A. Albert, Estimating the infinitesimal generator of a continuous time finite state Markov process. The Annals of Mathematical Statisics, pp.727-753, 1962.

L. J. Allen, An Introduction to Stochastic Processes with Applications to Biology, 2010.

T. W. Anderson and L. A. Goodman, Statistical inference about Markov chains. The Annals of Mathematical Statisics, pp.89-110, 1957.
DOI : 10.1214/aoms/1177707039

W. J. Anderson, Continuous-time Markov Chains, 1991.
DOI : 10.1007/978-1-4612-3038-0

S. Asmussen, Applied Probabilities and Queues, 2003.

M. B. Dumitrescu, Some informational properties of Markov pure-jump processes. ?asopis pro p?stování matematiky, pp.429-434, 1986.

G. P. Basharin, On a statistical estimation for the entropy of a sequence of independent random variables, Theory of Probability and its Applications, pp.333-336, 1959.

C. Beck and F. Shclögl, Thermodynamics of chaotic systems, 1993.
DOI : 10.1017/CBO9780511524585

J. Bercher, Source coding with escort distributions and R??nyi entropy bounds, Physics Letters A, vol.373, issue.36, pp.3235-3238, 2009.
DOI : 10.1016/j.physleta.2009.07.015

P. Billingsley, Statistical Inference for Markov Processes, 1968.

M. Bladt and M. Sørensen, Statistical inference for discretely observed Markov jump processes, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.11, issue.3, pp.395-410, 2005.
DOI : 10.1093/biomet/88.3.603

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.379.7943

L. Breuer and D. Baum, An Introduction to Queueing Theory Matrix-Analytic Methods, 2005.

J. Chazottes and D. Gabrielli, -measures, Nonlinearity, vol.18, issue.6, pp.2545-2563, 2005.
DOI : 10.1088/0951-7715/18/6/007

URL : https://hal.archives-ouvertes.fr/hal-01108783

J. Chiquet and N. Limnios, Estimating Stochastic Dynamical Systems Driven by a Continuous-Time Jump Markov Process, Methodology and Computing in Applied Probability, vol.53, issue.4, pp.431-447, 2006.
DOI : 10.1007/s11009-006-0423-z

URL : https://hal.archives-ouvertes.fr/hal-00260731

G. Ciuperca and V. Girardin, Estimation of the Entropy Rate of a Countable Markov Chain, Communications in Statistics - Theory and Methods, vol.27, issue.14, pp.1-15, 2007.
DOI : 10.1137/1118080

T. M. Cover and J. A. Thomas, Elements of Information Theory, 2006.

D. Crommelin and E. Vanden-e?nden, Data-Based Inference of Generators for Markov Jump Processes Using Convex Optimization, Multiscale Modeling & Simulation, vol.7, issue.4, pp.1751-1778, 2009.
DOI : 10.1137/080735977

I. Csiszár, $I$-Divergence Geometry of Probability Distributions and Minimization Problems, The Annals of Probability, vol.3, issue.1, pp.141-158, 1975.
DOI : 10.1214/aop/1176996454

W. J. Culver, On the existence and uniqueness of the real logarithm of a matrix, Proceedings of the, pp.1146-1151, 1966.
DOI : 10.1090/S0002-9939-1966-0202740-6

D. Dacunha-castelle and M. Duflo, Probabilités et statistiques ; Problèmes à temps fixe, 1994.

D. Dehay and J. Yao, On likelihood estimation for a discretely observed jump process, Comptes Rendus Mathematique, vol.342, issue.5, pp.93-107, 2007.
DOI : 10.1016/j.crma.2005.12.025

URL : https://hal.archives-ouvertes.fr/hal-00451438

A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, 1998.
DOI : 10.1007/978-1-4612-5320-4

N. G. Duffield, J. T. Lewis, N. O-'connel, R. Russel, and F. Toomey, Entropy of ATM traffic streams: a tool for estimating QoS parameters, IEEE Journal on Selected Areas in Communications, vol.13, issue.6, pp.981-990, 1995.
DOI : 10.1109/49.400654

K. Duffy, E. A. Peshersky, Y. M. Suhov, and N. D. Vvedenskaya, Using estimated entropy in a queueing system with dynamic routing, Markov Processes and Related Fields, pp.57-84, 2007.

