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In this paper, we optimize low speed networks access for designing an efficient Voice over Internet Protocol network, especially in 64 kbps, 128 kbps, and 256 kbps bandwidth capacities. We draw some analytical approach based on Extended E-model to quantify some levels of quality of service. Using the model, those levels are determined by network parameters such as delay, jitter, packet loss level, network utilization, and bandwidth capacity and by implementation configuration such as voice coder, packetization scheme, and size of jitter buffer. Our objective is to find maximum number of calls in some given bandwidth capacities while maintaining a certain level of the quality of service. Using numeric estimation, we found that the optimum solution for some given bandwidth capacities can be achieved by applying G.723.1 5.3 kbps voice coder, packet loss level less than 1%, jitter less than 80 ms, and utilization network less than 80%.