In this paper, we propose a packet-lossless fast rerouting scheme at a link/node fault in MPLS (Multiprotocol Label Switching) network with minimized accumulated buffer delay problem at ingress node. The proposed scheme uses a predefined, alternative LSP (Label Switched Path) In order to restore user traffic. We propose two restoration approaches. In the first approach, an alternative LSP is initially allocated with more bandwidth than the protected working LSP during the failure recovery phase. After the failure recovery, the excessively allocated bandwidth of the alternative LSP is readjusted to the bandwidth of the working LSP. In the second approach, we reduce the length of protected working LSP by using segment-based restoration. The proposed approaches have merits of (ⅰ) no buffer delay problem after failure recovery at ingress node, and (ⅱ) the smaller required buffer size at the ingress node than the previous approach.