M. Adamou, Contribution à la modélisation en vue de la conduite des systèmes flexibles d'assemblage à l'aide des réseaux de Petri orientés objet, Thèse de doctorat, 1997.

S. [. Adlmo, M. Andreasson, P. Fabian, B. Gullander, and . Lennartson, Towards a true flexible manufacturing system, Proceedings of the 10 th ISPE ? IFAC Conference on CAD/CAM, Robotics and Factories of the future, pp.401-410, 1994.

P. [. Akella and . Kumar, Optimal control of production rate in a failure prone manufacturing system, IEEE Transactions on Automatic Control, vol.31, issue.2, pp.116-126, 1986.
DOI : 10.1109/TAC.1986.1104206

R. Alvarez-vargas, Y. Dallery, and R. David, A study of the continuous flow model of production lines with unreliable machines and finite buffers, Journal of Manufacturing Systems, vol.13, issue.3, pp.221-234, 1994.
DOI : 10.1016/0278-6125(94)90006-X

. [. Armijo, Minimization of functions having Lipschitz continuous first partial derivatives, Pacific Journal of Mathematics, vol.16, issue.1, pp.1-3, 1966.
DOI : 10.2140/pjm.1966.16.1

M. Bello, The estimation of delay gradient for purpose of routing in data communication networks, S. M. Thesis, Electrical Engineering Department, M.I.T, 1977.

T. Bielecki and P. R. Kumar, Optimality of Zero-Inventory Policies for Unreliable Manufacturing Systems, Operations Research, vol.36, issue.4, pp.532-541, 1988.
DOI : 10.1287/opre.36.4.532

K. Boonlertvanich, Extended-CONWIP-Kanban system: control and performance analysis, thèse de doctorat, Georgia Institute of Technology, 2005.

J. A. Buzacott, AUTOMATIC TRANSFER LINES WITH BUFFER STOCKS, International Journal of Production Research, vol.1, issue.3, pp.183-200, 1967.
DOI : 10.1287/mnsc.5.4.410

J. A. Buzacott and L. E. Hanifin, Models of automatic transfer lines with inventory banks a review and comparison, A I I E Transactions, vol.24, issue.10, pp.197-207, 1978.
DOI : 10.1002/nav.3800230306

J. A. Buzacott and J. G. Shanthikumar, Stochastic Models of Manufacturing Systems, 1992.

X. R. Cao, Convergence of parameter sensitivity estimates in a stochastic environment, IEEE Transaction on Automatic Control, issue.30, pp.834-843, 1985.

M. Caramanis and G. Liberopoulos, Perturbation Analysis for the Design of Flexible Manufacturing System Flow Controllers, Operations Research, vol.40, issue.6, pp.1107-1125, 1992.
DOI : 10.1287/opre.40.6.1107

C. G. Cassandras, Discrete-Event Systems, 1993.
DOI : 10.1007/0-8176-4404-0_4

C. G. Cassandras and S. Lafortune, Introduction to Discrete Event Systems, 1999.

]. C. Cas02a and . Cassandras, From discrete event to hybrid systems, Proceeding of 6 th International Workshop on Discrete Event Systems (WODES'02), 2002.

]. C. Cas02b, Y. Cassandras, B. Wardi, G. Melamed, C. G. Sun et al., Perturbation analysis for on line control and optimization of stochastic Fluid models, IEEE Transactions on Automatic Control, vol.47, pp.1234-1248, 2002.

G. [. Cassandras, C. G. Sun, Y. Panayiotou, and . Wardi, Perturbation analysis and control of two-class stochastic fluid models for communication networks, IEEE Transactions on Automatic Control, vol.48, issue.5, pp.770-782, 2003.
DOI : 10.1109/TAC.2003.811253

P. Ciprut, M. Hongler, and Y. Salama, Hedging point for non-markovian piecewise deterministic production processes, Discrete Event Dynamic Systems: Theory and Applications, pp.365-375, 1998.

