A data communication network subject to bursty traffic employs a bandwidth allocation scheme to avoid congestion. When a source node has a burst of traffic to send, it first sends a bandwidth request message through the network from source to destination. At each intermediate node, this bandwidth request is examined and the node determines how much of the requested traffic level it will be able to support at a time in the future of one round-trip interval hence, and this node either grants the request or marks down the request to a level that it can support, then passes it on. When the request reaches the destination, it is returned along the same path to the source, and the source then employs the marked-down allocation to select the rate used to send the burst of data. The allocation for this source node remains in effect for a limited time, depending upon the amount of data to be sent in the burst, then returns to a "residual" level.