R. Agrawal, R. L. Cruz, C. M. Okino, and R. Rajan, A framework for adaptive service guarantees, Proceedings of Allerton Conf, pp.693-702, 1998.

M. Akian, S. Gaubert, and A. Lakhoua, The Max-Plus Finite Element Method for Solving Deterministic Optimal Control Problems: Basic Properties and Convergence Analysis, SIAM Journal on Control and Optimization, vol.47, issue.2, pp.817-848, 2008.
DOI : 10.1137/060655286

URL : https://hal.archives-ouvertes.fr/inria-00071395

K. Altisen and M. Moy, Arrival curves for real-time calculus: the causality problem and its solutions, TACAS, pp.358-372, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00442257

K. Altisen and M. Moy, Causality closure for a new class of curves in real-time calculus, Proceedings of the 1st International Workshop on Worst-Case Traversal Time, WCTT '11, pp.3-10, 2011.
DOI : 10.1145/2071589.2071590

URL : https://hal.archives-ouvertes.fr/hal-00648628

F. Baccelli and B. Blaszczyszyn, Stochastic Geometry and Wireless Networks: Volume I Theory, Foundations and Trends?? in Networking, vol.3, issue.3-4, pp.249-449, 2009.
DOI : 10.1561/1300000006

URL : https://hal.archives-ouvertes.fr/inria-00403039

F. Baccelli and B. Blaszczyszyn, Stochastic Geometry and Wireless Networks, Volume II -Applications . Foundations and Trends in Networking, pp.1-312, 2009.
DOI : 10.1561/1300000026

URL : https://hal.archives-ouvertes.fr/inria-00403040

F. Baccelli, G. Cohen, G. Y. Olsder, and J. Quadrat, Synchronization and linearity, 1992.

F. Baccelli, D. R. Mcdonald, and J. Reynier, A mean-field model for multiple TCP connections through a buffer implementing RED. Performance Evaluation Residuation of tropical series: rationality issues, CDC-ECC'11, pp.77-97, 2002.
URL : https://hal.archives-ouvertes.fr/inria-00072139

P. Barta, F. Nemeth, R. Szabo, and J. Biro, End-to-end delay bound calculation in generalized processor sharing networks, Proceedings. Sixth IEEE Symposium on Computers and Communications, 2001.
DOI : 10.1109/ISCC.2001.935388

L. Bisti, L. Lenzini, E. Mingozzi, and G. Stea, Estimating the Worst-case Delay in FIFO Tandems Using Network Calculus, Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools, pp.1-6710, 2008.
DOI : 10.4108/ICST.VALUETOOLS2008.4388

L. Bisti, L. Lenzini, E. Mingozzi, and G. Stea, DEBORAH: A Tool for Worst-Case Analysis of FIFO Tandems, Leveraging Applications of Formal Methods, Verification, and Validation, pp.152-168, 2010.
DOI : 10.1109/SURV.2010.020110.00019

B. Bollobás, Random Graphs, Studies in Advanced Mathematics. Cambridge Studies in Advanced Mathematics, 2001.

A. Bouillard, Composition of service curves in network calculus, Proceedings of the 1st International Workshop on Worst-Case Traversal Time, WCTT '11, 2011.
DOI : 10.1145/2071589.2071594

A. Bouillard, B. Cottenceau, B. Gaujal, L. Hardouin, S. Lagrange et al., COINC library: a toolbox for network calculus, ValueTools'09, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00858918

A. Bouillard, E. Faou, and M. Zavidovique, Fast weak KAM integrators for separable hamiltonian systems. preprint, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00743462

A. Bouillard, N. Farhi, and B. Gaujal, Packetization and Aggregate Scheduling, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00608852

A. Bouillard, N. Farhi, and B. Gaujal, Packetization and Packet Curves in Network Calculus, Proceedings of the 6th International Conference on Performance Evaluation Methodologies and Tools, 2012.
DOI : 10.4108/valuetools.2012.250208

URL : https://hal.archives-ouvertes.fr/hal-00780073

A. Bouillard, B. Gaujal, S. Lagrange, and . Thierry, Optimal routing for end-to-end guarantees: the price of multiplexing, Proceedings of the 2nd International ICST Conference on Performance Evaluation Methodologies and Tools, 2007.
DOI : 10.4108/valuetools.2007.1949

URL : https://hal.archives-ouvertes.fr/ensl-00151655

A. Bouillard, B. Gaujal, S. Lagrange, and . Thierry, Optimal routing for end-to-end guarantees using network calculus. Performance Evaluation, pp.11-12883, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00859086

