The recent introduction of conferencing products such as telepresence has led to immense growth in the number of voice conferencing calls on the internet protocol (IP) network. Currently, voice conferencing users are provided with many options, such as free session initiation protocol (SIP) soft phone and voice over internet protocol (VOIP) calls at a lower rate. As technology and social networking sites continue to grow, there is a good possibility that these sites could be integrated with VOIP conferencing solution, which would lead to enormous growth in IP voice traffic. The recent addition of core routers by network software companies also indicates an increased prediction for real-time and multimedia traffic. With such a prediction in the growth of voice traffic, it becomes essential to estimate the delay as well as voice quality analytically. The SIP conferencing solution includes a key centralized entity called a conference server, the role of which is not limited to maintain the media sessions between participants and forwarding traffic from the active speaking user to other participants. Considering the finite endtoend delay of 150msec for VOIP traffic, the conference server should handle the job efficiently so that more delay is not introduced to voice traffic. Since voice traffic must pass through several middle agents such as Session Border Controllers and proxy servers for specific purposes, the delay increases with these centralized devices in addition to that introduced by devices such as routers, firewalls, and switches. Therefore, the delay management of voice traffic in the conference server becomes prominent as the voice traffic becomes futile beyond the finite end-to-end delay of 150msec. The delay of voice traffic in the SIP conference call scenario increases due to many factors. The factors that were influenced by the conference server are the application processing capacity of the server and traffic intensity. In this thesis, a model has been proposed to estimate the number of sessions that the conference server can handle at a specific processing capacity with less delay. This model was simulated using Matlab, and the observed results verify the proposed model, with graphs showing the necessary optimum processing capacity of the conference server.