Diffusion approximations for a single node accessed by congestion-controlled sources

IEEE Transactions on Automatic Control

Volumn 45, Issue 10, 2000, Pages 1783-1799

  Das, Atanu ^a   Srikant, R ^a  

^a University of Illinois at Urbana Champaign   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; MATHEMATICAL MODELS; NETWORK PROTOCOLS; NORMAL DISTRIBUTION; ON-OFF CONTROL SYSTEMS; POISSON DISTRIBUTION; RESOURCE ALLOCATION; TELECOMMUNICATION NETWORKS; TELECOMMUNICATION SERVICES; TELECOMMUNICATION TRAFFIC;

DIFFUSION APPROXIMATIONS; EXPONENTIAL DISTRIBUTION; GAUSSIAN DISTRIBUTION; SERVICE TIME DISTRIBUTION;

CONGESTION CONTROL (COMMUNICATION);

EID: 0034291839     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2000.880966     Document Type: Article

References (40)

1. E. Altman, T. Başar, and R. Srikant, "Multi-user rate-based flow control with action delays: A team-theoretic approach," in Proc. 36th IEEE Conf. Decision Contr., San Diego, CA, Dec. 1997.
2. _, "Robust rate control for ABR sources," in Proc. IEEE INFOCOM, San Francisco, CA, Mar. 1998.
3. P. Barford and M. E. Crovella, "Generating representative web workloads for network and server performance evaluation," in Proc. Performance'98/ACM SIGMETRICS'98, Madison, WI, 1998, pp. 151-160.
4. L. Benmohamed and S. M. Meerkov, "Feedback control of congestion in packet switching networks: The case of a single congested node," IEEE/ACM Trans. Networking, vol. 1, no. 6, pp. 693-707, 1993.
5. L. Benmohamed and Y. T. Wang, "A control-theoretic ABR explicit rate algorithm for ATM switches with per-VC queueing," in Proc. IEEE INFOCOM, San Francisco, CA, Mar. 1998.
6. D. Bertsekas and R. Gallager, Data Networks. Englewood Cliffs, NJ: Prentice-Hall, 1987.
7. P. Billingsley, Convergence of Probability Measures. New York: Wiley, 1968.
8. _, Probability and Measure, 2nd ed. New York: Wiley, 1986.
9. A. A. Borovkov, "On limit laws for service processes in multi-channel systems," Siberian Math. J., pp. 745-763. (English transl.).
10. _, Stochastic Processesin Queueing Theory. New York: Springer-Verlag, 1976.
11. A. E. Eckberg, "Generalized peakedness of teletraffic processes," in Proc. 10th Int. Teletraffic Congr., Montreal, Canada, June 1983, p. 4.4b3.
12. S. N. Ethier and T. G. Kurtz, Markov Processes: Characterization and Convergence. New York: Wiley, 1994.
13. P. W. Glynn, "On the Markov property of the GI/G/∞ Gaussian limit," Adv. Appl. Prob., vol. 14, pp. 191-194, 1982.
14. P. W. Glynn and W. Whitt, "A new view of the heavy-traffic limit theorem for infinite-server queues," Adv. Appl. Prob., vol. 23, pp. 188-209, 1991.
15. S. Halfin and W. Whitt, " Heavy-traffic limitsfor queues with many exponential servers," Oper. Res, vol. 29, no. 3, pp. 567-588, 1981.
16. D. Heyman, T. V. Lakshman, and A. Niedhart, "A new method for analyzing feedback-based protocols with applications to engineering Web traffic over the Internet," in Sigmetrics 97, 1997, pp. 24-38.
17. D. Iglehart, "Limit diffusion approximations for the many server queue and the repairman problem," J. Appl. Prob., pp. 429-441, 1965.
18. V. Jacobson, "Congestion avoidance and control," ACM Comput. Commun. Rev., vol. 18, pp. 314-329, Aug. 1988.
19. S. Kalyanaraman, R. Jain, S. Fahmy, R. Goyal, and B. Vandalore. (1997) The ERICA switch algorithm for ABR traffic management in ATM networks. [Online] http://www.cis.ohio-state.edu/jain/papers
20. I. Karatzas and S. Shreve, Brownian Motion and Stochastic Calculus. New York: Springer, 1996.
21. S. Karlin and H. Taylor, A Second Course in Stochastic Processes. New York: Academic, 1981.
22. F. P. Kelly, Reversibility and Stochastic Networks. New York: Wiley, 1976.
23. S. Keshav, An Engineering Approach to Computer Networks. Reading, MA: Addison-Wesley, 1997.
24. L. Kleinrock, Queueing Systems, Volume 2: Computer Applications. New York: Wiley-Interscience, 1975.
25. C. Knessl, "The WKB approximation to the G/M/m queue," SIAM J. Appl. Math., vol. 51, pp. 1119-1133, 1991.
26. H. J. Kushner, "Control of trunk line systems in heavy traffic," SIAM J. Contr. Optimiz., vol. 33, pp. 765-803, 1995.
27. _, "Heavy traffic analysis of controlled multiplexing systems," Queueing Syst., vol. 28, pp. 79-107, 1998.
28. H. J. Kushner and P. G. Dupuis, Numerical Methodsfor Stochastic Control Problems in Continuous Time. New York: Springer-Verlag, 1992.
29. H. J. Kushner and L. F. Martins, "Limit theorems for pathwise average cost per unit ti me problems for controlled queues in heavy traffic," Stoch. and Stoch. Rep., vol. 42, pp. 25-51, 1993.
30. S. Mascolo, D. Cavendish, and M. Gerla, "ATM rate based congestion control using a Smith predictor: An EPRCA implementation," in Proc. IEEE INFOCOM, San Francisco, CA, Mar. 1996.
31. K. W. Ross, Multiservice Loss Models for Broadband Telecommunication Networks. London: Springer, 1995.
32. R. Srikant and W. Whitt, "Simulation run lengths to estimate blocking probabilities in multiserver loss models," ACM Trans. Modeling and Comput. Simulation, pp. 7-52, Jan. 1996.
33. _, "Variance reduction in simulation of loss models," Oper. Res., June 1999.
34. C. Stone, "Limit theorems for random walks, birth and death processes and diffusion processes," Illinois J. Math., pp. 638-660, 1961.
35. D. Stoyan, Comparison Methods for Queues and Other Stochastic Models. New York: Wiley, 1983.
36. D. W. Stroock and S. R. S. Varadhan, Multidimensional Diffusion Processes. New York: Springer-Verlag, 1979.
37. L. Tàkacs, Introduction to the Theory of Queues. Oxford, England: Oxford Univ. Press, 1962.
38. P. Varaiya and J. Walrand, High-Performance Communication Networks. San Francisco, CA: Morgan Kaufman, 1996.
39. W. Whitt, "On the heavy-traffic limit theorems for GI/G/∞ queues," Adv. Appl. Prob., vol. 14, pp. 171-190, 1982.
40. _, "Heavy traffic approximations for service systems with blocking," AT&T Tech. J., pp. 689-707, May-June 1984.