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We present a performance analysis of OFDMA based cellular systems with dynamic packet assignment (DPA). Most approaches in the current literature to analyze wireless data networks do not take into account the interference conditions on the radio channel. We propose an analytical model based on a two-dimensional continuous time Markov chain (CTMC), that takes into account, the interference conditions on the OFDMA sub-carriers. We derive expressions for the mean delay and the average system throughput on the downlink in OFDMA based cellular systems with data-only traffic.