Reduced-load equivalence for Gaussian processes

Operations Research Letters

Volumn 33, Issue 5, 2005, Pages 502-510

  Zwart, Bert ^a,b   Borst, Sem ^a,b,c   Dȩbicki, Krzysztof ^b,d  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b CWI   (Netherlands)

^c LUCENT TECHNOLOGIES   (United States)

^d UNIVERSITY OF WROC AW   (Poland)

Author keywords

Extremes; Fractional Brownian motion; Gaussian processes; Perturbed risk models; Regular variation; Ruin probabilities

Indexed keywords

ACOUSTIC NOISE; BROWNIAN MOVEMENT; PARAMETER ESTIMATION; PERTURBATION TECHNIQUES; PROBABILITY; RANDOM PROCESSES; THEOREM PROVING;

EXTREMES; FRACTIONAL BROWNIAN MOTION; GAUSSIAN PROCESSES; PERTURBED RISK MODELS; REGULAR VARIATION; RUIN PROBABILITIES;

LOADS (FORCES);

EID: 18244395640     PISSN: 01676377     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.orl.2004.09.004     Document Type: Article

References (18)

1. R. Agrawal, A.M. Makowski, and Ph. Nain On a reduced load equivalence for fluid queues under subexponentiality Queueing Syst. 33 1999 5 41
2. N.H. Bingham, C.M. Goldie, and J.L. Teugels Regular Variation 1987 Cambridge University Press Cambridge
3. J. Choe, and N.B. Shroff Use of the supremum distribution of Gaussian processes in queueing analysis with long-range dependence and self-similarity Stochastic Models 16 2000 209 231
4. K. Dȩbicki A note on LDP for supremum of Gaussian processes over infinite horizon Stat. Probab. Lett. 44 1999 211 219
5. K. Dȩbicki Ruin probability for Gaussian integrated processes Stoch. Proc. Appl. 98 2002 151 174
6. K. Dȩbicki, and Z. Palmowski On-off fluid models in heavy traffic environment Queueing Syst. 33 1999 327 338
7. K. Dȩbicki, A.P. Zwart, and S.C. Borst The supremum of a Gaussian process over a random interval Stat. Probab. Lett. 68 2004 221 234
8. A.B. Dieker, Conditional limit theorems for queues with Gaussian input, a weak convergence approach, Report PNA R0305, CWI, Amsterdam, 2003 Available at http://www.cwi.nl/ ∼ ton.
9. A.B. Dieker, Extremes of Gaussian processes with stationary increments, 2004, to appear in Stoch. Proc. Appl.
10. P. Embrechts, C. Klüppelberg, and T. Mikosch Modelling Extremal Events 1997 Springer Berlin
11. J. Hüsler, and V.I. Piterbarg Extremes of a certain class of Gaussian processes Stochastic Process. Appl. 83 1999 257 271
12. P.R. Jelenković, and A.A. Lazar Asymptotic results for multiplexing subexponential on-off processes Adv. Appl. Probab. 31 1999 394 421
13. P.R. Jelenković, P. Momčilović, and A.P. Zwart Reduced-load equivalence and subexponentiality Queueing Syst. 46 2004 97 112
14. T.G. Kurtz Limit theorems for workload input models F.P. Kelly S. Zachary I. Ziedins Stochastic Networks 1996 Springer Berlin
15. M. Lifshits Gaussian Random Functions 1995 Kluwer Academic Publishers Boston
16. V.I. Piterbarg, Asymptotic Methods in the Theory of Gaussian Processes and Fields, Translations of Mathematical Monographs, vol. 148, AMS, Providence, RI, 1996.
17. H.P. Schmidli Perturbed risk processes a review Theory Stochastic Process. 5 1999 145 165
18. D.J. Wischik, Moderate deviations in queueing theory, submitted for publication, 2001. Available at http://www.statslab.cam.ac.uk/ ∼ djw1005/Stats/Research/moddev.html.