Operating proton exchange membrane fuel cells in dead-ended anode mode results in fewer subsystem components and a lower cost and less complex system. However, dead-ended operation results in a gradual accumulation of water and impurities within the anode compartment, which leads to performance degradation. Therefore, anode purging is required to partially remove impurities and water from the anode and to recover performance. In the present study, a mathematical model, incorporating nitrogen crossover from the cathode to the anode and water build-up in the anode is developed. This model simulates the dead-ended anode proton exchange membrane fuel cell performance during the purge and the subsequent performance recovery. The model is in good agreement with experimental results. By using this model and introducing the concept of the 'total wasted energy', the purge parameters (purge interval and purge duration) can be optimized. The predicted optimum purge duration and purge interval for a sample single cell are 25 ms and 260 s, respectively. The effect of operating condition parameters on this optimization are investigated, showing that the hydrogen purity has a strong effect on the total wasted energy. By increasing the hydrogen purity from 99.5% to 99.99%, the efficiency increases by 2.4%. (C) 2019 Elsevier Ltd. All rights reserved.