Abstract: For each of a plurality of sources, which has a peak transmission rate p, the cells coming from the source are stored in a FIFO access buffer memory; reserves (R.sub.1, . . . , R.sub.i, . . . , R.sub.n) of tokens are allocated to the source, the reserves having respective determined token capacities (M.sub.1, . . . , M.sub.i, . . . , M.sub.n) and replenishing at respective rates (r.sub.1, . . . , r.sub.i, . . . , r.sub.n) verifying r.sub.1 >. . . >r.sub.i >. . . >r.sub.n and ##EQU1## a first cell is sent as soon as each reserve contains a number of tokens that is at least equal to the length of the cell, at a transmission rate corresponding to the bandwidth of the network; all reserves are decremented by a number of tokens corresponding to the length of the cell; once the first reserve R.sub.1 is exhausted, the message continues to be sent automatically at the replenishment rate r.sub.1 until the second reserve R.sub.