Solving recursive equations in analytical modeling of distributed systems

With rapid development of distributed systems and cloud systems and also increasing tendency to Network on Chip Architectures, need to description and analysis of these systems has been more felt. To evaluate performance of distributed systems, analytical modeling is a very notable for designers and developers. A class of issues that makes obstacles in the way of modeling these systems is finding solution for series that are recursive and the current term value related to values which are themselves related to the current term value. In this study, several solutions proposed that not only can solve the problem in specific and complicated situation, but also can obtain answers with high precision.