Some practical applications of generating functions and LSTS

• Autorzy: Ziółkowski M.
• Języki publikacji: EN

Abstrakty

EN

In many various practical problems we often deal with computing distribution functions of sums of independent non-negative random variables. In applied mathematics (ex. queueing theory) we can find many formulas with Stieltjes convolutions of distribution functions of random variables of the same type. Finding convolutions on the base of definition is not easy and convenient, because there are some technical problems connected with computations. There are some interesting ways to obtain such distribution functions applying other methods. In this paper we present methods connected with applications of generating functions and Laplace-Stieltjes transforms.

Słowa kluczowe

EN

applied mathematics; queuing theory; Laplace transforms

PL

matematyka stosowana; teoria kolejkowania; transformata Laplace'a-Stieltjesa; transformaty Laplace'a

• Wydawca: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego im. Jana Długosza w Częstochowie
• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 2012
• Tom: Vol. 17
• Strony: 97–110
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Ziółkowski M.

• Jan Długosz University, Institute of Mathematics and Computer Science, 42-200 Częstochowa, Al. Armii Krajowej 13/15, Poland

Bibliografia

• [1] A. A. Borowkow, Rachunek prawdopodobieństwa, PWN, Warszawa, 1975.
• [2] W. Feller, An introduction to Probability Theory and its Applications. Vol. 1, 2., John Wiley and Sons, New York, 1970, 1971.
• [3] O. Tikhonenko, K. G. Klimovich, Queueing systems for random-length arrivals with limited cumulative volume, Problems of Information Transmission. Vol.37, No. 1. (2001), p. 70-79.
• [4] O. Tikhonenko, Metody probabilistyczne analizy systemów informacyjnych, Akademicka Oficyna Wydawnicza EXIT, Warszawa, 2006.
• [5] O. Tikhonenko. Generalized Erlang Problem for Service Systems with Finite Total Capacity, Problems of Information Transmission. Vol. 41, No.3. (2005), p. 243-253.
• [6] G. A. Coon and D. L. Bernstein, Some properties of the double Laplace transformation, Transactions of the American Mathematical Society, Vol. 74, No.1. (1953), p. 135-176.