Analysis of Slotted ALOHA with an Age Threshold

We present a comprehensive steady-state analysis of threshold-ALOHA, a distributed age-aware modification of slotted ALOHA proposed in recent literature. In threshold-ALOHA, each terminal suspends its transmissions until the Age of Information (AoI) of the status update flow it is sending reaches a certain threshold $\Gamma$. Once the age exceeds $\Gamma$, the terminal attempts transmission with constant probability $\tau$ in each slot, as in standard slotted ALOHA. We analyze the time-average expected AoI attained by this policy, and explore its scaling with network size, $n$. We derive the probability distribution of the number of active users at steady state, and show that as network size increases the policy converges to one that runs slotted ALOHA with fewer sources: on average about one fifth of the users is active at any time. We obtain an expression for steady-state expected AoI and use this to optimize the parameters $\Gamma$ and $\tau$, resolving the conjectures in \cite{doga} by confirming that the optimal age threshold and transmission probability are $2.2n$ and $4.69/n$, respectively. We find that the optimal AoI scales with the network size as $1.4169n$, which is almost half the minimum AoI achievable with slotted ALOHA, while the loss from the maximum throughput of $e^{-1}$ remains below $1\%$. We compare the performance of this rudimentary algorithm to that of the SAT policy that dynamically adapts its transmission probabilities

Analysis of Age-Aware Slotted ALOHA

We present a steady-state analysis of threshold-ALOHA, a distributed age-aware modification of slotted ALOHA. Under threshold-ALOHA, each source remains passive until a certain age threshold G is reached. Nodes whose ages exceed the threshold attempt transmission with a fixed probability t in each slot. We study the scaling of the time average Age of Information (AoI) with the network size, n. We derive the distribution of the number of active users and establish that the policy converges into a slotted ALOHA with fewer participants, specifically, approximately one-fifth of all users under age-optimal parameter settings. We derive an expression for the average AoI and obtain that the optimal age threshold and transmission probability scale respectively as 2.2n and 4.69/n. We show that optimal AoI scales linearly as 1.4169n, at nearly half the minimum slope achievable using slotted ALOHA, while the loss from the maximum achievable throughput of e(-1) remains below 1%