AIMD algorithms and exponential functionals

Annals of Applied Probability

Volumn 14, Issue 1, 2004, Pages 90-117

  Guillemin, Fabrice ^a   Robert, Philippe ^b,c   Zwart, Bert ^b,c  

^a ORANGE LABS   (France)

^b INRIA   (France)

^c EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Autoregressive processes; Communication protocols; Compound Poisson processes; Exponential functionals; q hypergeometric functions

Indexed keywords

EID: 26844563763     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/aoap/1075828048     Document Type: Article

References (29)

1. ALDOUS, D. (1989). Probability Approximations via the Poisson Clumping Heuristic. Springer, New York.
2. ALTMAN, E., AVRACHENKO, K., BARAKAT, C. and NUN̄EZ-QUEIJA, R. (2001). State dependent A//G/1 type queueing analysis for congestion control in data networks. In Infocom 2001. IEEE, New York.
3. ANDREWS, G. E., ASKEY, R. and ROY, R. (1999). Special Functions. Cambridge Univ. Press.
4. BERTOIN, J., BIANE, P. and YOR, M. (2002). Poissonian exponential functional, q-series, (q-integrals and the moment problem for log-normal distributions. Technical Report PMA-705, Laboratoire de Probabilités, Univ. Paris 6.
5. BERTOIN, J. and YOR, M. (2001). On the entire moments of self-similar Markov processes and exponential functionals of Lévy processes. Technical Report PMA-702, Laboratoire de Probabilités, Univ. Paris 6.
6. BOLOT, J. (1993). End-to-end packet delay and loss behavior in the Internet. In ACM SIGCOMM'93 289-298. ACM Press, New York.
7. CARMONA, P., PETIT, F. and YOR, M. (1997). On the distribution and asymptotic results for exponential functionals of Lévy processes. In Exponential Functionals and Principal Values Related to Brownian Motion (M. Yor, ed.) 73-130. Rev. Mat. Iberoam., Madrid.
8. DUMAS, V., GUILLEMIN, F. and ROBERT, P. (2002). A Markovian analysis of Additive-Increase Multiplicative-Decrease (AIMD) algorithms. Adv. in Appl. Probab. 34 85-111.
9. FELLER, W. (1971). An Introduction to Probability Theory and Its Applications, 2nd ed. Wiley, New York.
10. FERGUSON, T. S. (1972). Lose a dollar or double your fortune. Proc. Sixth Berkeley Symp. Math. Statist. Probab. 3 657-666. Univ. California Press, Berkeley.
11. FLAJOLET, P., GOURDON, X. and DUMAS, P. (1995). Mellin transforms and asymptotics: Harmonic sums. Theoret. Comput. Sci. 144 3-58.
12. FLOYD, S. (1991). Connections with multiple congested gateways in packet-switched networks 1: One way traffic. Computer Comm. Rev. 21 30-47.
13. GASPER, G. and RAHMAN, M. (1990). Basic Hypergeometric Series. Cambridge Univ. Press.
14. HARRISON, J. M. (1977). Ruin problems with compounding assets. Stochastic Process. Appl. 5 67-79.
15. JACOBSON, V. (1988). Congestion avoidance and control. In SIGCOMM'88 Symposium: Communications Architectures and Protocols. ACM, New York.
16. KINGMAN, J. F. C. (1993). Poisson Processes. Clarendon Press, New York.
17. KOORNWINDER, T. H. (1994). q-special functions, a tutorial. In Representation of Lie Groups and Quantum Groups (V. Baldoni and M. A. Picardello, eds.) 46-128. Longman, New York.
18. MISRA, V., GONG, W. and TOWSLEY, D. (1999). Stochastic differential equation modeling and analysis of TCP windowsize behavior. In Performance'99.
19. NEVEU, J. (1977). Processus ponctuels. École d'Été de Probabilités de Saint-Flour VI. Lecture Notes in Math. 598 249-445. Springer, Berlin.
20. OTT, T. J., KEMPERMAN, J. H. B. and MATHIS, M. (1996). The stationary behavior of ideal TCP congestion avoidance. Unpublished manuscript.
21. PADHYE, J., FIROIU, V., TOWSLEY, D. and KUROSE, J. (1998). Modeling TCP throughput: A simple model and its empirical validation. In ACM Sigcomm'98. ACM, New York.
22. PAXSON, V. (1999). End-to-end internet packet dynamics. IEEE/ACM Trans. Networking 7 277-292.
23. STEVENS, W. R. (1994). TCP-IP Illustrated I: The Protocols. Addison-Wesley, Reading, MA.
24. STOYAN, D. (1983). Comparison Methods for Queues and Other Stochastic Models. Wiley, New York.
25. YAJNIK, M., KUROSE, J. and TOWSLEY, D. (1995). Packet loss correlation in the MBone multicast network experimental measurements and Markov chain models. Technical Report UM-CS-1995-115, Univ. Massachusetts, Amherst.
26. YOR, M. (1992). Some Aspects of Brownian Motion. Part I. Some Special Functionals. Birkhäuser, Basel.
27. YOR, M. (1997). Some Aspects of Brownian motion. Part II. Some Recent Martingale Problems. Birkhäuser, Basel.
28. YOR, M. (2001). Exponential Functionals of Brownian Motion and Related Processes. Springer, Berlin.
29. ZHANG, Y., PAXSON, V. and SHENKER, S. (2000). The stationarity of internet path properties: Routing, loss, and throughput. Technical report ACIRI.