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The analysis of stochastic systems is notoriously hard, especially when their performance is described by multidimensional Markov chains. Approximation of general distribution functions by phase-type distributions rise to large Markov chains. If the model is too large to analyze in its entirety, it is divided into subsystems. Each subsystem is analyzed separately and global solution is constructed from the partial solutions. Numerical algorithm to solve for the steady-state probabilities of these Markov chains from a system of linear equations by decomposition method is presented in the paper. Based on these probabilities, we can compute a wide range of relevant performance characteristics, such as average number of customers of a certain type in the system and expected postponement time for each customer class. [ABSTRACT FROM AUTHOR]