Abstract
An analogy between celebrated Kendall equation for busy periods in the system M|GI|1 and analytical results for busy periods in the priority systemsM r |GI r |1 is drawn. These results can be viewed as generalizations of the functional Kendall equation. The methodology and algorithms of numerical solution of recurrent functional equations which appear in the analysis of such queueing systems are developed. The efficiency of the algorithms is achieved by acceleration of the numerical procedure of solving the classical Kendall equation. An algorithm of calculation of the system workload coefficient calculation is given.
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Original Russian Text © Gh.K. Mishkoy, V.V. Rykov, S. Giordano, A.Iu. Bejan, 2008, published in Avtomatika i Telemekhanika, 2008, No. 6, pp. 82–95.
This work was supported by the Russian Foundation for Basic Research, project nos. 07-07-00088, 06-07-90929 in collaboration with the Academy of Sciences of Moldova, project no. 06.44CRF, and the program SNF SCOPES, project no. IB7320-110720.
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Mishkoy, G.K., Rykov, V.V., Giordano, S. et al. Multidimensional analogs of the kendall equation for priority queueing systems: computational aspects. Autom Remote Control 69, 980–992 (2008). https://doi.org/10.1134/S0005117908060088
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DOI: https://doi.org/10.1134/S0005117908060088