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1.  EPFL, I&C, CH1015 Lausanne, Switzerland 
References:
[1] 
M. Benaïm, Recursive algorithms, urn processes and chaining number of chain recurrent sets, Ergodic Theory and Dynamical System, 18 (1998), 5387. doi: 10.1017/S0143385798097557. 
[2] 
M. Benaïm and J.Y. Le Boudec, A class of mean field interaction models for computer and communication systems, Performance Evaluation, 65 (2008), 823838. 
[3] 
M. Benaïm and J. Weibull, Deterministic approximation of stochastic evolution, Econometrica, 71 (2003), 873904. doi: 10.1111/14680262.00429. 
[4] 
M. Benaïm, Dynamics of stochastic approximation algorithms, in "Séminaire de Probabilités XXXIII," Lecture Notes in Math., 1709, Springer, Berlin, (1999), 168. doi: 10.1007/BFb0096509. 
[5] 
G. Bianchi, IEEE 802.11Saturation throughput analysis, IEEE Communications Letters, 2 (1998), 318320. doi: 10.1109/4234.736171. 
[6] 
C. Bordenave, D. McDonald and A. Proutière, A particle system in interaction with a rapidly varying environment: Mean field limits and applications, Networks and Heterogeneous Media, 5 (2010), 3162. doi: 10.3934/nhm.2010.5.31. 
[7] 
J. A. M Borghans, R. J. De Boer, E. Sercarz and V. Kumar, T cell vaccination in experimental autoimmune encephalomyelitis: A mathematical model, The Journal of Immunology, 161 (1998), 10871093. 
[8] 
L. Bortolussi, J.Y. Le Boudec, D. Latella and M. Massink, Revisiting the limit behaviour of "El Botellon," Technical Report EPFLREPORT179935, EPFL, 2012. Available from: https://infoscience.epfl.ch/record/179935. 
[9] 
V. Capasso and D. Bakstein, "An Introduction to ContinuousTime Markov Processes. Theory, Models, and Applications to Finance, Biology, and Medicine," Modeling and Simulation in Science, Engineering and Technology, Birkhäuser, Boston, Inc., Boston, MA, 2005. 
[10] 
J.W. Cho, J.Y. Le Boudec and Y. Jiang, On the asymptotic validity of the fixed point equation and decoupling assumption for analyzing the 802.11 MAC protocol, IEEE Transactions on Information Theory, 58 (2012), 68796893. doi: 10.1109/TIT.2012.2208582. 
[11] 
J.P. Crametz and P. J. Hunt, A limit result respecting graph structure for a fully connected loss network with alternative routing, The Annals of Applied Probability, 1 (1991), 436444. doi: 10.1214/aoap/1177005876. 
[12] 
S. N. Ethier and T. G. Kurtz, "Markov Processes. Characterization and Convergence," Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons, Inc., New York, 1986. doi: 10.1002/9780470316658. 
[13] 
C. Graham and S. Méléard, Propagation of chaos for a fully connected loss network with alternate routing, Stochastic Processes and Their Applications, 44 (1993), 159180. doi: 10.1016/03044149(93)900434. 
[14] 
F. P. Kelly, "Reversibility and Stochastic Networks," Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, Ltd., Chichester, 1979. 
[15] 
F. P. Kelly, Loss networks, The Annals of Applied Probability, 1 (1991), 319378. doi: 10.1214/aoap/1177005872. 
[16] 
A. Kumar, E. Altman, D. Miorandi and M. Goyal, New insights from a fixedpoint analysis of single cell ieee 802.11 wlans, IEEE/ACM Transactions on Networking, 15 (2007), 588601. 
[17] 
T. G. Kurtz, Solutions of ordinary differential equations as limits of pure jump Markov processes, Journal of Applied Probability, 7 (1979), 4958. doi: 10.2307/3212147. 
[18] 
Thomas G. Kurtz, "Approximation of Population Processes," CBMSNSF Regional Conference Series in Applied Mathematics, 36, SIAM, Philadelphia, Pa., 1981. 
[19] 
J.Y. Le Boudec, D. McDonald and J. Mundinger, A generic mean field convergence result for systems of interacting objects, in "Fourth International Conference on the Quantitative Evaluation of Systems" (QEST 2007), IEEE, (2007), 318. doi: 10.1109/QEST.2007.8. 
[20] 
J.Y. Le Boudec, "Performance Evaluation of Computer and Communication Systems," EPFL Press, Lausanne, Switzerland, 2010. Available from: http://perfeval.epfl.ch. 
[21] 
J.Y. Le Boudec, Interinput and interoutput time distribution in classical productform networks, IEEE Transactions on Software Engineering, 6 (1987), 756759. 
[22] 
M. Massink, D. Latella, A. Bracciali and J. Hillston, Modelling nonlinear crowd dynamics in bioPEPA, in "Fundamental Approaches to Software Engineering," Lecture Notes in Computer Science, 6603, Springer Berlin Heidelberg, (2011), 96110. doi: 10.1007/9783642198113_8. 
[23] 
R. Merz, J.Y. Le Boudec and S. Vijayakumaran, Effect on network performance of common versus private acquisition sequences for impulse radio UWB networks, in "IEEE International Conference on UltraWideband" (ICUWB 2006), IEEE, (2006), 375380. doi: 10.1109/ICU.2006.281579. 
[24] 
J. E. Rowe and R. Gomez, El Botellón: Modeling the movement of crowds in a city, Complex Systems, 14 (2003), 363370. 
[25] 
W. H. Sandholm, "Population Games and Evolutionary Dynamics," Economic Learning and Social Evolution, MIT press, Cambridge, MA, 2010. 
show all references
References:
[1] 
M. Benaïm, Recursive algorithms, urn processes and chaining number of chain recurrent sets, Ergodic Theory and Dynamical System, 18 (1998), 5387. doi: 10.1017/S0143385798097557. 
