A particle system in interaction with a rapidly varying environment: Mean field limits and applications

Networks and Heterogeneous Media

Volumn 5, Issue 1, 2010, Pages 31-62

  Bordenave, Charles ^a   McDonald, David ^b   Proutière, Alexandre ^c  

^a UNIVERSITÉ DE TOULOUSE   (France)

^b UNIVERSITY OF OTTAWA   (Canada)

^c MICROSOFT RESEARCH   (United States)

Author keywords

Mean field analysis; Particle system

Indexed keywords

EID: 79951556098     PISSN: 15561801     EISSN: 1556181X     Source Type: Journal    
DOI: 10.3934/nhm.2010.5.31     Document Type: Article

References (27)

1. "IEEE Standard for Information Technology, Telecommunications and Information Exchange Between Systems," Local and metropolitan area networks, IEEE std., 1983.
2. "IEEE Standard for Wireless LAN Medium Access Protocol and Physical Layer Specifica- tions," IEEE std., August 1999.
3. N. Abramson, "The ALOHA System - Another Alternative for Computer Communications," Proc. of AFIPS press, 37, 1970.
4. F. Baccelli and C. Bordenave, The radial spanning tree of a Poisson point process, Ann. Appl. Probab., 17 (2007), 305-359.
5. F. Baccelli and P. Brémaud, "Elements of Queueing Theory: Palm-Martingale Calculus and Stochastic Recurrences," Springer-Verlag, New York, 1994.
6. A. Bensoussan, J-L. Lions and G. Papanicolaou, "Asymptotic Analysis for Periodic Structures. Studies in Mathematics and its Applications," 5, North-Holland Publishing Co., Amsterdam- New York, 1978.
7. G. Bianchi, Performance analysis of the IEEE 802.11 distributed coordination function, IEEE Journal on Selected Areas in Communications, 18 (2000), 535-547.
8. P. Billingsley, "Convergence of Probability Measures," 2nd ed. Wiley, New York, 1999.
9. C. Bordenave, D. McDonald and A. Proutiere, "Random Multi-Access Algorithms: A Mean Field Analysis," Proc. of the 43th Allerton conference on communication, control, and computing, 2005.
10. C. Bordenave, D. McDonald and A. Proutiere, Asymptotic stability region of slotted-Aloha, preprint, arXiv:0809.5023.
11. S. Cordier, L. Pareschi and G. Toscani, On a kinetic model for a simple market economy, Journal of Statistical Physics, 120 (2005), 253-277.
12. D. A. Dawson, Critical dynamics and fluctuations for a mean-field model of cooperative behavior, Journal of Statistical Physics, 31 (1983), 29-85.
13. P. Donnelly and T. Kurtz, Particle representations for measure-valued population models, Annals of Probability, 27 (1999), 166-205.
14. M. Durvy and P. Thiran, "A Packing Approach to Compare Slotted and Non-slotted Medium Access Control," Proc. of IEEE Infocom, 2006.
15. S. Ethier and T. Kurtz, "Markov Processes," Wiley, New york, 1985.
16. W. Feller, "Introduction to Probability Theory and its Applications," Vol. 2, Wiley, New York, 1971.
17. C. Graham and S. Méléard, Stochastic particle approximations for generalized Boltzmann models and convergence estimates, Annals of Probability, 28 (1997), 115-132.
18. C. Graham, Chaoticity on path space for a queueing network with selection of the shortest queue among several, Journal of Applied Probability, 37 (2000), 198-211.
19. L. Jiang and S. C. Liew, "Improving Throughput and Fairness by Reducing Exposed and Hidden Nodes in 802.11 Networks," IEEE Transactions on Mobile Computing, January 2008.
20. Y. Karatzas, M. Shubik and W. Sudderth, A strategic market game with secured lending, Journal of Mathematical Economics, 28 (1997), 207-247.
21. F. P. Kelly, Stochastic models of computer communication systems, Journal of the Royal Statistical Society, 47 (1985), 379-395, 415-428.
22. F. P. Kelly, Loss networks, The Annals of Applied Probability, 1 (1991), 319-378.
23. T. G. Kurtz, "Averaging for Martingale Problems and Stochastic Approximation," Lecture Notes in Control and Information Sciences 177, Springer Berlin / Heidelberg, 1992.
24. S. Meyn and R. Tweedie, "Markov Chains and Stochastic Stability," Springer-Verlag, New York, 1993.
25. A. Müller and D. Stoyan, "Comparison Methods for Stochastic Models and Risks," Wiley, New York, 2002.
26. T. Shiga and H. Tanaka, Central limit theorem for a system of Markovian particles with mean field interaction, Z. Wahrscheinlichkeitsth., 69 (1985), 439-459.
27. A. S. Sznitman, "Propagation of Chaos," Ecole d'été de probabilités de Saint-Flour XIX, lecture notes in Maths 1464, Springer, Berlin, 1991.