M. [. Ciprut, Y. Hongler, and . Salama, On the variance of the production output of transfer lines, IEEE Transactions on Robotics and Automation, vol.15, issue.1, pp.33-43, 1999.
DOI : 10.1109/70.744600

H. [. Chang and . Keisler, Model theory Optimal policies for the multi-echelon inventory problem, Series Studies in Logic, pp.475-490, 1960.

C. Commault and A. Semery, Taking Into Account Delays in Buffers For Analytical Performance Evaluation of Transfer Lines, IIE Transactions, vol.16, issue.2, pp.133-142, 1990.
DOI : 10.1080/00207548708919865

R. [. Dallery, X. David, and . Xie, An Efficient Algorithm for Analysis of Transfer Lines With Unreliable Machines and Finite Buffers, IIE Transactions, vol.4, issue.3, pp.280-283, 1988.
DOI : 10.1137/1107040

R. [. Dallery, X. David, and . Xie, Approximate analysis of transfer lines with unreliable machines and finite buffers, IEEE Transactions on Automatic Control, vol.34, issue.9, pp.943-953, 1989.
DOI : 10.1109/9.35807

S. [. Dallery and . Gershwin, Manufacturing flow line systems: a review of models and analytical results, Queueing Systems, vol.36, issue.6, pp.3-94, 1992.
DOI : 10.1080/05695557908974399

Y. Dallery and H. L. Bihan, An improved decomposition method for the analysis of production lines with unreliable machines and finite buffers, International Journal of Production Research, vol.37, issue.5, pp.1093-1117, 1999.
DOI : 10.1080/002075499191427

URL : https://hal.archives-ouvertes.fr/hal-01151085

X. [. David, Y. Xie, and . Dallery, Properties of Continuous Models of Transfer Lines with Unreliable Machines and Finite Buffers, IMA Journal of Mathematics Applied in Business and Industry, vol.6, pp.281-308, 1990.

R. David and H. Alla, Petri Nets and Grafcet-Tools for Modeling Discrete Event Systems, 1992.

F. D. Vericourt, F. Karaesmen, and Y. Dallery, Dynamic Scheduling in a Make-to-Stock System: A Partial Characterization of Optimal Policies, Operations Research, vol.48, issue.5, pp.811-819, 2000.
DOI : 10.1287/opre.48.5.811.12404

URL : https://hal.archives-ouvertes.fr/hal-00133255

D. Dubois and J. Forestier, Productivité et en-cours moyens d'un ensemble de deux machines séparées par un zone de stockage, R.A.I.R.O. Automatique/System Analysis and Control, vol.16, issue.2, pp.105-132, 1982.

Y. Feng and H. Yan, Optimal production control in a discrete manufacturing system with unreliable machines and random demands, IEEE Transactions on Automatic Control, vol.45, issue.12, pp.2280-2296, 2000.
DOI : 10.1109/9.895564

[. Forestier and R. A. , Modélisation stochastique et comportement asymptotique d'un système automatisée de production, Automatique/System Analysis and Control, vol.14, issue.2, pp.127-143, 1980.

M. Fu, J. Hu, and R. Nagi, Bias properties of infinitesimal perturbation analysis for systems with parallel servers, Computers & Operations Research, vol.19, issue.5, pp.409-423, 1992.
DOI : 10.1016/0305-0548(92)90070-L

M. Fu, Sample Path Derivatives for (s, S) Inventory Systems, Operations Research, vol.42, issue.2, 1994.
DOI : 10.1287/opre.42.2.351

M. Fu and X. Xie, Derivative Estimation for Buffer Capacity of Continuous Transfer Lines Subject to Operation-Dependent Failures, Discrete Event Dynamic Systems, vol.12, issue.4, pp.447-469, 2002.
DOI : 10.1023/A:1019759524969

B. Fu, L. Shi, and R. Suri, Analysis of Departure Times in Discrete and Continuous Tandem Production Lines, Discrete Event Dynamic Systems: Theory and Application, pp.159-186, 2002.

