As the amount of mobile traffic carried over IP keeps increasing, the military networks face the scalability challenges of VoIP protocols. When the message arrival rate including retransmissions exceeds the message serving capacity of a Session Initiation Protocol (SIP) server, the queue size increases and eventually the SIP server can be crashed. In our previous studies, we proposed a priority based request scheduling mechanism (PRSM) to guarantee the survivability of SIP server under heavily loaded traffic conditions. In this paper, we introduce a fluid-flow analytical model to study the behavior of the overloaded SIP server with PRSM under various test scenarios. The experiments performed using both analysis and simulation tools indicate that the proposed model can accurately capture the dynamic behavior of a SIP server with the PRSM. The numerical results verify the effectiveness of the PRSM which provides consistently better scalability compared to the conventional SIP thus enable us to prevent server overload.