A stochastic model of TCP/IP with stationary random losses

IEEE/ACM Transactions on Networking

Volumn 13, Issue 2, 2005, Pages 356-369

  Altman, Eitan ^a   Avrachenkov, Konstantin ^a   Barakat, Chadi ^a  

^a INRIA   (France)

Author keywords

Fluid model; Markov arrival process; Stationary ergodic losses; TCP IP

Indexed keywords

CONGESTION CONTROL (COMMUNICATION); CORRELATION METHODS; DATA COMMUNICATION SYSTEMS; INTERNET; MARKOV PROCESSES; MATHEMATICAL MODELS;

FLUID MODEL; MARKOV ARRIVAL PROCESS; STATIONARY ERGODIC LOSSES;

NETWORK PROTOCOLS;

EID: 18844364753     PISSN: 10636692     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNET.2005.845536     Document Type: Article

References (41)

1. M. Allman, H. Balakrishnan, and S. Floyd, "Enhancing TCP's loss recovery using limited transmit," RFC 3042, Jan. 2001.
2. E. Altman, K. Avratchenkov, and C. Barakat, "TCP in presence of bursty losses," presented at the ACM SIGMETRICS, Santa Clara, CA, Jun. 2000. An extended version has appeared in Perform. Eval., vol. 42, no. 2-3, pp. 129-147, Oct. 2000.
3. E. Altman, K. Avranchenkov, and C. Barakat, "A stochastic model for TCP/ IP with stationary random losses," presented at the ACM SIGCOMM, Stockholm, Sweden, Aug. 2000.
4. E. Altman, K. Avrachenkov, C. Barakat, and R. N. Queija, "State-dependent M/G/1 type queueing analysis for congestion control in data networks," in IEEE INFOCOM, vol. 3, Apr. 2001, pp. 1350-1359.
5. E. Altman, K. Avrachenkov, C. Barakat, and R. N. Queija, "TCP modeling in the presence of nonlinear window growth," presented at the Int. Teletraffic Congr. (ITC-i7), Salvador da Bahia, Brazil, 2001, pp. 883-894.
6. S. Asmussen and G. Koole, "Marked point processes as limits of Markovian arrival streams," J. Appl. Prob., vol. 30. pp. 365-372, 1993.
7. F. Baccelli and P. Bremaud, Elements of Queueing Theory: Palm-Martingale Calculus and Stochastic Recurrences. New York: Springer-Verlag, 1994.
8. C. Barakat, "TCP modeling and validation," IEEE Network, vol. 15, no. 3, pp. 38-47, May 2001.
9. C. Barakat and A. Al Fawal, "Analysis of link-level hybrid FEC /ARQ-SR for wireless links and long-lived TCP traffic," Perform. Eval. J., vol. 57, no. 4, pp. 423-500, Aug. 2004.
10. R. Bellman, Introduction to Matrix Analysis. New York: McGraw-Hill, 1960.
11. A. A. Borovkov and S. G. Foss, "Stochastically recursive sequences and their generalizations," Siberian Adv. Math., vol. 2, no. 1, pp. 16-81, 1992.
12. n with stationary coefficients," Adv. Appl. Prob., vol. 18, pp. 211-220, 1986.
13. K. Fall and S. Floyd, "Simulation-based comparisons of Tahoe, Reno, and SACK TCP," ACM Comput. Commun. Rev., vol. 26, no. 3, pp. 5-21, Jul. 1996.
14. W. Fischer and K. Meier-Hellstern, "The Markov-modulated Poisson process (MMPP) cookbook," Perform. Eval., vol. 18, pp. 149-171, 1992.
15. S. Floyd, "Connections with multiple congested gateways in packet-switched networks - Part 1: One-way traffic," ACM Comput. Commun. Rev., vol. 21, no. 5, pp. 30-47, Oct. 1991.
16. S. Floyd and K. Fall, "Promoting the use of end-to-end congestion control in the internet," IEEE/ACM Trans. Netw., vol. 7, no. 4, pp. 458-472, Aug. 1999.
17. S. Floyd, M. Handley, and J. Padhye, "Equation-based congestion control for unicast applications: the extended version," presented at the ACM SIGCOMM, Stockholm, Sweden, Aug. 2000.
18. P. Glasserman and D. D. Yao, "Stochastic vector difference equations with stationary coefficients," J. Appl. Prob., vol. 32, pp. 851-866, 1995.
