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This paper presents a novel mathematical model for Anti-collision protocols based on Framed Slotted Aloha scheme. Using recursive calculations, the proposed model accurately estimates the probability of discovering tags in multiple rounds discovery system. First, the model estimates the probability of detecting a given number of tags in one single interrogation round. Then using a probability map, the model estimates the probability of detecting the given number of tags in multiple interrogation rounds. Our results show that the proposed model accurately predicts the tags detection probability. We then use the proposed model to optimally configure the reader parameters (i.e. the frame size and the number of interrogation rounds).