Our previously proposed method is further applied to find the queue length distribution of MMPP/D1 in an ATM multiplexer. We derive some useful relationship between the queue distribution seen by arriving cells and for a server befor each service. The relations were used to improve out approximation. For MMPP/D1 the calculated results show a good agreement with those obtained by a simulation of the system. Furthermore, our approximation provides fast numerical algorithms for general traffic models. These advantages demomstrate that our approximation method is useful for a fast and accurate traffic analysis in ATM networks.