Time Aware Closed Form Frame Slotted ALOHA Frame Length Optimization Hazem A. Ahmed, Hamed Salah, Joerg Robert, Albert Heuberger Lehrstuhl für Informationstechnik Schwerpunkt Kommunikationselektronik (LIKE) Friedrich-Alexander-Universität Erlangen-Nürnberg Email: {hazem.a.elsaid, hamed.kenawy, joerg.robert, albert.heuberger}@fau.de Abstract—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 UHF- RFID standard. However, the results can also be applied to other systems based on Frame Slotted ALOHA. I. INTRODUCTION Over the recent years, the number of applications that use Radio-Frequency Identification Systems (RFID) has increased, and their number is expected to further grow in the near future. One main application is the area of logistics, where e.g. hun- dreds of tags (transponders) may be closely placed on pallets. This naturally requires fast RFID readers (interrogators), in order not to slow down the delivery process of the actual goods. Commonly used RFID standards in the area of logistics (e.g. ISO 18000-6C [1]) is based on TDMA (time division multiple access), which leads to a certain probability of tag- collisions on the communications channel. As the tags are of low price and simple design, they neither can sense the channel nor communicate with the others. Moreover, they are identified once during the reading process [1]. Hence, the readers are responsible for coordinating the network, and for the avoidance of collisions using anti-collision algorithms. According to the previously published RFID work, Frame Slotted Aloha (FSA) [2] is the most widely used anti-collision protocol for RFID systems due to its simplicity and robustness. In FSA, the communication timing between the reader and the tags is divided into TDMA frames, each frame includes a specific number of slots. During the reading process, each active tag randomly assigns itself to one of the available slots in a frame. Therefore, each slot can take one of the three different states: 1) Successful Slot: Only one tag chooses this slot, is fully identified, and then deactivated by the reader within the following frames. 2) Collided Slot: Multiple tags reply, Figure 1: Equal and unequal views of slots in Frame Slotted ALOHA with frame length L =6. resulting in a collision. The collided tags normally remain in their active state and retry their transmission in the next frame. 3) Idle Slot: No tag responds and the slot remains unused. Increasing the reading speed can directly be translated into the maximization of the number of successful slots wrt. the number of idle or collided slots. Based on the Random Access Theory, for a given number of tags n, the expected number of empty E, successful S, and collided C slots in each frame with a length of L slots can be expressed by the following equations [3]: E = L  1 − 1 L  n ,S = n  1 − 1 L  n-1 ,C = L − E − S (1) The conventional definition of the expected reading efficiency η conv is given by the ratio between the expected number of successful slots S in a frame and the frame length L [4]: ηconv = S L (2) Based on (1) and (2), this results in the conventional efficiency: ηconv = n L  1 − 1 L  n-1 (3) The main goal for optimizing the FSA algorithm is finding the optimal frame length L, which maximizes the reading efficiency η conv . Based on (3), the reading efficiency η conv is maximized when L opt = n as shown in [4]. In [5], [6] the authors proposed another formula for the optimal frame length that minimizes the total census delay, i.e L opt = n ln(2) . Moreover, [3] computes the optimum frame length empirically, which minimizes the reading time which almost matches the results in [5], [6]. However, in practice efficient RFID readers can quickly identify the type of a slot (i.e. idle, successful, or collided). Hence, the durations of the different slot types are not identical, which reduces the overall reading time. Figure