This paper presents a more complete analytical model of multiple TCP connections established between a busy server and multiple receivers. In such case, the server may become the bottleneck of the whole system, and TCP behaviors are different from the model presented before. Based on the analysis of working flows in the system and a M/G/1 queueing model, the RTT and long-term TCP throughput formulae are derived in terms of number of TCP connections, packet loss rate, and end-to-end delay. And the effect of maximum window size is also investigated. Finally, the simulation results confirm the effectiveness of analytical model.