[2] 
M. Benaïm and J.Y. Le Boudec, A class of mean field interaction models for computer and communication systems, Performance Evaluation, 65 (2008), 823838. 
[3] 
M. Benaïm and J. Weibull, Deterministic approximation of stochastic evolution, Econometrica, 71 (2003), 873904. doi: 10.1111/14680262.00429. 
[4] 
M. Benaïm, Dynamics of stochastic approximation algorithms, in "Séminaire de Probabilités XXXIII," Lecture Notes in Math., 1709, Springer, Berlin, (1999), 168. doi: 10.1007/BFb0096509. 
[5] 
G. Bianchi, IEEE 802.11Saturation throughput analysis, IEEE Communications Letters, 2 (1998), 318320. doi: 10.1109/4234.736171. 
[6] 
C. Bordenave, D. McDonald and A. Proutière, A particle system in interaction with a rapidly varying environment: Mean field limits and applications, Networks and Heterogeneous Media, 5 (2010), 3162. doi: 10.3934/nhm.2010.5.31. 
[7] 
J. A. M Borghans, R. J. De Boer, E. Sercarz and V. Kumar, T cell vaccination in experimental autoimmune encephalomyelitis: A mathematical model, The Journal of Immunology, 161 (1998), 10871093. 
[8] 
L. Bortolussi, J.Y. Le Boudec, D. Latella and M. Massink, Revisiting the limit behaviour of "El Botellon," Technical Report EPFLREPORT179935, EPFL, 2012. Available from: https://infoscience.epfl.ch/record/179935. 
[9] 
V. Capasso and D. Bakstein, "An Introduction to ContinuousTime Markov Processes. Theory, Models, and Applications to Finance, Biology, and Medicine," Modeling and Simulation in Science, Engineering and Technology, Birkhäuser, Boston, Inc., Boston, MA, 2005. 
[10] 
J.W. Cho, J.Y. Le Boudec and Y. Jiang, On the asymptotic validity of the fixed point equation and decoupling assumption for analyzing the 802.11 MAC protocol, IEEE Transactions on Information Theory, 58 (2012), 68796893. doi: 10.1109/TIT.2012.2208582. 
[11] 
J.P. Crametz and P. J. Hunt, A limit result respecting graph structure for a fully connected loss network with alternative routing, The Annals of Applied Probability, 1 (1991), 436444. doi: 10.1214/aoap/1177005876. 
[12] 
S. N. Ethier and T. G. Kurtz, "Markov Processes. Characterization and Convergence," Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons, Inc., New York, 1986. doi: 10.1002/9780470316658. 
[13] 
C. Graham and S. Méléard, Propagation of chaos for a fully connected loss network with alternate routing, Stochastic Processes and Their Applications, 44 (1993), 159180. doi: 10.1016/03044149(93)900434. 
[14] 
F. P. Kelly, "Reversibility and Stochastic Networks," Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, Ltd., Chichester, 1979. 
[15] 
F. P. Kelly, Loss networks, The Annals of Applied Probability, 1 (1991), 319378. doi: 10.1214/aoap/1177005872. 
[16] 
A. Kumar, E. Altman, D. Miorandi and M. Goyal, New insights from a fixedpoint analysis of single cell ieee 802.11 wlans, IEEE/ACM Transactions on Networking, 15 (2007), 588601. 
[17] 
T. G. Kurtz, Solutions of ordinary differential equations as limits of pure jump Markov processes, Journal of Applied Probability, 7 (1979), 4958. doi: 10.2307/3212147. 
[18] 
Thomas G. Kurtz, "Approximation of Population Processes," CBMSNSF Regional Conference Series in Applied Mathematics, 36, SIAM, Philadelphia, Pa., 1981. 
[19] 
J.Y. Le Boudec, D. McDonald and J. Mundinger, A generic mean field convergence result for systems of interacting objects, in "Fourth International Conference on the Quantitative Evaluation of Systems" (QEST 2007), IEEE, (2007), 318. doi: 10.1109/QEST.2007.8. 
[20] 
J.Y. Le Boudec, "Performance Evaluation of Computer and Communication Systems," EPFL Press, Lausanne, Switzerland, 2010. Available from: http://perfeval.epfl.ch. 
[21] 
J.Y. Le Boudec, Interinput and interoutput time distribution in classical productform networks, IEEE Transactions on Software Engineering, 6 (1987), 756759. 
[22] 
M. Massink, D. Latella, A. Bracciali and J. Hillston, Modelling nonlinear crowd dynamics in bioPEPA, in "Fundamental Approaches to Software Engineering," Lecture Notes in Computer Science, 6603, Springer Berlin Heidelberg, (2011), 96110. doi: 10.1007/9783642198113_8. 
[23] 
R. Merz, J.Y. Le Boudec and S. Vijayakumaran, Effect on network performance of common versus private acquisition sequences for impulse radio UWB networks, in "IEEE International Conference on UltraWideband" (ICUWB 2006), IEEE, (2006), 375380. doi: 10.1109/ICU.2006.281579. 
[24] 
J. E. Rowe and R. Gomez, El Botellón: Modeling the movement of crowds in a city, Complex Systems, 14 (2003), 363370. 
[25] 
W. H. Sandholm, "Population Games and Evolutionary Dynamics," Economic Learning and Social Evolution, MIT press, Cambridge, MA, 2010. 
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