. [. Gershwin, An Efficient Decomposition Method for the Approximate Evaluation of Tandem Queues with Finite Storage Space and Blocking, Operations Research, vol.35, issue.2, pp.291-305, 1987.
DOI : 10.1287/opre.35.2.291

. [. Gershwin, Assembly/Disassembly Systems: An Efficient Decomposition Algorithm for Tree-Structured Networks, IIE Transactions, vol.20, issue.4, pp.302-314, 1991.
DOI : 10.1080/15326348508807022

S. B. Gershwin and M. H. Burman, A Decomposition Method for Analysing Inhomogeneous Assembly/disassembly Systems, 1998.

P. Glasserman, Gradient Estimation via Perturbation Analysis, 1990.

. [. Glasserman, Hedging-point production control with multiple failure modes, IEEE Transactions on Automatic Control, vol.40, issue.4, pp.707-712, 1995.
DOI : 10.1109/9.376104

J. [. Gousty and . Kieffer, Une nouvelle typologie pour les systèmes industriels de production, Revue française de gestion, pp.104-112, 1988.

H. Groenvelt, The Just-in-Time System, a. E. Handbooks in OR & MS, vol.4, pp.629-671, 1993.

S. [. Gu, X. Hennequin, and . Xie, OPTIMAL CONTROL OF A CONTINUOUS-FLOW FAILURE PRONE MANUFACTURING SYSTEM, Proceeding of IFAC'05, 2005.
DOI : 10.3182/20050703-6-CZ-1902.01429

A. Haurie, P. L. Ecuyer, and C. Van-delft, Convergence of stochastic approximation coupled with perturbation analysis in a class of manufacturing flow control models, Discrete Event Dynamic Systems, vol.14, issue.1, pp.87-111, 1994.
DOI : 10.1080/17442508508833338

URL : https://hal.archives-ouvertes.fr/hal-00471357

. [. Hess, Optimal control approximations for time delay systems., AIAA Journal, vol.23, issue.2, 1972.
DOI : 10.1109/TAC.1968.1098829

R. Hess and J. G. Hyde, Suboptimal control of time-delay systems, IEEE Transactions on Automatic Control, vol.18, issue.6, 1973.
DOI : 10.1109/TAC.1973.1100428

A. [. Ho, T. T. Eyler, and . Chien, A gradient technique for general buffer storage design in a production line, International Journal of Production Research, vol.8, issue.6, pp.557-580, 1979.
DOI : 10.1080/05695557708975134

X. [. Ho and . Cao, Perturbation analysis of discrete event dynamic systems, 1991.

. [. Ho, Perturbation analysis, Proceedings of the 24th conference on Winter simulation , WSC '92, 1992.
DOI : 10.1145/167293.167340

M. Hongler, Chaotic and stochastic behavior in automatic production lines, Lecture Notes in Physics, vol.22, 1994.

M. Hongler, Analytical results for the performance and the control of stochastic flow systems, Journal of Intelligent Manufacturing, vol.8, issue.5, pp.435-447, 1997.
DOI : 10.1023/A:1018514401057

M. Hongler and P. Ciprut, Production indices obtained by a myopic policy for non-Markovian dynamics, International Journal of Production Economics, vol.74, issue.1-3, pp.115-123, 2001.
DOI : 10.1016/S0925-5273(01)00112-8

W. J. Hopp and M. L. Spearman, Factory Physics, 1996.

]. Hu94a, D. Hu, and . Xiang, Structural properties of optimal production controllers in failure prone manufacturing systems, IEEE Transactions on Automatic Control, vol.39, pp.640-643, 1994.

J. Hu, P. Vakili, and G. Yu, Optimality of hedging point policies in the production control of failure prone manufacturing systems, IEEE Transactions on Automatic Control, vol.39, issue.9, pp.1875-1880, 1994.

J. Hu, Production rate control for failure-prone production systems with no backlog permitted, IEEE Transaction on Automatic Control, vol.40, issue.2, pp.291-295, 1995.

