Reduced-load equivalence for Gaussian processes

We consider a fluid model fed by two Gaussian processes. We obtain necessary and sufficient conditions for the workload asymptotics to be completely determined by one of the two processes, and apply these results to the case of two fractional Brownian motions.

[1]  T. Kurtz.  Limit theorems for workload input models , 2000 .

[2]  PAUL EMBRECHTS,et al.  Modelling of extremal events in insurance and finance , 1994, Math. Methods Oper. Res..

[3]  Elena Yudovina,et al.  Stochastic networks , 1995, Physics Subject Headings (PhySH).

[4]  K. Dȩbicki,et al.  Ruin probability for Gaussian integrated processes , 2002 .

[5]  Krzysztof Debicki,et al.  On–off fluid models in heavy traffic environment , 1999, Queueing Syst. Theory Appl..

[6]  M. Lifshits.  Gaussian Random Functions , 1995 .

[7]  A. Lazar,et al.  Asymptotic results for multiplexing subexponential on-off processes , 1999, Advances in Applied Probability.

[8]  Armand M. Makowski,et al.  On a reduced load equivalence for fluid queues under subexponentiality , 1999, Queueing Syst. Theory Appl..

[9]  Ness B. Shroff,et al.  Use of the supremum distribution of Gaussian Processes in queueing analysis with long-range Dependence and self-similarity , 2000 .

[10]  Krzysztof Dȩbicki.  A note on LDP for supremum of Gaussian processes over infinite horizon , 1999 .

[11]  A. P. Zwart,et al.  The supremum of a Gaussian process over a random interval , 2002 .

[12]  Predrag R. Jelenkovic,et al.  Reduced Load Equivalence under Subexponentiality , 2004, Queueing Syst. Theory Appl..

[13]  A. B. Dieker,et al.  Conditional limit theorems for queues with Gaussian input, a weak convergence approach , 2003 .

[14]  J. Hüsler,et al.  Extremes of a certain class of Gaussian processes , 1999 .

[15]  C. Klüppelberg,et al.  Modelling Extremal Events , 1997 .

[16]  A. B. Dieker,et al.  Extremes of Gaussian processes over an infinite horizon , 2005 .

[17]  Vladimir I. Piterbarg,et al.  Asymptotic Methods in the Theory of Gaussian Processes and Fields , 1995 .