Available bandwidth utilization during transfer of large files over a TCP/IP network, is improved by segmenting the file and concurrently transmitting portions in an optimal number of logical distinct data streams which may all utilize a single physical medium and communications path. An initial number of data streams, is used to begin transmission of segments, each on a different data stream. During the first seconds of the transfer, individual and aggregate transmission bandwidths are determined, together with a backbone limit computed from the sliding window and round trip times. If the individual transmission bandwidths are approximately equal to the backbone limit, additional data stream(s) and segment(s) are started. Individual and aggregate transmission bandwidths are again determined, and the process is repeated until no substantial increase in aggregate bandwidth is achieved by adding an additional data stream. Aggregate transmission bandwidths are checked upon completion of each segment to determine if a data stream should be terminated.