Admission control strategies play an important role in congestion control and in guaranteeing the quality of service in Asynchronous Transfer Mode (ATM) networks. Three categories of algorithms have been proposed for use in admission control. These algorithms include deterministic approaches that examine worst-case behavior, statistical approaches that use statistical means to guess behavior, and dynamic approaches that look at past behavior to predict future behavior. This paper examines the parallel monitoring algorithm for dynamic admission control. This algorithm has been proven to have a finite learning time. This paper expands on this work by examining the effectiveness of the algorithm under different conditions and comparing it with several other approaches. It is shown that the parallel monitoring algorithm performs well when the learning period is of sufficient length and outperforms most of the other non-dynamic approaches. When the learning period is too small it is shown ...