GI/GI/1 queues with infinite means of service time and interarrival time

• Autorzy: Szczotka W.
• Języki publikacji: EN

Abstrakty

EN

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).

Słowa kluczowe

EN

Lévy process; stable distribution; GI/GI/1 queueing system; heavy traffic; stationary waiting time; tightness

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2016
• Tom: Vol. 36, Fasc. 2
• Strony: 279--293
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Szczotka W.

• 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).