F. Karaesmen and Y. Dallery, A performance comparison of pull type control mechanisms for multi-stage manufacturing, International Journal of Production Economics, vol.68, issue.1, pp.59-71, 2000.
DOI : 10.1016/S0925-5273(98)00246-1

URL : https://hal.archives-ouvertes.fr/hal-01617225

J. G. Kimemia and S. B. Gershwin, An algorithm for the computer control of production in a flexible manufacturing system, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes, pp.353-362, 1983.
DOI : 10.1109/CDC.1981.269285

G. Kimball, General principles of inventory control, Journal of Manufacturing and Operations Management, vol.1, issue.1, pp.119-130, 1988.

L. Kleinrock, Queuing systems, 1975.

D. P. Kroese, On the decay rates of buffers in continuous flow lines, Methodology And Computing In Applied Probability, vol.2, issue.4, pp.425-441, 2000.
DOI : 10.1023/A:1010066319278

F. Lambersend, Organisation et genie de production, 1999.

L. H. Landweber and E. L. Robertson, Properties of Conflict-Free and Persistent Petri Nets, Journal of the ACM, vol.25, issue.3, pp.352-364, 1978.
DOI : 10.1145/322077.322079

A. M. Law and W. D. Kelton, Simulation Modeling and Analysis, MacGraw-Hill Higher Education, 1997.

R. Levantesi, A. Matta, and T. Tolio, Performance evaluation of continuous production lines with machines having different processing times and multiple failure modes, Performance Evaluation, vol.51, issue.2-4, pp.247-268, 2003.
DOI : 10.1016/S0166-5316(02)00098-6

G. Liberopoulos and M. Caramanis, Production control of manufacturing systems with production rate-dependent failure rates, IEEE Transactions on Automatic Control, vol.39, issue.4, pp.889-895, 1994.
DOI : 10.1109/9.286278

Y. Monden, Toyota Production System: Practical Approach to Production Management, Industrial Engineering, 1983.
DOI : 10.1007/978-1-4615-9714-8

. [. Murata, Petri nets: Properties, analysis and applications, Proceeding of IEEE, pp.541-580, 1989.
DOI : 10.1109/5.24143

D. [. Nedi? and . Bertsekas, Incremental Subgradient Methods for Nondifferentiable Optimization, SIAM Journal on Optimization, vol.12, issue.1, pp.109-138, 2002.
DOI : 10.1137/S1052623499362111

T. Ohno, Toyota Production System, 1988.
DOI : 10.1007/978-3-642-27922-5_14

C. G. Panayiotou, C. G. Cassandras, and P. Zhang, On-line inventory cost minimization for make-to-stock manufacturing systems, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301), pp.4469-4474, 2002.
DOI : 10.1109/ACC.2002.1025354

C. [. Panayiotou and . Cassandras, Infinitesimal perturbation analysis for make-to-stock manufacturing systems based on stochastic fluid models, seventh International Workshop on Discrete Event Systems, pp.247-252, 2004.

J. R. Perkines and R. Srikant, Failure-prone production systems with uncertain demand, IEEE Transactions on Automatic Control, vol.46, issue.3, pp.441-449, 2001.
DOI : 10.1109/9.911420

C. A. Petri, Kommunikation mit automaten, Schriften des Rheinisch, Westfalischen Inst. für Instrum. Math., 1962.

. Greene, Applied Data Research 1 to report RADC-TR-65-337, 1965.

E. Polak, Optimization: algorithms and consistent approximations, Applied Mathematical Sciences, vol.124, 1997.
DOI : 10.1007/978-1-4612-0663-7

L. Pontriaguine, V. Boltianski, R. Gamkrélidzé, and E. Michtchenko, Théorie mathématique des processus optimaux, Editions Mir-MOSCOU, 1974.

J. Proth and X. Xie, Petri nets: A tool for design and management of manufacturing systems, 1996.

W. [. Ramadge and . Wonham, The control of discrete event systems, Proc. IEEE, pp.81-98, 1989.
DOI : 10.1109/5.21072

I. M. Repin, On the approximate replacement of systems with lag by ordinary dynamical systems, Journal of Applied Mathematics and Mechanics, vol.29, issue.2, pp.254-264, 1965.
DOI : 10.1016/0021-8928(65)90029-8

G. Rodde, Les systèmes de production Stochastic modelling of an integrated pulp and paper factory with intermediate storage, International Journal of Systems Science, vol.27, issue.12, pp.1251-1264, 1989.

