Abstract. We analyze the problem of the computation of the solution of the nonlinear matrix equation $X=\sum_{i=0}^{+\infty}X^iA_i$, arising in queueing models.  We propose a technique based on regular splittings, that one hand leads to a new method for computing the solution, on the other hand it may be used to construct nonlinear matrix equations equivalent to starting one, that can be possibly solved by applying different algorithms.
 

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