A closed form solution for frame slotted ALOHA utilizing time and multiple collision recovery coefficients

Minimizing the reading time of large tag populations is a critical issue in Radio Frequency Identification (RFID) systems. The usual approach to reduce the reading time is to select the frame size attaining the highest throughput per frame. Previous studies have focused on conventional frame length calculations. In such systems, only the answer of a single tag is considered as a successful slot. If multiple tags respond simultaneously within a slot a collision occurs. Then, all tags within this slot are discarded. However, modern system have the capability of converting part of the collided slots into successful slots. This is called Collision Recovery. Moreover, modern RFID readers have the ability to identify the type of the slot (successful, collided, or empty). Then, the readers are able to terminate the slot earlier when they recognizes that there is no tag reply. This system is called a time aware system. Recent studies focused on calculating the optimal frame length taking into consideration the time aware and the collision recovery properties. However, these studies have assumed constant collision recovery probability coefficients, i.e. the probability to recover one tag from i collided tags is constant, regardless of the number of collided tags i. Moreover, they proposed only numerical solutions for the optimum frame length. In this paper we propose a novel closed form solution for the optimal Frame Slotted ALOHA (FSA) frame length. The novel solution considers the multiple collision recovery probability coefficients, and the different slot durations. Timing comparisons are presented in the simulation results to show the reading time reduction using the proposed frame length compared to other the state-of- the-art algorithms.