Large deviation properties of data streams that share a buffer

Annals of Applied Probability

Volumn 8, Issue 4, 1998, Pages 1070-1129

  Ramanan, Kavita ^a   Dupuis, Paul ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

Data networks; Effective bandwidths; Fluid models; Large deviations; Rate function; Skorokhod problem

Indexed keywords

EID: 0032268839     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1028903374     Document Type: Article

References (24)

1. ANICK, D., MITRA, D. and SONDHI, M. M. (1982). Stochastic theory of a data handling system with multiple sources. Bell Syst. Tech. J. 61 1871-1894.
2. BREIMAN, L. (1968). Probability. Addison-Wesley, Reading, MA.
3. CHANG, C.-S. (1993). Approximations of ATM networks: effective bandwidths and traffic descriptors. Technical report IBM RC 18954, T.J. Watson Research Center.
4. DEMBO, A. and ZEITOUNI, O. (1993). Large Deviations Techniques and Applications. Jones and Bartlett, Boston.
5. DE VECIANA, G., COURCOUBETIS, C. and WALRAND, J. (1993). Decoupling bandwidths for networks: a decomposition approach to resource management. Memorandum UCB/ERL M93/50, Univ. California, Berkeley, CA.
6. DUPUIS, P. and ELLIS, R. S. (1996). A Weak Convergence Approach to the Theory of Large Deviations. Wiley, New York.
7. DUPUIS, P. and ISHII, H. (1991). On Lipschitz continuity of the solution mapping to the Skorokhod problem, with applications. Stochastics Stochastics Rep. 35 31-62.
8. DUPUIS, P. and NAGURNEY, A. (1993). Dynamical systems and variational inequalities. Ann. Oper. Res. 44 9-42.
9. DUPUIS, P. and WILLIAMS, R. (1994). Lyapunov functions for semimartingale reflecting Brownian motions. Ann. Probab. 22 680-702.
10. ELWALID, A. I. and MITRA, D. (1993). Effective bandwidth of general Markovian traffic sources and admission control of high speed networks. IEEE/ACM Trans. Networking 1 329-343.
11. ETHIER, S. N. and KURTZ, T. G. (1986). Markov Processes: Characterization and Convergence. Wiley, New York.
12. FREIDLIN, M. I. and WENTZELL, A. D. (1984). Random Perturbations of Dynamical Systems. Springer, New York.
13. HSU, I. and WALRAND, J. (1995). Admission control for ATM networks. In Stochastic Networks (F. P. Kelly and R. J. Williams, eds.) 411-427. Springer, New York.
14. KELLY, F. P. (1991). Effective bandwidths at multi-class queues. Queueing Systems 9 5-16.
15. KESIDIS, G., WALRAND, J. and CHANG, C. S. (1993). Effective bandwidths for multiclass Markov fluids and other ATM sources. IEEE/ACM Trans. Networking 1 424-428.
16. LOYNES, R. M. (1962). The stability of a queue with non-indepedent inter-arrivals and service times. Math. Proc. Cambridge Philos. Soc. 58 497-520.
17. MAJEWSKI, K. (1996). Large deviations of feedforward queueing networks. Ph.D. thesis, Ludwig-Maximilian-Univ., München.
18. O'BRIEN, G. L. and VERVAAT, W. (1991). Capacities, large deviations and loglog laws. In Stable Processes and Related Topics (S. Cambanis, G. Samorodnitsky and M. Taqqu, eds.) 43-84. Birkhäuser, Boston.
19. O'CONNELL, N. (1995). Large deviations in queueing networks. Preprint.
20. PUHALSKII, A. A. (1991). On functional principles of large deviations. In New Trends in Probability and Statistics (V. Sazonov and T. Shervashidze, eds.) 198-218. VSP-Mokslas, Utrecht.
21. RAMANAN, K. and DUPUIS, P. (1995). Large deviation properties of data streams that share a buffer. LCDS Technical Report 95-8, Brown Univ.
22. SHWARTZ, A. and WEISS, A. (1995). Large Deviations for Performance Analysis: Queues, Communication, and Computing. Chapman and Hall, New York.
23. STROOCK, D. W. (1984). An Introduction to the Theory of Large Deviations. Springer, New York.
24. WEISS, A. (1986). A new technique for analyzing large traffic systems. Adv. in Appl. Probab. 21 506-532.