In this paper an algorithm of Connection Admission Control in ATM is considered. It is shown that it works under many different kinds of dependence among arrivals, including long range dependence. This point is relevant, since recent papers show that ATM traffic is characterised by self-similarity, and hence by long range dependence. An upper bound for CLR is given, without assuming any specific cell arrival process. Applications to simulated and real data (obtained by segmenting and shaping Ethernet packets) are considered. They show the goodness and the tightness of the considered upper bound.