Asymptotic buffer overflow probabilities in multiclass multiplexers: An optimal control approach

IEEE Transactions on Automatic Control

Volumn 43, Issue 3, 1998, Pages 315-335

  Bertsimas, Dimitris ^a,b   Paschalidis, Ioannis Ch ^a,c   Tsitsiklis, John N ^a,d  

^a IEEE   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^c BOSTON UNIVERSITY   (United States)

^d USA   (United States)

Author keywords

ATM based B ISDN; Communication networks; Large deviations

Indexed keywords

ASYNCHRONOUS TRANSFER MODE; BROADBAND NETWORKS; CONGESTION CONTROL (COMMUNICATION); CONTROL SYSTEM ANALYSIS; OPTIMAL CONTROL SYSTEMS; PROBABILITY; QUEUEING THEORY; TELECOMMUNICATION TRAFFIC; VOICE/DATA COMMUNICATION SYSTEMS;

GENERALIZED LONGEST QUEUE FIRST POLICY (GLQF); GENERALIZED PROCESSOR SHARING POLICY (GPS); MULTICLASS MULTIPLEXERS;

MULTIPLEXING EQUIPMENT;

EID: 0032026986     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.661587     Document Type: Article

References (34)

1. D. Bertsimas, I. Ch. Paschalidis, and J. N. Tsitsiklis, "On the large deviations behavior of acydic networks of G/G/1 queues," Lab. Inf. Decision Systems, Massachusetts lnst. Technol., Tech. Rep. LIDS-P-2278, Dec. 1994.
2. _, "On the large deviations behavior of acyclic single class networks and multiclass queues," Talk at the RSS Workshop in Stochastic Networks, Edinburgh, U.K., 1995.
3. _, "Large deviations analysis of the generalized processor sharing policy," Tech. Rep. MNS-97-108, Dept. Manufacturing Eng., Boston Univ., June 1996, to be published.
4. J. A. Bucklew, Large Deviation Techniques in Decision, Simulation, and Estimation. New York: Wiley, 1990.
5. C. S. Chang, "Sample path large deviations and tree networks," Queueing Syst., vol. 20, pp. 7-36, 1995.
6. H. Cramér, "Sûr un nouveau théoréme-limite de la théorie des probabilités," in Actualités Scientifiques et Industrielles, no. 736, in Colloque consacrée à la théorie des probabilités, Hermann, Paris, 1938, pp. 5-23.
7. C. Courcoubetis and R. Weber, " Estimation of overflow probabilities for state dependent service of traffic streams with dedicated buffers," Talk at the RSS Workshop in Stochastic Networks, Edinburgh, U.K., 1995.
8. C. S. Chang and T. Zajic, "Effective bandwidths of departure process from queues with time varying capacities," in Proc. IEEE lnfocom, Boston, MA, Apr. 1995, vol. 3, pp. 1001-1009.
9. A. Demers, S. Keshav, and S. Shenker, "Analysis and simulation of a fair queueing algorithm," J. Internetworking: Research and Experience, vol. 1, pp. 3-26, 1990.
10. G. de Veciana, C. Courcoubetis, and J. Walrand, "Decoupling bandwidths for networks: A decomposition approach to resource management," Electronics Research Lab., Univ. California, Berkeley, Memorandum, 1993.
11. G. de Veciana and G. Kesidis, "Bandwidth allocation for multiple qualities of service using generalized processor sharing," IEEE Trans. Inform. Theory, vol. 42, 1995.
12. A. Dembo and T. Zajic, "Large deviations: From empirical mean and measure to partial sums processes," to be published.
13. A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications. Jones and Bartlett, 1993.
14. R. Ellis, "Large deviations for a general class of random vectors," Ann. Probability, vol. 12, pp. 1-12, 1984.
15. A. I. Elwalid and D. Mitra, "Effective bandwidth of general Markovian traffic sources and admission control of high speed networks," IEEE/ACM Trans. Networking, vol. 1, pp. 329-343, 1993.
16. A. I. Elwalid and D. Mitra, "Analysis, approximations and admission control of a multiple-service multiplexing system with priorities," to be published.
17. J. Gärtner, "On large deviations from the invariant measure," Theory Appl. Prob., vol. 22, pp. 24-39, 1977.
18. A. Ganesh and V. Anantharam, "The stationary tail probability of an exponential server tandem fed by renewal arrivals," to be published.
19. H. R. Gail, G. Grover, R. Guérin, S. L. Hantler, Z. Rosberg, and M. Sidi, " Buffer size requirements under longest queue first," Performance Eval., vol. 18, pp. 133-140, 1993.
20. R. J. Gibbens and P. J. Hunt, "Effective bandwidths for the multi-type UAS channel," Queueing Syst., vol. 9, pp. 17-28, 1991.
21. P. W. Glynn and W. Whitt, "Logarithmic asymptotics for steady-state tail probabilities in a single-server queue," J. Appl. Prob., vol. 31A, pp. 131-156, 1994.
22. J. Y. Hui, "Resource allocation for broadband networks," IEEE J. Select. Areas Commun., vol. 6, pp. 1598-1608, 1988.
23. F. P. Kelly, "Effective bandwidths at multi-class queues," Queueing Syst., vol. 9, pp. 5-16, 1991.
24. G. Kesidis, J. Walrand, and C. S. Chang, "Effective bandwidths for multiclass Markov fluids and other ATM sources," IEEE/ACM Trans. Networking, vol. 1, pp. 424-428, 1993.
25. N. O'Connell, " Large deviations in queueing networks," preprint, 1995.
26. _, "Queue lengths and departures at single-server resources," Talk at the RSS Workshop in Stochastic Networks, Edinburgh, U.K., 1995.
27. I. Ch. Paschalidis, "Large deviations in high speed communication networks," Ph.D. dissertation, Massachusetts Inst. Technol., May 1996.
28. _, "Quality of service provision in multimedia communication networks," Dept. Manufacturing Eng., Boston Univ., Tech. Rep. MNS-97-101, Jan. 1997, to be published.
29. A. K. Parekh and R. G. Gallager, "A generalized processor sharing approach to flow control in integrated services networks: The single node case," IEEE/ACM Trans. Networking, vol. 1, pp. 344-357, 1993.
30. _, "A generalized processor sharing approach to flow control in integrated services networks: The multiple node case," IEEE/ACM Trans. Networking, vol. 2, pp. 137-150, 1994.
31. A. Shwartz and A. Weiss, Large Deviations for Performance Analysis. New York: Chapman and Hall, 1995.
32. D. Tse, R. G. Gallager, and J. N. Tsitsiklis, "Statistical multiplexing of multiple time-scale Markov streams," IEEE J. Select. Areas Commun., vol. 13, 1995.
33. A. Weiss, "An introduction to large deviations for communication networks," IEEE J. Select. Areas in Commun., vol. 13, pp. 938-952, 1995.
34. Z.-L. Zhang, "Large deviations and the generalized processor sharing scheduling: Upper and lower bounds - Part I: Two-queue systems," Computer Sci. Dept., Univ. Massachusetts, Tech. Rep., Amherst, 1995.