. [. Sharifnia, Production control of a manufacturing system with multiple machine states, IEEE Transactions on Automatic Control, vol.33, issue.7, pp.620-625, 1988.
DOI : 10.1109/9.1270

. [. Shingo, A Study of the Toyota Production System from an Industrial Engineering Viewpoint, 1989.

D. P. Song and Y. X. Sun, Optimal hedging point control for a failure-prone manufacturing system, International Journal of Systems Science, vol.32, issue.6, pp.681-688, 2001.
DOI : 10.1080/00207720120546

M. L. Spearman, D. L. Woodruff, and W. J. Hopp, CONWIP: a pull alternative to kanban, International Journal of Production Research, vol.28, issue.5, pp.879-894, 1990.
DOI : 10.1080/00207549008942761

M. L. Spearman, An Analytic Congestion Model for Closed Production Systems with IFR Processing Times, Management Science, vol.37, issue.8, pp.1015-1029, 1991.
DOI : 10.1287/mnsc.37.8.1015

M. L. Spearman and M. A. Zazanis, Push and Pull Production Systems: Issues and Comparisons, Operations Research, vol.40, issue.3, pp.521-532, 1992.
DOI : 10.1287/opre.40.3.521

Y. [. Srivatsan and . Dallery, Partial Characterization of Optimal Hedging Point Policies in Unreliable Two-Part-Type Manufacturing Systems, Operations Research, vol.46, issue.1, pp.36-45, 1998.
DOI : 10.1287/opre.46.1.36

URL : https://hal.archives-ouvertes.fr/hal-01151677

G. Sun, C. G. Cassandras, Y. Wardi, and C. G. Panayiotou, Perturbation analysis of stochastic flow networks, Proceedings of 42th IEEE conference on decision and control, pp.4831-4836, 2003.

. [. Suri, Infinitesimal perturbation analysis for general discrete event systems, Journal of the ACM, vol.34, issue.3, pp.686-717, 1987.
DOI : 10.1145/28869.28879

R. Suri and B. Fu, On using continuous flow lines for performance estimation of discrete production lines, 1991 Winter Simulation Conference Proceedings.
DOI : 10.1109/WSC.1991.185712

B. [. Suri and . Fu, On using continuous flow lines to model discrete production lines, Discrete Event Dynamic Systems: Theory and Applications, vol.27, issue.1, pp.129-169, 1994.
DOI : 10.1080/05695557908974399

. [. Takacs, An introduction to the theory of queues, 1962.

B. Tan, Variance of the throughput of an N-station production line with no intermediate buffers and time dependent failures, European Journal of Operational Research, vol.101, issue.3, pp.560-576, 1997.
DOI : 10.1016/S0377-2217(96)00191-9

B. Tan, Production control of a pull system with production and demand uncertainty, IEEE Transactions on Automatic Control, vol.47, issue.5, pp.779-783, 2002.
DOI : 10.1109/TAC.2002.1000272

T. Tolio, A. Matta, and S. B. Gershwin, Analysis of two-machine lines with multiple failure modes, IIE Transactions, vol.34, issue.1, pp.51-62, 2002.
DOI : 10.1080/002075497194642

G. J. Van-ryzin, S. X. Lou, and S. B. Gershwin, Scheduling job shops with delays, International Journal of Production Research, vol.3, issue.7, pp.1407-1422, 1991.
DOI : 10.1137/0307044

G. J. Van-ryzin, S. X. Lou, and S. B. Gershwin, PRODUCTION CONTROL FOR A TANDEM TWO-MACHINE SYSTEM, IIE Transactions, vol.13, issue.5, pp.5-20, 1993.
DOI : 10.1007/BF02096607

