We study the age of information (AoI) in a random access network consisting of multiple source-destination pairs, where each source node is empowered by energy harvesting capability. Every source node transmits a sequence of data packets to its destination using only the harvested energy. Each data packet is encoded with finite-length codewords, characterizing the nature of short codeword transmissions in random access networks. By combining tools from bulk-service Markov chains with stochastic geometry, we derive an analytical expression for the network average AoI and obtain closed-form results in two special cases, i.e., the small and large energy buffer size scenarios. Our analysis reveals the trade-off between energy accumulation time and transmission success probability. We then optimize the network average AoI by jointly adjusting the update rate and the blocklength of the data packet. Our findings indicate that the optimal update rate should be set to one in the energy-constrained regime where the energy consumption rate exceeds the energy arrival rate. This also means if the optimal blocklength of the data packet is pre-configured, an energy buffer size supporting only one transmission is sufficient.

翻译：我们研究了一个由多个源-目的地对组成的随机接入网络中的信息年龄（AoI），其中每个源节点具备能量收集能力。每个源节点仅利用收集的能量向其目的地传输一系列数据包。每个数据包均采用有限长度码字进行编码，这表征了随机接入网络中短码字传输的特性。通过将批量服务马尔可夫链工具与随机几何相结合，我们推导出了网络平均AoI的解析表达式，并在两个特殊场景（即小能量缓冲区规模和大能量缓冲区规模）下获得了闭式结果。我们的分析揭示了能量累积时间与传输成功概率之间的权衡关系。随后，我们通过联合调整数据包的更新速率和块长度来优化网络平均AoI。研究结果表明，在能量受限机制下（即能量消耗速率超过能量到达速率），最优更新速率应设置为1。这也意味着，如果数据包的最优块长度已预先配置，那么仅支持一次传输的能量缓冲区规模就足够了。