The ATM Forum has defined a new service category, called the available bit rate service (ABR), which is intended for applications requiring tightly constrained cell loss but no bound on the delay or delay variation. Appropriate traffic control schemes are necessary for ABR service to achieve very low cell loss and maximize the network resource utilization by taking advantage of the available bandwidth remaining after CBR/VBR services have been supported. This paper compares the performance of a burst-level traffic control scheme and a rate-based feedback control scheme, through simulation in an ATM LAN environment. Our results indicate that the burst-level control scheme is more suitable for loss-sensitive but delay-insensitive applications such as ABR service, because it requires nearly zero buffers to achieve zero cell loss and potentially high network resource utilization, at the cost of an acceptable burst transfer delay.