The subject matter herein relates to a method to “accelerate” the delivery of a portion of a data stream across nodes of a stream transport network. A portion of a live stream is forwarded from a first node to a second node in a transport network at a high bitrate as compared to the stream's encoded bitrate, and thereafter, the stream continues to be forwarded from the first node to the second node at or near the encoded bitrate. The disclosed technique of forwarding a portion of a stream at a high bitrate as compared to the encoded bitrate of the stream is sometimes referred to as “prebursting” the stream. This technique provides significant advantages in that it reduces stream startup time, reduces unrecoverable stream packet loss, and reduces stream rebuffers as the stream is viewed by a requesting end user that has been mapped to a media server in a distributed computer network such as a content delivery network.