In the evolutionary path to Broadband-ISDN based on the Asynchronous Transfer Mode, the interconnection of LANs and MANs will be one of the first high-speed applications. However, interworking between LANs/MANs and ATM is an open problem. since LANs and MANs use a connectionless transfer mode, whereas ATM is a connection-oriented technique. This paper focuses on a main problem arising within the interworking unit connecting a LAN/MAN and the ATM network: the bandwidth allocation for the ATM virtual channel established between the IWU and a CL-server. A possible bandwidth allocation mechanism based on an estimation of the bandwidth requirements of the incoming traffic stream which is routed to the CL-server is described. To investigate the performance behaviour of this mechanism, an analytical model based on a fluid flow approach is developed which will be validated by simulation. Comparing different bandwidth allocation strategies we show, besides other results, the trade-off between buffer size and the allocated bandwidth on the ATM virtual channel to provide a certain quality of service in terms of packet loss and delay.