Matrix algorithm for Polling models with PH distribution

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.