To selectively route stand-by packets in input modules (IMi) to destination output modules (OMj) via a switching matrix (1), distributed arbitration functions are executable by successive arbitration cycles. Each cycle comprises: a first phase executable by each input controller (ICi) to send each output controller (OCj) requests representative of the quantities of “required” stand-by packets, a second phase executable by each output controller (OCj) to determine the quantity of “admissible” packets depending on the requests. a third phase executable by a central arbitration unit (CSC) to determine “allowed aggregate” quantities depending on all the admissible quantities. a fourth phase executable by each input controller (ICi) to determine the allowed packet quantities depending on the admissible quantities and of the allowed aggregate quantities.