The heterogeneous nature of traffic sources into the Broadband Integrated Services Digital Network (B-ISDN) Communication systems requires the switching centers to allocate resources dynamically. The strategy used to allocates the resources among these streams should consider their particular requirements. We are considering a system with two input traffic, one with high priority which can tolerate some loss, and the lower priority which cannot experience any loss. The switching scheme is a movable boundary system with overflow traffic. This system bounds the observed delay by the overflow traffic by restricting their access.