In process of networks convergence traditional network management systems have been replaced by variety of standards. Also, new principles of management have been emerged. Regarding to these changes new alternative network management techniques are needed. There are a lot of efforts in management protocols improvement based on advanced computer simulation techniques. But, there is a lack in development of fundamental theoretical models for management architectures. According to that we develop in our paper an analytical modeling tool for the converged network management, e.g., queuing model for signaling management of SIP network, as well as PSTN, by IN application layer. This management structure is used for the transparent end-to-end services support in both networks. We model its distributed architecture as a finite source queuing model. Furthermore, we evaluate the steadystate performance measures such as expected waiting time and time in system, and present numerical results providing corresponding curves for them.