M. H. Veatch and L. M. Wein, Optimal Control of a Two-Station Tandem Production/Inventory System, Operations Research, vol.42, issue.2, pp.337-350, 1994.
DOI : 10.1287/opre.42.2.337

Y. Wardi, B. Melamed, C. G. Cassandras, and C. G. Panayiotou, Online IPA Gradient Estimators in Stochastic Continuous Fluid Models, Journal of Optimization Theory and Applications, vol.65, issue.2, pp.369-405, 2002.
DOI : 10.1016/S0304-4149(96)00103-2

Y. Wardi and G. F. Riley, IPA for loss volume and buffer workload in tandem SFM networks, Sixth International Workshop on Discrete Event Systems, 2002. Proceedings., pp.393-398, 2002.
DOI : 10.1109/WODES.2002.1167716

J. Wijngaard, The Effect of Interstage Buffer Storage on the Output of Two Unreliable Production Units in Series, with Different Production Rates, A I I E Transactions, vol.8, issue.1, pp.42-47, 1979.
DOI : 10.1080/05695557508975025

. [. Xie, Real time scheduling and routing for flexible manufacturing systems with unreliable machines, RAIRO - Operations Research, vol.23, issue.4, pp.355-374, 1989.
DOI : 10.1109/MCS.1986.1105071

X. Xie, Hierarchical production control of a flexible manufacturing system, Applied Stochastic Models and Data Analysis, vol.17, issue.4, pp.343-360, 1991.
DOI : 10.1002/asm.3150070405

. [. Xie, PERFORMANCE ANALYSIS OF A TRANSFER LINE WITH UNRELIABLE MACHINES AND FINITE BUFFERS, IIE Transactions, vol.4, issue.1, pp.99-108, 1993.
DOI : 10.1109/9.35807

URL : https://hal.archives-ouvertes.fr/inria-00075470

X. Xie, Evaluation and Optimization of two-stage Continuous Transfer Lines Subject to Time-Dependent Failures, Discrete Event Dynamic Systems, vol.12, issue.1, pp.109-122, 2002.
DOI : 10.1023/A:1013391904853

]. X. Xie02b and . Xie, Fluid-stochastic-event graphs for evaluation and optimization of discreteevent system with failures, IEEE Transactions on Robotics and Automation, vol.18, issue.3, pp.360-367, 2002.

I. [. Xie, S. Mourani, and . Hennequin, Performance evaluation of production lines subject to time and operation dependent failures using Petri Nets, Proceeding of Eighth International Conference on Control Automation, Robotics and Vision (ICARCV), pp.2122-2127, 2004.

H. Yan, G. Yin, and S. X. Lou, Using stochastic optimization to determine threshold values for the control of unreliable manufacturing systems, Journal of Optimization Theory and Applications, vol.36, issue.3, pp.511-539, 1994.
DOI : 10.1002/9780470316658

H. Yan, The optimal number of kanbans in a manufacturing system with general machine breakdowns and stochastic demands, International Journal of Operations & Production Management, vol.15, issue.9, pp.89-103, 1995.
DOI : 10.1214/aoms/1177729586

H. Yan, X. Y. Zhou, and G. Yin, Approximating an Optimal Production Policy in a Continuous Flow Line: Recurrence and Asymptotic Properties, Operations Research, vol.47, issue.4, pp.535-549, 1999.
DOI : 10.1287/opre.47.4.535

H. Yu and C. G. Cassandras, Perturbation analysis and optimisation of a flow controlled manufacturing systems, Proceeding of 6 th International Workshop on Discrete Event Systems (WODES'02), 2002.

H. Yu and C. G. Cassandras, Perturbation analysis for production control and optimization of manufacturing systems, Automatica, vol.40, issue.6, pp.945-956, 2004.
DOI : 10.1016/j.automatica.2004.02.001

B. Zimmern, Etude de la propagation des arrêts aléatoires dans les chaînes de production, Revue de Statistique Appl, vol.4, pp.85-104, 1956.

. [. Zipkin, Does manufacturing need a JIT revolution, Harvard Business Review, pp.40-50, 1991.