M. A. El-affendi and D. D. Kouvatsos, A maximum entropy analysis of the M/G/1 and G/M/1 queueing systems at equilibrium, Acta Informatica, vol.11, issue.1, pp.339-355, 1986.
DOI : 10.1007/BF00290731

T. Engset, Emploi du calcul des probabilités pour la détermination du nombre de sélecteurs dans les bureaux téléphoniques centraux. Revue de génie électrique, pp.138-140, 1921.

A. K. Erlang, Telefon-ventetider. et stykke sandsynlighedsregning, Matematisk Tidsskrift, B, 1920.

S. N. Ethier and T. G. Kurtz, Markov Processes : Characterization and Convergence, 1986.
DOI : 10.1002/9780470316658

W. Feller, Die Grundlagen der Volterraschen Theorie des Kampfes ums Dasein in wahrscheinlichkeitstheoretischer Behandlung, Acta Biotheoretica, vol.VII, issue.8, pp.11-40, 1939.
DOI : 10.1007/BF01602932

Y. Gao, I. Kontoyiannis, and E. Bienenstosk, Estimating the Entropy of Binary Time Series: Methodology, Some Theory and a Simulation Study, Entropy, vol.10, issue.2, pp.71-99, 2008.
DOI : 10.3390/entropy-e10020071

V. Girardin, Entropy Maximization for Markov and Semi-Markov Processes, Methodology and Computing in Applied Probability, vol.6, issue.1, pp.109-127, 2004.
DOI : 10.1023/B:MCAP.0000012418.88825.18

V. Girardin, R. Baeza-yates, J. Glaz, H. Gzyl, J. Hüsler et al., On the Different Extensions of the Ergodic Theorem of Information Theory, Recent Advances in Applied Probability, pp.163-179, 2005.
DOI : 10.1007/0-387-23394-6_7

V. Girardin and N. Limnios, Probabilités en vue des applications, 2008.

V. Girardin and P. Regnault, Large deviation principle for the entropy of a finite distribution , with applications, 2011.

V. Girardin and P. Regnault, On the estimation of entropy for Markov chains, 58th World congress of Statistics, International Statistical Institute

V. Girardin and A. Sesboüé, Maximizing the entropy rate of state-dependent M???M???1 queues, AIP Conference Proceedings, pp.181-188, 2008.
DOI : 10.1063/1.3038998

V. Girardin and A. Sesboüé, Comparative Construction of Plug-in Estimators of the Entropy Rate of Two-state Markov Chains, Methodology and Computing in Applied Probability, vol.23, issue.14, pp.181-200, 2009.
DOI : 10.1007/s11009-008-9106-2

S. Guiasu, Maximum Entropy Condition in Queueing Theory, Journal of the Operational Research Society, vol.37, issue.3, pp.293-301, 1986.
DOI : 10.1057/jors.1986.47

B. Harris, The statistical estimation of entropy in the non-parametric case, Colloquium of the Mathematical Society János Bolyai, vol.16, pp.323-355, 1977.

E. T. Jaynes, Information Theory and Statistical Mechanics, Physical Review, vol.106, issue.4, pp.620-630, 1957.
DOI : 10.1103/PhysRev.106.620

]. N. Keiding, Maximum likelihood estimation in the birth-death process. The Annals of Statistics, pp.363-372, 1975.

D. Kendall, Stochastic Processes Occurring in the Theory of Queues and their Analysis by the Method of the Imbedded Markov Chain, The Annals of Mathematical Statistics, vol.24, issue.3, pp.338-354, 1953.
DOI : 10.1214/aoms/1177728975

J. F. Kingman, The imbedding problem for finite Markov chains, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.1, issue.1, pp.14-24, 1962.
DOI : 10.1007/BF00531768

A. N. Kolmogorov, On the Shannon theory of information transmission in the case of continuous signals, IRE Transactions on Information Theory, vol.2, issue.4, pp.102-108, 1956.
DOI : 10.1109/TIT.1956.1056823

S. Kullback and R. A. Leibler, On information and sufficiency. The Annals of, Mathematical Statistics, vol.29, pp.79-86, 1951.

