When Broadband Integrated Services Digital Network(BISDN) becomes commercially available In public network, conventional Local Area Network(LAN)s will still be in use. The first wide spread application for B-ISDN will be the interconnection of LANs. The equipment providing the connection between the LAN and the BISDN will be given the general name Inter Working Unit(IWU). We addresses the congestion problem of many interworking issues. In this paper, Our study is concentrated on applying connectionless network protocol for interworking. We suggest a rate control method in the network layer to prevent a buffer overflow in the IWU. Since this rate control method can be applied to prevent buffer overflow in a congested IWU, We investigate the use of rate control to solve congestion problems of IWU and parallize network layer with rate control to lessen the congestion problem in IWU.