1. A message switching system in a communication network, on a silicon chip, comprising: at least two inputs; at least one output; first arbitration means dedicated to said output; and management means wherein the management means is configured to: determine a relative order, OR(i,j), of one input relative to another input, for any pair of separate inputs belonging to the system, wherein said relative order OR(i,j) has a binary value; send requests for the assignment of said output; and assign said relative order to said output wherein said management means comprises: storage means configured to store said relative orders OR(i,j); initialization means configured to initialize said relative orders OR(i,j) such that only one of said inputs takes priority on initialization; and updating means configured to update all of said relative orders when a new request arrives at said first arbitration means, or when said output is assigned to one of said inputs.