AbstractIt has been demonstrated by Takacs that combinatorial methods can be successfully applied to derive certain probability distributions in queueing processes. Mohanty further illustrated the usefulness of combinatorial techniques and determined the stochastic law of the busy period in two queueing systems particularly involving batches. This paper describes an analysis of a simple queueing process based on the number of minimal lattice paths, which is counted in terms of the Catalan number as the special case. The proposed procedure is comparatively convenient and practical.