Stochastic approximation in queuing system is already well known and established approach. The main reason is that such systems are very large and so it is difficult and often impossible to handle them by usual methods of Markov and semi-Markov processes. The specific queuing system is that the series scheme is considered with phase merging procedure. In this article study the queuing system where the input flow is described by a semi-Markov process, the service time is exponentially distributed. This article is about of the weak convergence in average scheme. It is study average scheme for semi-Markov queuing systems [SM|M|1|∞]N by a random evolution approach and using compensating operator of the corresponding extended Markov process.