This paper analyzes and optimizes the average Age of Information (AAoI) of Frame Slotted ALOHA with Reservation and Data slots (FSA-RD) in a multi-access network, where multiple users transmit their randomly generated status updates to a common access point in a framed manner. Each frame consists of one reservation slot and several data slots. The reservation slot is further split into several mini-slots. In each reservation slot, users that want to transmit a status update will randomly send short reservation packets in one of the mini-slots to contend for data slots of the current frame. The reservation is successful only if one reservation packet is sent in a mini-slot. The data slots are then allocated to those users that succeed in the reservation slot. In the considered FSA-RD scheme, one user with a status update for transmission, termed active user, may need to perform multiple reservation attempts before successfully delivering it. As such, the number of active user(s) in different frames are dependent and thus the probability of making a successful reservation varies from frame to frame, making the AAoI analysis non-trivial. We manage to derive an analytical expression of AAoI for FSA-RD by characterizing the evolution of the number of active user(s) in each frame as a discrete-time Markov chain. We then consider the FSA-RD scheme with one reservation attempt per status update, termed FSA-RD-One. Thanks to the independent frame behaviors of FSA-RD-One, we attain a closed-form expression for its AAoI, which is further used to find the near-optimal reservation probability. Our analysis reveals the impact of key protocol parameters, such as frame size and reservation probability, on the AAoI. Simulation results validate our analysis and show that the optimized FSA-RD outperforms the optimized slotted ALOHA.

翻译：本文分析和优化了帧时隙ALOHA结合预留与数据时隙（FSA-RD）在多址接入网络中的平均信息时效性（AAoI）。在该网络中，多个用户以帧结构方式将其随机生成的状态更新传输至公共接入点。每帧包含一个预留时隙和多个数据时隙，其中预留时隙进一步划分为若干微时隙。在每个预留时隙中，需要发送状态更新的用户会随机选择一个微时隙发送短预留包，以竞争当前帧的数据时隙。仅当单个微时隙内只有一个预留包被发送时，预留才视为成功。随后，数据时隙被分配给在预留时隙中成功的用户。在FSA-RD方案中，一个有状态更新待传输的用户（称为活跃用户）可能需要在成功交付前进行多次预留尝试。因此，不同帧中的活跃用户数量相互依赖，导致成功预留的概率随帧变化，使得AAoI的分析变得复杂。我们通过将每帧中活跃用户数量的演化建模为离散时间马尔可夫链，推导出FSA-RD的AAoI解析表达式。接着，我们考虑每个状态更新仅允许一次预留尝试的FSA-RD方案（称为FSA-RD-One）。由于FSA-RD-One的帧行为相互独立，我们得到了其AAoI的闭式表达式，并进一步用于获取近优的预留概率。分析揭示了帧大小和预留概率等关键协议参数对AAoI的影响。仿真结果验证了我们的分析，并表明优化后的FSA-RD优于优化后的时隙ALOHA。