G/D/1 is a theoretic model for ATM network queueing based on processing cells. We investigate the G/D/1 system by discrete time modeling. Takacs' combinatorial methods are applied to analyze the system performance. An approximation for the survivor function P[Q > q], which is the probability that the queue length Q in the stationary state exceeds q, is obtained. The obtained formula requires only very small computational complexity and gives good approximation for the true value of P[Q > q].