An efficient and reliable transmission protocol for transmitting multimedia streams from a server to a client computer over a diverse computer network including local area networks (LANs) and wide area networks (WANs) such as the internet. The client computer includes a playout buffer for temporary storage of incoming data packets. When the client computer detects that a data packet has not arrived at said client computer by an expected time of arrival (ETA), a round trip time for the data packet is computed. The round trip time is an estimate of a period beginning from the time a retransmission request is sent to from the client computer to the stream server till the time a copy of the missing data packet is received at the client computer from the stream server in response to the retransmission request. If the round trip time is less than the time remaining before the missing packet is no longer useful to the on-demand application, then a retransmission request packet is sent to the server. Conversely if the round trip time is greater than the time remaining, i.e., the missing packet is likely to arrive after the usefulness of the packet has expired, then sending a retransmission request is likely to result in the late arrival of the missing data packet. Accordingly, the missing packet is discarded. This selective retransmission protocol can also be practiced with dynamic bandwidth selection wherein the transmission rate is dynamically matched to the available bandwidth capacity of the network connection between the server and the client computer.