Asymptotic characteristics of output flows in queueing networks
G. Sh. Tsitsiashvili, N. V. Markova
2003, issue 1, P. 36–43
|This paper is devoted to a construction of tail asymptotics of interdeparture intervals in queuing systems. These asymptotics are considered in a case when interarrival intervals and serving times have subexponential distributions. It is shown that such asymptotics depends mainly on heavier considered tail. An influence of the queuing system structure (one-server, multi-server, multi-phase and etc.) on the tails is investigated. Asymptotic of free period tail is investigated. It is proved that in wide assumptions this asymptotic is equivalent to interarrival tail asymptotic independently on the queuing system structure.|
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| P. Embrechts, C. Kluppelberg, T. Mikosch, Modelling Extremal Events for Insurance and Finance, Springer, Berlin, 1997.|
 S. Asmussen, Ruin Probabilities, World Scientific, Singapore, 2000.
 T. Rolski, H. Schmidli, V. Schmidt, J. Teugels, Stochastic Processes for Insurance and Finance, Wiley, New York, 1999.
 S. Foss, F. Baccelli, D. Korshunov, Asymptotics for Distributions of Stationary Characteristics in Queuing Networks with Heavy Tails, Abstracts of Workshop Modern Problems in Applied Probability, Novosibirsk, 2000, 9.
 J. Kiefer, J. Wolfowitz, On the theory of queues with many servers, Trans. Amer. Math. Soc., 78 (1955), 147–161.
 D. B. H. Cline, Convolution tails, product tails and domains of attraction, Probab. Theory Relat. Fields, 72:4 (1986), 529–557.
 D. B. H. Cline, Convolutions of distributions with exponential and subexponential tails, J. Austral. Math. Soc. Ser. A, 43 (1987), 347–365.
 P. Embrechts , C. M. Goldie, On closure and factorization properties of subexponential and related distributions, J. Austral. Math. Soc. Ser. A, 29:2 (1980), 243–256.