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With the wide deployment of intelligent network (IN) services, there is an urgent need to understand and solve teletraffic performance issues of the evolving network intelligence platform. This paper discusses a queuing system model for the performance analysis of IN call processing. The IN is presented as a network of queues where the total number of customers (e.g., SSPs) is fixed, thus forming a closed queuing network. The IN distributed architecture is modeled as a finite source queuing model - M/M/2/K/K. The expected response time for that model is analyzed and computed. The numerical results and the corresponding curves are provided. And, related to open questions, future work is summarized.