Numerical treatment of the Kendall equation in the analysis of priority queueing systems

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.