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Consider a real-time communication application running on top of an ATM network, we require the connection to provide a transmission guarantee for the real-time service. Such transmission guarantee can only be possible if there exists an absolute and deterministic worst case delay bound on all the ATM cells within the real-time connection. In this paper, we present our approach in finding this worst case cell delay within an ATM switch. In terms of computation complexity, we find out that our proposed method is no harder than any other existing methods in finding such worse case delay. Furthermore, while other researchers tackle different schedulers with different approaches, our method is general enough and is applicable to schedulers that adopt the FIFO, Static Priority (SP), Earliest Deadline First (EDF) and Generalized Processor Sharing (GPS) scheduling policies. In addition, in our proposed "Fixed Points" method, we trade-off accuracy with computation complexity for performance, as a result, our improved method is shown to be superior to all existing methods in terms of computation complexity. Through our simulation experiments based on real-time MPEG video streams, the loss in accuracy for estimating the worst case cell delay is shown to be negligible for the connection admission control for an ATM network.