The main challenge for internetting LAN/MAN across B-ISDN comes from the fact that B-ISDN is connection-oriented but LANs and MANs run connectionless protocols. The critical issue is for the gateway to estimate the incoming traffic bit rate and negotiate with the B-ISDN for bandwidth allocation. In this paper we propose an adaptive estimation method for connectionless DQDB MAN interworking with B-ISDN. Due to the inherent nature of DQDB, the time window of bandwidth estimation can be adjusted dynamically. This results in a smaller fluctuation of required bandwidth estimation, so the gateway doesn't need to renegotiate frequently. In addition, based on the knowledge of bandwidth required, we propose a strategy for bandwidth allocation. Performance results are compared for the following schemes: adaptive time window, fixed time window, fixed cell window and a buffer threshold scheme. It shows that the proposed scheme performs better than other such schemes.