A. Bouillard, S. Harr, and S. Rosario, Critical Paths in the Partial Order Unfolding of a Stochastic Petri Net, FORMATS'09, volume LNCS 5618, pp.43-57, 2009.
DOI : 10.1016/j.tcs.2006.01.015

URL : https://hal.archives-ouvertes.fr/inria-00407672

A. Bouillard, C. Jard, and A. Junier, Some synchronization issues in OSPF routing, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00840350

A. Bouillard, L. Jouhet, and . Thierry, Service curves in Network Calculus: dos and don'ts, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00431674

A. Bouillard, L. Jouhet, and . Thierry, Comparison of different classes of service curves in Network Calculus, WODES'10), pp.316-321, 2010.
DOI : 10.3182/20100830-3-DE-4013.00051

A. Bouillard, L. Jouhet, and . Thierry, Tight Performance Bounds in the Worst Case Analysis of Feed Forward Networks, INFOCOM'10, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00408717

A. Bouillard and A. Junier, Worst-case delay bounds with fixed priorities using network calculus, ValueTools'11, 2011.

A. Bouillard, A. Junier, and B. Ronot, Hidden anomaly detection in telecommunication networks
URL : https://hal.archives-ouvertes.fr/hal-00702587

A. Bouillard, A. Junier, and B. Ronot, Hidden anomaly detection in telecommunication networks, CNSM'12, pp.82-90, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00702587

A. Bouillard, A. Junier, and B. Ronot, Impact of rare alarms on event correlation, Proceedings of the 9th International Conference on Network and Service Management (CNSM 2013), 2013.
DOI : 10.1109/CNSM.2013.6727821

URL : https://hal.archives-ouvertes.fr/hal-00920685

A. Bouillard and J. L. Thierry, Computation of a (min,+) multi-dimensional convolution for end-to-end performance analysis., Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools, 2008.
DOI : 10.4108/ICST.VALUETOOLS2008.4349

A. Bouillard, L. T. Phan, and S. Chakraborty, Lightweight Modeling of Complex State Dependencies in Stream Processing Systems, 2009 15th IEEE Real-Time and Embedded Technology and Applications Symposium, pp.195-204, 2009.
DOI : 10.1109/RTAS.2009.27

URL : https://hal.archives-ouvertes.fr/inria-00429776

A. Bouillard, S. Rosario, A. Benveniste, and S. Haar, Monotonicity in Service Orchestrations, ICATPN'09, volume LNCS 5606, pp.263-282, 2009.
DOI : 10.1109/TSE.2004.11

URL : https://hal.archives-ouvertes.fr/inria-00638289

A. Bouillard and G. Stea, Exact Worst-case Delay for FIFO-multiplexing Tandems, Proceedings of the 6th International Conference on Performance Evaluation Methodologies and Tools, pp.158-167, 2012.
DOI : 10.4108/valuetools.2012.250090

URL : https://hal.archives-ouvertes.fr/hal-00778113

A. Bouillard and . Thierry, An algorithmic toolbox for network calculus. Discrete Event Dynamic Systems, pp.3-49, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00123643

M. Boyer and C. Fraboul, Tightening end to end delay upper bound for AFDX network calculus with rate latency FCFS servers using network calculus, WFCS'08, 2008.

M. Boyer, J. Migge, and M. Fumey, PEGASE - A Robust and Efficient Tool for Worst-Case Network Traversal Time Evaluation on AFDX, SAE Technical Paper Series, 2011.
DOI : 10.4271/2011-01-2711

M. Boyer, J. Migge, and M. Fumey, Experimental assessment of timing verification techniques for afdx, ERTSS'12, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01345472

M. Boyer, J. Migge, and N. Navet, An efficient and simple class of functions to model arrival curve of packetised flows, Proceedings of the 1st International Workshop on Worst-Case Traversal Time, WCTT '11, 2011.
DOI : 10.1145/2071589.2071595

M. Boyer, N. Navet, and M. Fumey, Experimental assessment of timing verification techniques for AFDX, ERTS'12, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01345472

M. Boyer, N. Navet, X. Olive, and . Thierry, The PEGASE Project: Precise and Scalable Temporal Analysis for Aerospace Communication Systems with Network Calculus, ISOLA'10, 2010.
DOI : 10.1016/j.peva.2005.10.003

URL : https://hal.archives-ouvertes.fr/inria-00551504

Y. Brenier, Un algorithme rapide pour le calcul de transofrméesde Legendre-Fenchel discrètes, C. R. Acad. Sci. Paris. Sér. I Math, vol.308, issue.20, pp.587-589, 1989.

