The paper addresses the analysis of a single multiplexing node of ATM networks. This problem has been studied in several papers providing both analytical and simulation results, however most of them assume a continuous time or fluid flow model of the system which is an approximation of the real situation. In this paper, a discrete time model based on a finite number of sources and a finite size buffer is introduced from which results on cell loss, average buffer length, and delay are given based on a two dimensional Discrete Time Markov Chain. The accurate analysis of the introduced physical model requires a detailed knowledge on the distribution of the incoming cells in the time slots and it is very hard to evaluate numerically even for small models. Based on the introduced Discrete Time Markov Chain model of the system, a Markov Decision Process is dened, with appropriate cost functions to determine the optimal and the worst cell arrival schedule, which is then used to calculate...