An arbitration method, for a data bus in an architecture having n functional blocks, regulates access to the bus. The method includes: receiving, at one of plural agents, information from one of the functional blocks via high level primitives. Each agent generates in response a critical rank vector comprising at least first and second components. An arbitrator receives the critical rank vectors generated by rival the agents and applies a maximum or minimum extracting mechanism to at least one of the two components of the critical rank vectors to uniquely identify the block accessing the resource. Thus, functional blocks can be separated from arbitration control, the agents implementing the arbitration control and being solely responsible for it.