A Closed-Form Solution for ALOHA Frame Length Optimizing Multiple Collision Recovery Coefficients’ Reading Efficiency

Minimizing the reading time of the tag population 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 the frame length calculations using the conventional framed slotted ALOHA (FSA) algorithms. In such systems, only the answer of a single tag is considered as a successful slot, and if multiple tags respond simultaneously, a collision occurs. Then all the replied tags are discarded. However, modern systems have the capability of recovering this collision and convert the collided slot into a successful slot. Recent studies focused on calculating the optimal frame length taking into consideration the collision recovery probability. However, these studies have assumed a constant collision recovery probability coefficient, i.e., the probability to recover one tag from $i$ collided tags per slot is constant regardless the value of $i$. In this work, we propose a novel closed-form solution for the optimal FSA frame length which considers the differences in the collision recovery probabilities. The values of the collision recovery coefficients are extracted from the physical layer parameters. Timing comparisons are presented in simulation results to show the mean reduction in reading time using the proposed frame length compared to the other proposals.