ATM is a connection-oriented technology. Before two hosts can communicate, a connection have to be established between them. Consider a real-time communication application running on top of an ATM network. In order to provide the real-time service, we require the connection to provide a performance guarantee. Such deterministic guarantee can only be possible if there exists an absolute worst case delay bound on all the ATM cells within the real-time connection. In this paper, we first present a framework for this worst case delay within an ATM switch. Later on, in estimating the real-time arrival traffic, we use the Deterministic Bounding Interval Dependent (D-BIND) traffic model to characterize the burstiness and the temporal correlation structure of a real-time message stream. We then derive the worst case delay bound for an ATM switch with some typical output port schedulers. We find out that our proposed method is no harder than the other existing methods in finding such worst case delay in terms of computation complexity. Hence, we have an efficient and effective way to estimate the worst case delay for the connection admission control for an ATM network.