E. Brugallé, Some aspects of tropical geometry, Eur. Math. Soc. Newsl, vol.83, pp.23-28

S. Chakraborty, L. T. Phan, and P. S. Thiagarajan, Event Count Automata: A State-Based Model for Stream Processing Systems, 26th IEEE International Real-Time Systems Symposium (RTSS'05), pp.87-98, 2005.
DOI : 10.1109/RTSS.2005.21

C. Chang, Stability, queue length, and delay of deterministic and stochastic queueing networks, IEEE Transactions on Automatic Control, vol.39, issue.5, pp.913-931, 1994.
DOI : 10.1109/9.284868

C. Chang, Performance Guarantees in Communication Networks, TNCS, 2000.

C. Chang, D. Lee, and Y. Jou, Load balanced Birkhoff-von Neumann switches with resequencing, IEEE Workshop on High Performance Switching and Routing, pp.276-280, 2001.
DOI : 10.1145/507553.507563

C. Chang, D. Lee, and Y. Jou, Load balanced Birkhoff???von Neumann switches, part I: one-stage buffering, Computer Communications, vol.25, issue.6, pp.611-622, 2002.
DOI : 10.1016/S0140-3664(01)00427-3

C. Chang, D. Lee, and C. Lien, Load balanced Birkhoff???von Neumann switches, part II: multi-stage buffering, Computer Communications, vol.25, issue.6, pp.623-634, 2002.
DOI : 10.1016/S0140-3664(01)00428-5

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.7.2094

E. M. Clarke, O. Grumberg, and D. A. Peled, Model Checking, 1999.

G. Contreras, R. Iturriaga, and H. Sanchez-morgado, Weak solutions of the Hamilton-Jacobi equation for time periodic Lagrangians, 2000.

R. L. Cruz, A calculus for network delay. I. Network elements in isolation, IEEE Transactions on Information Theory, vol.37, issue.1, pp.114-131, 1991.
DOI : 10.1109/18.61109

R. L. Cruz, A calculus for network delay. II. Network analysis, IEEE Transactions on Information Theory, vol.37, issue.1, pp.132-141, 1991.
DOI : 10.1109/18.61110

R. L. Cruz, Quality of service guarantees in virtual circuit switched networks, IEEE Journal on Selected Areas in Communications, vol.13, issue.6, pp.1048-1056, 1995.
DOI : 10.1109/49.400660

M. Draief and L. Massouli, Epidemics and Rumours in Complex Networks, 2010.
DOI : 10.1017/CBO9780511806018

N. G. Duffield, K. K. Ramakrishnan, and A. R. Reibman, SAVE: an algorithm for smoothed adaptive video over explicit rate networks, IEEE/ACM Transactions on Networking, vol.6, issue.6, pp.717-728, 1998.
DOI : 10.1109/90.748084

K. R. Duffy, Mean field markov models of wireless local area networks, Markov Processes and Related Fields, pp.295-328, 2010.

N. Farhi, H. Haj-salem, and J. Lebacque, Algebraic approach for performance bound calculus on transportation networks (road network calculus) Transportation Research, 2013.

A. Fathi, Weak KAM Theorem in Lagrangian Dynamics, preliminary version, 2005.

T. Ferrandiz, F. Frances, and C. Fraboul, A Network Calculus Model for SpaceWire Networks, 2011 IEEE 17th International Conference on Embedded and Real-Time Computing Systems and Applications, pp.295-299, 2011.
DOI : 10.1109/RTCSA.2011.42

M. Fidler, Survey of deterministic and stochastic service curve models in the network calculus, IEEE Communications Surveys & Tutorials, vol.12, issue.1, 2010.
DOI : 10.1109/SURV.2010.020110.00019

M. Fidler and V. Sander, A parameter based admission control for differentiated services networks, Computer Networks, vol.44, issue.4, pp.463-479, 2004.
DOI : 10.1016/j.comnet.2003.12.004

F. Frances, C. Fraboul, and J. Grieu, Using network calculus to optimize AFDX network, ERTS'06, 2006.

M. Franceschetti and R. Meester, Random networks for Communication: from statistical physics to information systems. Series in Statistical and probabilistic mathematics, 2008.
DOI : 10.1017/CBO9780511619632

L. T. Gangadharan, D. Phan, S. Chakraborty, R. Zimmermann, and I. Lee, Video Quality Driven Buffer Sizing via Frame Drops, 2011 IEEE 17th International Conference on Embedded and Real-Time Computing Systems and Applications, pp.319-328, 2011.
DOI : 10.1109/RTCSA.2011.49

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.650.7040

M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP- Completeness, 1979.

