This paper presents the Quality of Services analyses in ATM switch that serves different types of traffic sources, applies different priorities and different serving rates. Special attention is paid to the ATM traffic sources with different nature of cell generation. Only two types of traffic sources (deterministic e.g. telephone, slow video and HDTV, and elastic e.g. e-mail, ftp) are used. We detect some specific thresholds of cell loss and cell delay that depend on specific thresholds of queue length, intensity of traffic sources (load) and the ratio between high and low-priority traffic. Increasing load the effect of statistical multiplexing is almost lost because only the deterministic traffic flows. Priority schema applied influences the waiting times of cells (for real-time services), as well as number of cell lost, and increases fairness.
The main evidences with practical value from simulation results of proposed in this work method are new approach for packet discarding, through applying modification of push-out with PPD increasing fairness in ATM networks. As future work, we plan in next researches to determine these thresholds which give the maximum throughput. Previous study  indicates the importance of thresholds determination in order to achieve the maximum throughput.