Abstract: In an ATM network using a burst-level band-width allocation, a source terminal reserves, before a burst transmission, band-widths according to a peak rate of the burst and then sends the burst therethrough. When the transmission is finished, the band-widths are released. Where there exists a link to which the peak rate is not assigned, a non-reserving acknowledgement signal (NACK) is sent to the terminal and the reserved band-widths are released. On receiving the NACK, the terminal allocates a band-width with peak rate lower than that of the first request after a back-off time has elapsed, thereby minimizing the probability of a blocked transmission. The source terminal declares a minimum band-width together with the peak rate (maximum band-width) in the band-width request operation. Each node allocates the peak rate when the remaining band-width of a link controlled by the node is sufficient to allocate the peak rate.