N. Gast, B. Gaujal, and J. Boudec, Mean Field for Markov Decision Processes: From Discrete to Continuous Optimization, IEEE Transactions on Automatic Control, vol.57, issue.9, pp.2266-2280, 2012.
DOI : 10.1109/TAC.2012.2186176

URL : https://hal.archives-ouvertes.fr/hal-00473005

S. Gaubert and J. Mairesse, Idempotency, chapter Task Resource Models and (max,+) Automata, 1998.
DOI : 10.1017/cbo9780511662508.009

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.53.9408

S. Gaubert and J. Mairesse, Modeling and analysis of timed Petri nets using heaps of pieces, IEEE Transactions on Automatic Control, vol.44, issue.4, pp.683-697, 1999.
DOI : 10.1109/9.754807

URL : https://hal.archives-ouvertes.fr/hal-00165813

N. Gollan, F. A. Zdarsky, I. Martinovic, and J. B. Schmitt, The DISCO network calculator, Proc. of MMB, 2008.

G. Jiang and C. Shu, Efficient Implementation of Weighted ENO Schemes, Journal of Computational Physics, vol.126, issue.1, pp.202-228, 1996.
DOI : 10.1006/jcph.1996.0130

Y. Jiang and Y. Liu, Stochastic Network Calculus, 2008.

L. Jouhet, Algorithmique du Network Calculus. thèse, Ecole normale supérieure de lyon, 2012.
URL : https://hal.archives-ouvertes.fr/tel-00776381

G. Kemayo, F. Ridouard, H. Bauer, and P. Richard, Optimism due to serialization in the trajectory approach for switched ethernet networks, Proc. of the 7th Junior Researcher Workshop on Real- Time Computing, 2013.

G. Kemayo, F. Ridouard, H. Bauer, and P. Richard, Optimistic problems in the trajectory approach in FIFO context, 2013 IEEE 18th Conference on Emerging Technologies & Factory Automation (ETFA), p.2013, 2013.
DOI : 10.1109/ETFA.2013.6648054

D. Kirsten and S. Lombardy, Deciding unambiguity and sequentiality of polynomially ambiguous min-plus automata, STACS, pp.589-600, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00360205

I. Klimann, S. Lombardy, J. Mairesse, and C. Prieur, Deciding unambiguity and sequentiality from a finitely ambiguous max-plus automaton, Theoretical Computer Science, vol.327, issue.3, pp.349-373, 2004.
DOI : 10.1016/j.tcs.2004.02.049

URL : https://hal.archives-ouvertes.fr/hal-00174171

J. Boudec, D. Mcdonald, and J. Mundinger, A Generic Mean Field Convergence Result for Systems of Interacting Objects, Fourth International Conference on the Quantitative Evaluation of Systems (QEST 2007), pp.3-18, 2007.
DOI : 10.1109/QEST.2007.8

J. Boudec and P. Thiran, Network Calculus: A Theory of Deterministic Queuing Systems for the Internet, volume LNCS 2050, 2001.

E. , L. Corronc, B. Cottenceau, and L. Hardouin, Container of (min,+)-linear systems, Journal of Discrete Event Dynamic Systems, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00846229

L. Lenzini, L. Martorini, E. Mingozzi, and G. Stea, Tight end-to-end per-flow delay bounds in FIFO multiplexing sink-tree networks, Performance Evaluation, vol.63, issue.9-10, pp.9-10956, 2006.
DOI : 10.1016/j.peva.2005.10.003

L. Lenzini, E. Mingozzi, and G. Stea, End-to-end Delay Bounds in FIFO-multiplexing Tandems, Proceedings of the 2nd International ICST Conference on Performance Evaluation Methodologies and Tools, 2007.
DOI : 10.4108/valuetools.2007.1912

L. Lenzini, E. Mingozzi, and G. Stea, A methodology for computing end-to-end delay bounds in FIFO-multiplexing tandems. Performance Evaluation, pp.11-12922, 2008.

