In the evaluation of Broadband-ISDN, the main issue is to interconnect existing LANs and MANs to B-ISDN based on Asynchrous Transfer Mode. However, LANs provide connectionless services, whereas the ATM network provides connection-oriented services. So some problem arises from accessing ATM switchs to transparently transmit connectionless data via B-ISDN. Two methods then were recommended by ITU-TS to support the connectionaless services. In the paper, we do the numerical analysis, using the stochastic fluid flow method, of dynamic bandwidth allocation sheme with two class traffics in the virtual path established between Interworking Units(JWUS) interconnecting LANs to an ATM network and Connectionless Servers(CLSs). The loss mechanism of each traffic is controlled by the contents of buffer. The vandwidth which the IWU requests the CLS is estimated by the number of On-Off sources in the On state. We use the stochsastic fluide flow method which is to find the steady-state joint probability in each level of the IWU buffer. The length of the IWU buffer as the real random variable is changed by traffics entering the IWU.