Multidimensional analogs of the kendall equation for priority queueing systems: computational aspects

An analogy between celebrated Kendall equation for busy periods in the system $M|GI|1$ and analytical results for busy periods in the priority systems $M_r|GI_r|1$ 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.