Geodesic
Numerical treatment of the Kendall equation in the analysis of priority queueing systems
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2006), pp. 17-28.

Voir la notice de l'article provenant de la source Math-Net.Ru

We investigate here how to treat numerically the Kendall functional equation occuring in the theory of branching processes and queueing theory. We discuss this question in the context of priority queueing systems with switchover times. In numerical analysis of such systems one deals with functional equations of the Kendall type and efficient numerical treatment of these is necessary in order to estimate important system performance characteristics. 
@article{BASM_2006_2_a1,
     author = {A. Iu. Bejan},
     title = {Numerical treatment of the {Kendall} equation in the analysis of priority queueing systems},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {17--28},
     publisher = {mathdoc},
     number = {2},
     year = {2006},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/BASM_2006_2_a1/}
}
TY  - JOUR
AU  - A. Iu. Bejan
TI  - Numerical treatment of the Kendall equation in the analysis of priority queueing systems
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2006
SP  - 17
EP  - 28
IS  - 2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/BASM_2006_2_a1/
LA  - en
ID  - BASM_2006_2_a1
ER  - 
%0 Journal Article
%A A. Iu. Bejan
%T Numerical treatment of the Kendall equation in the analysis of priority queueing systems
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2006
%P 17-28
%N 2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/BASM_2006_2_a1/
%G en
%F BASM_2006_2_a1
A. Iu. Bejan. Numerical treatment of the Kendall equation in the analysis of priority queueing systems. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2006), pp. 17-28. https://geodesic-test.mathdoc.fr/item/BASM_2006_2_a1/

[1] Abate J., Whitt W., “Solving probability transform functional equations for numerical inversion”, Oper. Res. Lett., 12 (1992), 275–281 | DOI | MR | Zbl

[2] Abate J., Whitt W., “An operational calculus for probability distributions via Laplace transforms”, Adv. Appl. Probab., 28 (1996), 75–113 | DOI | MR | Zbl

[3] Bejan A., “On algorithms of busy time period evaluation in priority queues with orientation time”, Communications of the Second Conference of the Mathematical Society of the Republic of Moldova, 2004, 32–36

[4] Bernstein S. N., “Sur les fonctions absolument monotones”, Acta Math., 52 (1928), 1–66 | DOI | Zbl

[5] Doshi B. T., “An $M|G|1$ queue with a hybrid discipline”, Bell System Tech. J., 62 (1983), 1251–1271 | Zbl

[6] Feller W., An Introduction to Probability Theory and its Application, Vol. 2, Wiley, 1971 | MR | Zbl

[7] Gnedenko B. V. et al., Priority Queueing Systems, Moscow State University Press, 1973 (in Russian) | Zbl

[8] Kendall D. G., “Some problems in the theory of queues”, J. R. Stat. Soc. Ser. B: Stat. Methodol., 13:2 (1951), 151–185 | MR | Zbl

[9] Klimov G. P., Mishkoy G. K., Priority queueing systems with switching, Moscow State University Press, 1979 (in Russian)

[10] Mishkoy Gh., Giordano S., Andronati N., Bejan A., Priority Queueing Systems with Switchover Times: Generalized Models for QoS and CoS Network Technologies and Analysis, Technical report, WEB: http://www.vitrum.md/andrew/PQSST.pdf