A method for selection by a downstream device of data packets of connections of a network transmitted by at least one upstream device according to a predetermined threshold for quantities of data transmitted by the connections includes: for each connection, initialization by each upstream device of a counter for packets transmitted according to a set of predetermined initial values, with the difference between two initial consecutive values greater than the threshold, then incrementation by a predetermined value for each transmitted packet, defining the current counting value of the packet; reception by the downstream device of each IP packet of each connection, and comparison of the threshold with the difference between the current counting value and the initial value immediately lower than the set of initial values, enabling selection of packets for connections that have transmitted less data than the threshold, compared to packets for connections that have transmitted more.