P. Metzner, I. Horenko, and C. Schütte, Generator estimation of Markov jump processes based on incomplete observations nonequidistant in time, Physical Review E, vol.76, issue.6, p.66702, 2007.
DOI : 10.1103/PhysRevE.76.066702

A. Perez, Extensions of Shannon-McMillan's limit theorem to more general stochastic processes. Information Theory, Statistical Decision Functions, Random Processes, pp.545-574, 1964.

E. A. Peshersky, Y. M. Suhov, and N. D. Vvedenskaya, Large deviation in a two-servers system with dynamical routing, 2003.

P. Regnault, Estimation par plug-in du taux d'entropie d'un processus markovien de sauts à espace d'état fini, 2009.

P. Regnault, Plug-in Estimator of the Entropy Rate of a Pure-Jump Two-State Markov Process, Bayesian Inference and Maximum Entropy Methods in Science and Engineering AIP Conference Proceedings, vol.1193, pp.153-160, 2009.
DOI : 10.1063/1.3275609

P. Regnault, Entropy estimation for M/M/1 queueing systems, Bayesian Inference and Maximum Entropy Methods in Science and Engineering AIP Conference Proceedings, p.1305, 2010.
DOI : 10.1063/1.3703651

P. Regnault, Estimation using plug-in of the stationary distribution and Shannon entropy of continuous time Markov processes, Journal of Statistical Planning and Inference, vol.141, issue.8, pp.2711-2725, 2011.
DOI : 10.1016/j.jspi.2011.02.022

T. Rolski, H. Schmidli, V. Schmidt, and J. Teugels, Stochastic Processes for Insurance and Finance, 2008.
DOI : 10.1002/9780470317044

I. N. Sanov, On the probability of large deviations of random variables, Transactions on Mathematical Statistics and Probability, vol.1, pp.213-244, 1961.

A. Sgarro, An informational divergence geometry for stochastic matrices, Calcolo, vol.3, issue.1, pp.41-49, 1978.
DOI : 10.1007/BF02576044

C. E. Shannon, A mathematical theory of communication. The Bell System Technical Journal, pp.379-423, 1948.

J. Shao, Mathematical Statistics, 2003.
DOI : 10.1007/b97553

Y. Taga, On the limiting distributions in Markov renewal processes with finitely many states, Annals of the Institute of Statistical Mathematics, vol.32, issue.1, pp.1-10, 1963.
DOI : 10.1007/BF02865897

C. Tsallis, Nonextensive statistical mechanics: A brief introduction, Continuum Mechanics and Thermodynamics, vol.16, issue.3, 2009.
DOI : 10.1007/s00161-004-0174-4

URL : http://arxiv.org/abs/cond-mat/0305606

S. Turner, Large Deviations for Join the Shorter Queue, Fields Institute Communications, vol.28, pp.95-106, 2000.

K. Wang, S. Chuang, and W. Pearn, Maximum entropy analysis to the N policy M/G/1 queueing system with a removable server, Applied Mathematical Modelling, vol.26, issue.12, pp.1151-1162, 2002.
DOI : 10.1016/S0307-904X(02)00056-2

W. Yueh, Eigenvalues of several tridiagonal matrices, Applied Mathematics E-Notes, vol.5, pp.66-74, 2005.

J. Zamarlik, Les entropies liées à une file d'attente. Comptes Rendus de l'Académie des Sciences de Paris, pp.533-536, 1983.

J. Zamarlik, Quantité d'information contenue dans une file d'attente. Comptes Rendus de l'Académie des Sciences de Paris, pp.411-413, 1983.

J. Ziv and A. Lempel, Compression of individual sequences via variable-rate coding, IEEE Transactions on Information Theory, vol.24, issue.5, pp.24530-536, 1978.
DOI : 10.1109/TIT.1978.1055934

A. M. Zubkov, Limit distribution for a statistical estimator of the entropy. Theory of Probability and its Applications, pp.611-618, 1973.