This paper investigates, through simulation, the performance of five Connection Admission Control (CAC) algorithms namely, PCR CAC, SCR CAC, AVG CAC, GCAC, and Norros CAC, when presented with synthetically generated homogeneous self-similar traffic sources. Various traffic and system parameters have been used. The simulation results show that statistical multiplexing gains both within a source and across sources should be exploited to improve network resource utilization. Source granularity and variability have been shown to have the most impact on the CAC performance. The limited impact of the Hurst parameter shows that the long-range correlation structure of the traffic sources can be neglected in evaluating CAC performance, at least when the buffer size is small. The CAC algorithms should be more conservative when link capacity is low and more aggressive when link capacity is high. While none of the CAC algorithms performs satisfactorily in all scenarios, the Norrors CAC and AVG CAC perform better than the others.