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We present a session initiation protocol (SIP) network design for a voice-over-IP (VoIP) network to prevent congestion caused by people calling friends and family after a disaster. The design increases the capacity of SIP servers in a network by using all the SIP servers equally. The design uses a property that SIP network elements do not carry voice data packets but signaling packets instead. Furthermore, the design achieves simple routing based on telephone numbers. We evaluate the performance of preventing congestion through simulation. We show that the proposed design has roughly 20 times more capacity, which is 57 times of the normal load, than the conventional design if a disaster were to occur in Niigata Prefecture.