Eliminating livelock in flushable routing networks

This invention is comprised of a method for livelock-free message routing is provided in a network of interconnected nodes that is flushable in time T. An input message processor generates sequences of at least N time intervals, each of duration T. An input register provides for receiving and holding each input message, where the message is assigned a priority state p during an nth one of the N time intervals. At each of the network nodes a message processor reads the assigned priority state and awards priority to messages with priority state (p-1) during an nth time interval and to messages with priority state p during an (n + 1)th time interval. The messages that are awarded priority are output on an output path toward the addressed output message processor. Thus, no message remains in the network for a time longer than T.