The explosive increase of traffic in computer communications is a clear sign that we have entered the multimedia information age. To cope with this ever increasing need, economical optical access networks that support burst traffic such as in the Internet are expected to be developed. The ATM-PON is considered to be a promising candidate for such a network, and vigorous efforts in this direction are being promoted worldwide. This paper focuses on accommodating burst traffic in the ATM-PON. In order to do this, a mechanism to transport bandwidth requests from the ONU to the OLT and an algorithm to support dynamic bandwidth allocations based on ONU requests are needed. We have performed a comparative study on bandwidth request methods and bandwidth allocation algorithms, including bandwidth request dependence on time interval and correlation and/or impact between system design parameters. The results of computer simulations are useful in determining how to accommodate burst traffic efficiently in the ATM-PON.