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Abstrakty
The main results deal with the GI/GI/1 queues with Infinite means of the service times and interarrival times. Theorem 3.1 gives an asymptotic, in a heavy traffic situation, of the sequence of waiting times of the consecutive customers. Theorem 4.1 gives an asymptotic of stationary waiting times in a heavy traffic situation. In a special case, the asymptotic stationary waiting times have an exponential distribution (Corollary 4.1).
Czasopismo
Rocznik
Tom
Strony
279--293
Opis fizyczny
Bibliogr. 9 poz.
Twórcy
autor
- Institute of Mathematics, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Bibliografia
- [1] D. Applebaum, Lévy Processes and Stochastic Calculus, Cambridge University Press, Cambridge 2004.
- [2] P. Billingsley, Convergence of Probability Measures, Wiley, New York 1968.
- [3] N. H. Bingham, Maxima of sums of random variables and suprema of stable processes, Z. Wahrsch. Verw. Gebiete 26 (1973), pp. 273-296.
- [4] W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 2, second edition, Wiley, New York 1971.
- [5] S. Karlin and H. M. Taylor, A First Course in Stochastic Processes, second edition, Academic Press, New York-San Francisco-London 1975.
- [6] G. Samorodnitsky and M. S. Taqqu, Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance, Chapman & Hall, New York-London 1994.
- [7] K. Sato, Lévy Processes and Infinitely Divisible Distributions, Cambridge University Press, 1999.
- [8] W. Szczotka and W. A. Woyczyński, Heavy-tailed dependent queues in heavy traffic, Probab. Math. Statist. 24 (2004), pp. 67-96.
- [9] W. Whitt, Stochastic-Process Limits: An Introduction to Stochastic-Process Limits and TheirApplication to Queues, Springer, New York 2002.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
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Bibliografia
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