@inproceedings{f1e11324b63f4d119ec6f8df8ece2de8,
title = "Transient analysis of the output process in the GI/M/1-type queue with finite buffer",
abstract = "A finite-buffer single-server queueing system with a general-type recurrent arrival process and exponential service times is considered. A system of integral equations for the distribution function of the number of packets h(t) completely served before t, conditioned by the number of packets present in the system at the opening, is built. A compact representation for the probability generating function of the Laplace transform of distribution of h(t) is found and written down explicitly using the sequence, called potential, defined recursively by means of {"}input{"} parameters of the system. From this formula the mean of h(t) can be found efficiently using one of the algorithms of numerical Laplace transform inversion. Besides, a limit theorem for the output process in the {"}standard{"} system with large buffer is proved. A numerical example is attached as well.",
keywords = "Finite-buffer queue, numerical Laplace transform inversion, output process, potential method, transient state",
author = "Kempa, \{W. M.\}",
year = "2012",
doi = "10.1063/1.4758958",
language = "English",
isbn = "9780735410992",
series = "AIP Conference Proceedings",
pages = "193--200",
booktitle = "Application of Mathematics in Technical and Natural Sciences - 4th International Conference, AMiTaNS 2012",
note = "4th International Conference on Application of Mathematics in Technical and Natural Sciences: Memorial Volume devoted to Prof. Christo I. Christov, AMiTaNS 2012 ; Conference date: 11-06-2012 Through 16-06-2012",
}