of polling models to computer-networks. Computer Networks and ISDN systems, pp.193-211, 1991.

G. Zussman, A. Segall, and U. Yechiali, Bluetooth time division duplex - analysis as a polling system, 2004 First Annual IEEE Communications Society Conference on Sensor and Ad Hoc Communications and Networks, 2004. IEEE SECON 2004., 2004.
DOI : 10.1109/SAHCN.2004.1381957

H. Takagi, Analysis of polling systems, Performance Evaluation, vol.5, issue.3, 1986.
DOI : 10.1016/0166-5316(85)90016-1

H. Takagi, Queueing analysis of polling models: an update, Stochastic Analysis of Computer and Communication Systems, pp.267-318, 1990.

U. Yechiali, Analysis and control of polling systems, Performance Evaluation of Computer and Communication Systems, pp.630-650, 1993.
DOI : 10.1007/BFb0013871

H. Lévy and M. Sidi, Polling systems: applications, modeling, and optimization, IEEE Transactions on Communications, vol.38, issue.10, pp.1750-1760, 1990.
DOI : 10.1109/26.61446

A. Brandt, The Stochastic Equation Y n+1 = A n Y n +B n with Stationary Coefficients, Advances in Applied Probability, vol.18, issue.1, pp.211-220, 1986.
DOI : 10.2307/1427243

A. Brandt, P. Franken, and B. Lisek, Stationary Stochastic Models, 1992.

P. Glasserman and D. D. Yao, Stochastic vector difference equations with stationary coefficients, Journal of Applied Probability, vol.12, issue.04, pp.851-866, 1995.
DOI : 10.1214/aop/1176989931

I. J. Bienaymé, De la loi de la multiplication et de la durée des familles, pp.37-66

F. Galton and H. W. Watson, On the Probability of the Extinction of Families, Journal of the Royal Anthropological Institute, vol.4, pp.138-144, 1874.
DOI : 10.1007/978-3-642-81046-6_44

A. N. Kolmogorov, On the solution of a biological problem, Proceedings of Tomsk University, pp.7-12, 1938.

B. A. Sevastyanov, Limit theorem for branching processes of special form, TPA, vol.2, pp.121-136, 1957.

J. D. Biggins, H. Cohn, and O. Nerman, Multi-type branching in varying environment, Stochastic Processes and their Applications, pp.357-400, 1999.
DOI : 10.1016/S0304-4149(99)00049-6

K. B. Athreya and A. N. Vidyashankar, Branching processes, Handbook of statistics 19: Stochastic Processes: Theory and Methods, 2001.
DOI : 10.1007/978-3-642-65371-1

K. B. Athreya and P. Jaggers, Classical and Modern Branching Processes Series, volume 84 of The IMA Volumes in Mathematics and its Applications, 1997.

J. A. Resing, Polling systems and multitype branching processes, Queueing Systems, vol.32, issue.4, pp.409-426, 1993.
DOI : 10.1007/BF01149263

R. Groenevelt and E. Altman, Analysis of alternating-priority queueing models with (cross) correlated switchover times, Proceedings of IEEE Infocom 2005, 2005.

E. Altman, Stochastic recursive equations with applications to queues with dependent vacations, Annals of Operations Research, vol.112, issue.1/4, pp.43-61, 2002.
DOI : 10.1023/A:1020972803727

. Altman, On stochastic recursive equations and infinite server queues, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies., 2005.
DOI : 10.1109/INFCOM.2005.1498355

URL : https://hal.archives-ouvertes.fr/inria-00070782

S. A. Grishenchkin, On a relation between processor sharing queues and crump-mode-jager branching processes, Advances in Applied Probability, vol.24, pp.653-698, 1992.

R. and N. Queija, Processor-Sharing Models for Integrated-Services Networks, 2000.

H. Takagi, Analysis of polling systems, Performance Evaluation, vol.5, issue.3, 1986.
DOI : 10.1016/0166-5316(85)90016-1

R. A. Horn and C. R. Johnson, Matrix Analysis, 1996.

F. Baccelli and P. Brémaud, Elements of Queueing Theory, 2003.
DOI : 10.1007/978-3-662-11657-9

J. Bertoin, Subordinators, Lévy processes with no negative jumps and branching processes. Lecture notes, Centre for Mathematical Physics and Stochastics, 2000.

K. Sato, Lévy Processes and Infinitely Divisible Distributions, 1999.

J. Bertoin, Lévy Processes, 2002.

D. Khoshnevisan, Y. Xiao, and Y. Zhong, Local times of additive L??vy processes, Stochastic Processes and their Applications, pp.193-216, 2003.
DOI : 10.1016/S0304-4149(02)00237-5

O. E. Barndorff-nielsen, J. Federsen, and K. I. Sato, Multivariate subordination selfdecomposability and stability, Advances in Applied Probability, vol.33, pp.130-187, 2001.

H. K. Gjessing, O. O. Aalen, and N. L. Hjort, Frailty models based on lévy processes Advances in Applied Probability, route des Lucioles -BP 93 -06902 Sophia Antipolis Cedex (France) Unité de recherche INRIA Futurs : Parc Club Orsay Université -ZAC des Vignes 4, rue Jacques Monod -91893 ORSAY Cedex, pp.532-550, 2003.

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