The analysis of characteristics of nodes of the multiservice communication networks modelled by the G/G/1 systems when processing the modern traffic is the important technical task. In the assumption of independence of intervals of time between requests and independence of intervals of time of processing of the request in system the analysis of wait time of the request in queue can be realized on the basis of the solution of an integrable equation of Lindley by a spectral method. For use of a spectral method often resort to approximation of the distributions used in the G/G/1 system with the heavy tails characteristic of the modern traffic, the amounts of the fading exponents (or if it works well - the hyperexponential distributions). However approximation by the amounts of the fading exponents is rather difficult for the distributions containing the sections “ascending” from zero to some maximum and is, as a rule, executed with unacceptably big error. The method of the spectral solution of the equation of Lindley offered in operation the selects functions for approximation of distributions, the essence of which is that the “ascending” sections of distributions are approximated by polynomials of a small order, and the “falling-down” sections (from the negative derivative) - the amount of the fading exponents with small number of items in the amount is based on use. At the same time the analysis of wait time of the request in queue is consolidated to the numerical solution of the linear algebraic equation. Efficiency of a method is shown on the example of research of system W/P/1, where W - Weibull's distribution, P - Pareto's distribution.