19. J. J. Hunter, "On the moments of Markov renewal processes," Adv. Appl. Prob., vol. 1, pp. 188-210, 1969.
20. "Allowable Error Performance for a Hypothetical Reference Digital Path Operating at or Above the Primary Rate," ITU-R, Recommendation S.1062-1, 1994-1995.
21. V. Jacobson, "Congestion avoidance and control," presented at the ACM SIGCOMM, Stanford, CA, Aug. 1988.
22. S. H. Kang, Y. H. Kim, D. K. Sung, and B. D. Choi, "An application of Markovian Arrival Process (MAP) to modeling superposed ATM cell streams," IEEE Trans. Commun., vol. 50, no. 4, pp. 633-642, Apr. 2002.
23. A. Kumar, "Comparative performance analysis of versions of TCP in a local network with a lossy link," IEEE/ACM Trans. Netw., vol. 6, no. 4, pp. 485-498, Aug. 1998.
24. T. V. Lakshman and U. Madhow, "The performance of TCP/IP for networks with high bandwidth-delay products and random loss," IEEE/ACM Trans. Netw., vol. 5, no. 3, pp. 336-350, Jun. 1997.
25. R. Loynes, "The stability of a queue with nonindependent inter-arrival and service times," Proc. Cambr. Phil. Soc., vol. 58, no. 3, pp. 497-520, 1962.
26. D. M. Lucantoni, K. S. Meier-Hellstern, and M. F. Neuts, "A single-server queue with server vacations and a class of nonrenewal arrival processes," Adv. Appl. Prob., vol. 22, pp. 676-705, 1990.
27. M. Mathis, J. Mahdavi, S. Floyd, and A. Romanow, "TCP Selective Acknowledgment Options," RFC 2018, Oct. 1996.
28. M. Mathis, J. Semke, J. Mahdavi, and T. Ott, "The macroscopic behavior of the TCP congestion avoidance algorithm," ACM Comput. Commun. Rev., vol. 27, no. 3, Jul. 1997.
29. A. Misra, T. Ott, and J. Baras, "The window distribution of multiple TCPs with random queues," in Proc. IEEE GLOBECOM, vol. 3, Dec. 1999, pp. 1714-1726.
30. V. Mistra, W.-B. Gong, and D. Towsley, "Stochastic differential equation modeling and analysis of TCP-windowsize behavior," presented at the Performance'99 Conf., Istanbul, Turkey, Oct. 1999.
31. J. Nagle, "Congestion control in IP/TCP internetworks," RFC 896, Jan. 1984.
32. M. F. Neuts, "A versatile Markovian point process," J. Appl. Prob., vol. 16, pp. 764-779, 1979.
33. M. F. Neuts, Structured Stochastic Matrices of M/G/1 Type and Their Applications. New York: Marcel Dekker, 1989.
34. T. Ott, J. Kemperman, and M. Mathis. (1996, Aug) The stationary behavior of ideal TCP congestion avoidance [Online] Available: ftp:// ftp.research.telcordia.com/pub/tjo/TCPwindow.ps.
35. J. Padhye, V. Firoiu, D. Towsley, and I. Kurose, "Modeling TCP throughput: a simple model and its empirical validation," presented at the ACM SIGCOMM, Vancouver, BC, Canada, Sep. 1998. An extended version has appeared in IEEE/ACM Trans. Netw., vol. 8, no. 2, pp. 133-145, Apr. 2000..
36. LBNL's tcpdump Tool. [Online] Available: http://www-nrg.ee.lbl.gov
37. S. Savari and E. Telatar, "The behavior of certain stochastic processes arising in window protocols," in Proc. IEEE GLOBECOM, vol. 1B, Dec. 1999, pp. 791-795.
38. W. Stevens, "TCP slow start, congestion avoidance, fast retransmit, and fast recovery algorithms," RFC 2001, Jan. 1997.
39. K. Thompson, G. J. Miller, and R. Wilder, "Wide-area internet traffic patterns and characteristics," IEEE Network, vol. l1, no. 6, pp. 10-23, Nov. 1997.
40. M. Vojnovic and J.-Y. Le Boudec, "On the long-run behavior of equation-based rate control," presented at the ACM SIGCOMM, Pittsburgh, PA, Aug. 2002.
41. Y. Zhang, N. Duffield, V. Paxson, and S. Shenker, "On the constancy of internet path properties," presented at the ACM SIGCOMM Internet Measurement Workshop, San Francisco, CA, Nov. 2001.