For the superposition of ON/OFF sources, we propose a real-time computable two-state Markov modulated Poisson process [MMPP(2)] modeling method characterizing the aggregate cell arrival rate and the variance-time curve for cell counts. Numerical examples show that the proposed method yields a good estimation of cell loss ratio (CLR) in asynchronous transfer mode (ATM) multiplexers, Then, we propose an approximation method for calculating the workload for the MMPP(2)/D/1 system. By considering the workload as an upper bound of CLR of ATM multiplexers, He propose a connection admission control (CAC) algorithm utilizing peak cell rate, sustainable cell rate, and maximum burst size as user traffic descriptors. Using the proposed CAC algorithm, an acceptance decision is made with computational complexities of less than 3000 floating point operations. It is also observed from numerical evaluations that the proposed CAC algorithm yields a high multiplexing gain, compared with other methods in the literature.