D. V. Lindley, The theory of queues with a single server, Mathematical Proceedings of the Cambridge Philosophical Society, vol.24, issue.02, pp.277-289
DOI : 10.1007/BF01194620

S. Martin and P. Minet, Worst case end-to-end response times of flows scheduled with FP/FIFO, International Conference on Networking, International Conference on Systems and International Conference on Mobile Communications and Learning Technologies (ICNICONSMCL'06), p.54, 2006.
DOI : 10.1109/ICNICONSMCL.2006.231

J. M. Mcmanus and K. W. Ross, Video-on-demand over ATM: constant-rate transmission and transport, IEEE Journal on Selected Areas in Communications, vol.14, issue.6, pp.1087-1098, 2006.
DOI : 10.1109/49.508280

F. Nemeth, P. Barta, R. Szabo, and J. Biro, Network internal traffic characterization and end-to-end delay bound calculus for generalized processor sharing scheduling discipline, Computer Networks, vol.48, issue.6, pp.910-940, 2005.
DOI : 10.1016/j.comnet.2004.11.022

A. K. Parekh and R. G. Gallager, A generalized processor sharing approach to flow control in integrated services networks: the single-node case, IEEE/ACM Transactions on Networking, vol.1, issue.3, pp.344-357, 1993.
DOI : 10.1109/90.234856

A. K. Parekh and R. G. Gallager, A generalized processor sharing approach to flow control in integrated services networks: the multiple node case, IEEE/ACM Transactions on Networking, vol.2, issue.2, pp.137-150, 1994.
DOI : 10.1109/90.298432

L. T. Phan, S. Chakraborty, and P. S. Thiagarajan, A Multi-mode Real-Time Calculus, 2008 Real-Time Systems Symposium, pp.59-69, 2008.
DOI : 10.1109/RTSS.2008.47

L. T. Phan, S. Chakraborty, P. S. Thiagarajan, and L. Thiele, Composing functional and statebased performance models for analyzing heterogeneous real-time systems, RTSS, 2007.
DOI : 10.1109/rtss.2007.46

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.124.3709

F. Plateau, Modèle n-synchrone pour la programmation de réseaux de KahnàKahnà mémoire bornée, 2010.

Y. Qian, Z. Lu, and W. Dou, Analysis of worst-case delay bounds for best-effort communication in wormhole networks on chip, 2009 3rd ACM/IEEE International Symposium on Networks-on-Chip, pp.44-53, 2009.
DOI : 10.1109/NOCS.2009.5071444

H. Schioler, J. J. Jessen, J. Dalsgaard, and K. G. Larsen, Network calculus for real time analysis of embedded systems with cyclic task dependencies, Proc. of Computers and Their Applications, 2005.

H. Schioler, H. Schwefel, and M. B. Hansen, CyNC: A MATLAB/SimuLink Toolbox for Network Calculus, Proceedings of the 2nd International ICST Conference on Performance Evaluation Methodologies and Tools, 2007.
DOI : 10.4108/valuetools.2007.1804

J. B. Schmitt, N. Gollan, S. Bondorf, and I. Martinovic, Pay bursts only once holds for (some) non-FIFO systems, 2011 Proceedings IEEE INFOCOM, 2011.
DOI : 10.1109/INFCOM.2011.5935002

J. B. Schmitt and F. A. Zdarsky, The DISCO network calculator, Proceedings of the 1st international conference on Performance evaluation methodolgies and tools , valuetools '06, 2006.
DOI : 10.1145/1190095.1190105

J. B. Schmitt, F. A. Zdarsky, and M. Fidler, Delay Bounds under Arbitrary Multiplexing: When Network Calculus Leaves You in the Lurch..., IEEE INFOCOM 2008, The 27th Conference on Computer Communications, 2008.
DOI : 10.1109/INFOCOM.2008.228

J. B. Schmitt, F. A. Zdarsky, and I. Martinovic, Improving performance bounds in feed-forward networks by paying multiplexing only once, Proc. of MMB, 2008.

A. Schrijver, Theory of Linear and Integer Programming, 1998.

W. M. Sofack and M. Boyer, Non preemptive static priority with network calculus, ETFA2011, pp.1-8, 2011.
DOI : 10.1109/ETFA.2011.6058996

W. M. Sofack and M. Boyer, Non preemptive static priority with network calculus, ETFA2011, pp.258-272, 2012.
DOI : 10.1109/ETFA.2011.6058996

L. Thiele and N. Stoimenov, Modular performance analysis of cyclic dataflow graphs, Proceedings of the seventh ACM international conference on Embedded software, EMSOFT '09, pp.127-136, 2009.
DOI : 10.1145/1629335.1629353

E. Wandeler, Modular Performance Analysis and Interface-Based Design for Embedded Real-Time Systems, 2006.

E. Wandeler and L. Thiele, Real-Time Calculus (RTC) Toolbox, 2006.

E. Wandeler, L. Thiele, M. Verhoef, and P. Lieverse, System architecture evaluation using modular performance analysis: a case study, International Journal on Software Tools for Technology Transfer, vol.21, issue.5, pp.649-667, 2006.
DOI : 10.1007/s10009-006-0019-5