Abstract: A transmit scheduler maps connections to scheduled time slots in an ATM network in such a manner that minimizes burstiness in an output cell stream. The smoothness in the resulting cell streams reduces the probability of loss in the network and also assures that a connection does not exceed a preestablished bandwidth. The invention can be utilized with service with a constant bit rate (CBR), a variable bit rate (VBR) and an available bit rate (ABR) traffic. Bandwidth factors are established for cells to be transmitted as a percentage of total bandwidth of the ATM network. Lists are maintained for cells to be transmitted with each list assigned a bandwidth factor. The total bandwidth in the ATM network is apportioned into time slots according to established bandwidth factors and with different bandwidths being multiplexed across the total bandwidth. Cells are selected for transmission from the list of cells in accordance with available time slots and the bandwidth factors thereof.