A new approach for bandwidth allocation of heterogeneous regulated traffics is proposed for cases of lossless multiplexing and statistical multiplexing under the constraint of maximum delay. Minimum bandwidth required for lossless multiplexing can be expressed as 1-dimensional unconstrained-optimization problem. The corresponding optimality condition gives an optimal bandwidth and buffer requirements. This optimality condition is extended to the case of statistical multiplexing. In case of statistical multiplexing with independent, periodic on-off fluid sources, two random variables representing stochastic worst cases for the amount of traffics generated in an arbitrary time interval are introduced and these are combined optimally. This combined model guarantees the worst case bound for the regulated traffics. Using the proposed approach, bandwidth and buffer requirements of each virtual circuit are obtained simultaneously. As these values are sensitive to multiplexing environments, an effective bandwidth considering trade-off between bandwidth and buffer requirements is introduced. The proposed effective bandwidth can be matched directly with the boundary of the acceptance region, which is less sensitive to mutiplexing environments.