1. A computer system comprising: a plurality of routers, including a first router; a communications network, wherein the communications network connects to each one of the plurality of routers; and a synchronization domain coupled to the communications network, the synchronization domain comprising: synchronization messaging apparatus that sends and receives synchronization messages across the communications network between pairs of the plurality of routers, wherein the synchronization messages include a barrier-join message and a barrier-complete message; and for each one of the plurality of routers, a synchronization state register, wherein the synchronization state register for the first router stores an indication of one of a plurality of synchronization states and a sequence value that is changed upon a changing of a synchronization state.