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In recent years, Session Initiation Protocol (SIP) based Voice over IP (VoIP) based applications are alternative to the traditional Public Switched Telephone Networks (PSTN) because of its flexibility in the implementation of new features and services. The Session Initiation Protocol (SIP) is becoming a popular signaling protocol for Voice over IP (VoIP) based applications. The SIP Proxy server is a software application that provides call routing services by parsing and forwarding all the incoming SIP packets in an IP telephony network. The efficiency of this process can create large scale, highly reliable packet voice networks for service providers and enterprises. Since, SIP Proxy server performance can be characterized by its transaction states of each SIP session, we proposed the M/M/c performance model of the SIP Proxy Server and studied some of the key performance benchmarks such as server utilization, queue size and memory utilization. Provided the comparative results between the predicted results with the experimental results conducted in a lab environment.