Geodesic
Matrix algorithm for Polling models with PH distribution
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2012), pp. 70-80 
Gheorghe Mishkoy; Udo R. Krieger; Diana Bejenari. Matrix algorithm for Polling models with PH distribution. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2012), pp. 70-80. http://geodesic.mathdoc.fr/item/BASM_2012_1_a6/
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     title = {Matrix algorithm for {Polling} models with {PH} distribution},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2012_1_a6/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Polling systems provide performance evaluation criteria for a variety of demand-based, multiple-access schemes in computer and communication systems [1]. For studying this systems it is necessary to find their important characteristics. One of the important characteristics of these systems is the $k$-busy period [2]. In [3] it is showed that analytical results for $k$-busy period can be viewed as the generalization of classical Kendall functional equation [4]. A matrix algorithm for solving the gene- ralization of classical Kendall functional equation is proposed. Some examples and numerical results are presented.

[1] Vishnevsky V. M., Semenova O. V., Polling Systems: The theory and applications in the broadband wireless networks, Texnocfera, Moscow, 2007 (in Russian)

[2] Rycov V. V., Mishkoy Gh. K., “A new approach for analysis of polling systems”, Proceedings of the International Conference on Control Problems, 2009, 1749–1758

[3] Mishkoy Gh. K., Generalized Priority Systems, Academy of Sciences of Moldova, Stiinta, 2009 (in Russian)

[4] Kendall D. G., “Some problems in the theory of queues”, J. Roy. Statist. Soc. (B), 13:2 (1951), 151–173 | MR

[5] Kriger Udo R., Bejenari D., Mishcoy Gh., “Matrix algorithm for solving Kendall equation in Polling models”, Proceedings of International Conferece on Informational Technologies, Systems and Networks, 2010, 95–102

[6] Marcel Neuts F., Matrix-Geometric Solutions in Stochastic Models, An algorithmic Approach, The Johns Hopkins University Press, Baltimore–London, 1981 | MR