Analysis Methodology for Age of Information under Sequence Based Scheduling

We focus on the Age of Information (AoI) performance in a system where each user generates packets periodically to send to a common access point (AP) for status updating. To avoid heavy overhead, we assume that channel sensing, feedback information from the AP, and time synchronization are not available in the system. We adopt a multi-access scheme called the sequence scheme, where each user is assigned a periodic binary sequence to schedule their transmissions. In our previous work [18], we have thoroughly studied the AoI performance under sequence scheme when the period of schedule sequences, $L$, is equal to the status generating period, $T$. The results can be extended to the case where $T>L$. However, the case of $T<L$ is not covered by [18]. Therefore, in this paper, we concentrate on analyzing the AoI performance in the case of $T<L$, which is more challenging and requires different approaches. We conduct in-depth analysis on this case and develop a mathematical tool based on integer partitions to facilitate the analysis. We derive low-complexity closed-form expressions for two scenarios under $T<L$. Based on the obtained analytical results, we propose an algorithm to optimize the construction parameters of the sequence scheme. Finally, we compare our proposed sequence scheme with two commonly used baselines, and show that our proposed scheme outperforms the baselines in terms of AoI performance while consuming less energy.