In this paper we develop an approximation formalism for the queue length distribution of general queueing models. Our formalism is based on two steps of analytic approximation employing both the lower and upper bound techniques. It is favorable to a fast numerical calcuation for the queue length distribution of a superposition of a superposition of arbitary type traffic sources. In the application. M+ N D /M/1 is considered. The calculated result for queue length distribution measured by arriving or leaving customers show a good agreement with the direct simulation of the system. Especially, we demonstrate that our formula for M/M/1 is equivalent to the exact solution, while that D/M/1 is simplified in an analytic form.