On the supremum distribution of integrated stationary gaussian processes with negative linear drift

Advances in Applied Probability

Volumn 31, Issue 1, 1999, Pages 135-157

  Choe, Jinwoo ^a   Shroff, Ness B ^b  

^a UNIVERSITY OF TORONTO   (Canada)

^b PURDUE UNIVERSITY   (United States)

Author keywords

Asymptotic upper bound; Extreme value theory; Gaussian process; Queue length distribution; Stationary increment with linear drift; Supremum distribution; Tail probability

Indexed keywords

EID: 0032593234     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1029954270     Document Type: Article

References (20)

1. Addie, R. G. and ZUKERMAN, M. (1994). An approximationforperformanceevaluation of stationary single server queues. IEEE Trans. Commun. 42, 3150-3160.
2. Adler, R. J. (1990). An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes. Institute of Mathematical Statistics, Hayward, CA.
3. Berman, S. M. and Kono, N. (1989). The maximum of a Gaussian process with non-constant variance: a sharp bound for the distribution tail. Ann. Prob. 17, 632-650.
4. BRATLEY, P., Fox, B. L. and SCHRAGE, L. E. (1987). A Guide to Simulation, 2nd edn. Springer, New York.
5. Chang, C. -S., Heidelberger, P., Juneja, S. and Shahabuddin, P. (1994). Effective bandwidth and fast simulation of ATM intree networks. Performance Evaluation 20, 45-65.
6. Choe, J. and Shroff, N. B. (1997). A central limit theorem based approach to analyse queue behavior in ATM networks. In Proc. 15th Internat. Teletraffic Congress, Washington DC, pp. 1129-1138.
7. CHOE, J. and Shroff, N. B. (1997). A new method to determine the queue length distribution at an ATM multiplexer. In Proc. IEEE INFOCOM 97, Kobe, Japan. pp. 550-557.
8. Choe, J. and Shroff, N. B. (1998). A central limit theorem based approach for analyzing queue behavior in high-speed networks. Technical report, Purdue University, West Lafayette, IN.
9. Choudhury, G. L., Lucantoni, D. M. and Whitt, W. (1996). Squeezing the most out of ATM. IEEE Trans. Commun. 44, 203-217.
10. Elwalid, A. I. (1991). Markov modulated rate processes for modeling, analysis and control of communication networks. PhD thesis, Graduate School of Arts and Sciences, Columbia University.
11. Gihman, I. I. and SKOROHOD, A. V. (1974). The Theory of Stochastic Processes. I. Springer, New York.
12. Glynn, P. W. and Whitt, W. (1994). Logarithmic asymptotics for steady-state tail probabilities in a singleserver queue. In Studies in Applied Probability, ed. J. Galambos and J. Gani (J. Appl. Prob. 31A). Applied Probability Trust, Sheffield, UK, pp. 131-155.
13. KESIDIS, G., Walrand, J., and Chang, C. -S. (1993). Effective bandwidth for multiclass Markov fluid and other ATM sources. IEEE/ACM Trans. Networking 1, 424-428.
14. Loynes, R. M. (1962). The stability of a queue with non-independent inter-arrival and service times. Proc. Cam. Philos. Soc. 58, 497-520.
15. Maglaris, B., Anastassiou, D., Sen, P., Karlsson, G. and Robbins, J. D. (1988). Performance models of statistical multiplexing in packet video communication. IEEE Trans.Commun. 36, 834-843.
16. ROSS, S. M. (1983). Stochastic Processes. Wiley, New York.
17. Samorodnitsky, G. (1991). Probability tails of Gaussian extrema. Stochast. Proc. Appl. 38, 55-84.
18. SHROFF, N. B. and Schwartz, M. (1998). Improvedloss calculations at an ATM multiplexer. IEEE/ACM Trans. Networking 6, 411-422.
19. SIMONIAN, A. (1991). Stationary analysis of a fluid queue with input rate varying as an Ornstein-Uhlenbeck process. SIAM J. Appl. Math. 51, 828-842.
20. TALAGRAND, M. (1988). Small tails for the supremum of a Gaussian process. Ann. Inst. Henri Poincare 24, 307-315.