An ingress node configured to receive a first request for a temporal label switched path (LSP) in the network. The first request indicates the ingress node, egress node, network constraint, and scheduled time interval having a predetermined start time and a predetermined end time for the temporal LSP to carry traffic. The ingress node computes a shortest path in the network for the temporal LSP that satisfies the network constraint in a shifted time interval when the request indicates that the time interval is elastic, and reserves a network resource for use during the shifted time interval for the temporal LSP in advance of the predetermined start time on a link extending from the ingress node to a next hop node on the path. The ingress node sends a path message to the next hop node to set up the temporal LSP in the shifted time interval.