In this paper, we present a heuristic approach to analyze a boundary of network bandwidth allocated to the source(s). This approach can be applied for Call Admission Control(CAC) in ATM Networks. Our approach applies two characteristic functions, a time $\epsilon$-quantile function to characterize the source behavior and a function to characterize a maximum amount of network bandwidth served by the multiplexer. These two functions are computed independently and when used simultaneously, it allows us to obtain a new and useful notion of the statistical bandwidth allocation. Moreover, we demonstrate the use of our approach on stochastic and deterministic sources. For the deterministic source, we apply our approach to the source characterized by Dual Leaky Bucket-based traffic descriptor. Its upper bound on bandwidth requirement can be easily obtained for performing a CAC function in real time while providing a significant improvement of network utilization when compared to the peak rate-based bandwidth allocation.