Introducing adaptive online data compression at network-internal nodes is considered for alleviating traffic congestion on the network. In this paper, we assume that advanced relay nodes, which possess both a relay function (network resource) and a processing function (computational and storage resources), are placed inside the network, and we propose an adaptive online lossless packet compression scheme utilized at these nodes. This scheme selectively compresses a packet according to its waiting time in the queue during congestion. Through preliminary investigation using actual traffic datasets, we investigate the compression ratio and processing time of packet-by-packet compression in actual network environments. Then, by means of computer simulations, we show that the proposed scheme reduces the packet delay time and discard rate and investigate factors necessary in achieving efficient packet relay.