ATM is a connection-oriented technology. Before two hosts can communicate, a connection has 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. There are two types of performance guarantees: deterministic and statistical guarantees. While a deterministic guarantee provides an absolute bound on the worst case cell delay, a statistical guarantee provides a probabilistic bound on the worst case cell delay. We use a self-similar stochastic process to characterize the arrival of the real-Time traffic. Extending from our previous work on deterministic delay guarantee, we provide methods for determinating the statistical delay bound for the cell delay in an ATM network with various output port schedulers. We conclude with two case studies: one based on ordinary LAN traffic and one on the variable bit-rate MPEG video transmission of the movie "Star Wars". To show the effectiveness of our statistical delay guarantee, we compare it with the delay derived by Cruz (1991) as well as the actual cell delay determined by the two traffic traces.