Abstract: In this paper, we study a double-ended queueing system with nonzero matching time and nonpersistent customers. For this model, we aim at studying the exact tail asymptotics for the boundary distribution, the marginal distribution and the joint distribution of the queue length, respectively. We model the queueing process as a random walk in the quarter plane. By applying the kernel method, we firstly determine the location of the dominated singularity of the unknown generating function. Then we analyze the asymptotic behaviors of the generating function at the dominated singularity. Finally, we obtain the exact tail asymptotics of the stationary distributions by using Tauberian-like theorem.