Calculating the optimal frame length for Frame Slotted ALOHA in RFID systems is a critical issue as it highly affects the reading efficiency, and hence the reading time. Most previous studies have focused mainly on the conventional definition of the reading efficiency, which is the ratio between the number of successful slots and the total number of slots (frame length). However, the duration of the slots in RFID systems depends on whether the slot is idle, successful, or collided. Some other state-of-the-art studies have focused on optimizing the frame length taking into consideration the differences in slot durations. However, they do not deliver a closed form solution for the optimum frame length in terms of the differences in slots durations. Therefore, this paper proposes a closed form solution for the optimum frame length for FSA by optimizing the Time-Aware Framed Slotted ALOHA (TAFSA) efficiency, which considers the differences in the slot durations. Simulations indicate that the proposed solution gives the most accurate results with respect to the exact solution. Moreover a gain of approx. 10% in terms of reading time wrt. the classical algorithm using parameters of the ISO 18000-6C UHFRFID standard. However, the results can also be applied to other systems based on Frame Slotted ALOHA.
