1. Message switching system ( 5 1 ) comprising at least two inputs ( 52 , 53 , 54 , 55 ) and at least one output ( 56 ), first arbitration means ( 62 ) dedicated to said output ( 56 ), and management means ( 64 ) designed to determine a relative order OR(i,j) of one input relative to the other, for any pair of separate inputs belonging to the system ( 51 ) and having sent requests for the assignment of said output ( 56 ), and designed to assign said output ( 56 ), characterized in that said management means ( 64 ) comprise storage means ( 70 ) designed to store said relative orders OR(i,j), initialization means ( 66 ) designed to initialize said relative orders OR(i,j) such that only one of said inputs takes priority on initialization, and updating means ( 68 ) designed to update all of said relative orders when a new request arrives at said first arbitration means ( 62 ), or when said output is assigned to one of said inputs.