Analysis of Slotted ALOHA with an Age Threshold

TL;DR

This paper analyzes a threshold-based modification of slotted ALOHA that improves Age of Information (AoI) by suspending transmissions until a certain age threshold, optimizing parameters for large networks, and demonstrating near-half minimal AoI with minimal throughput loss.

Contribution

It provides a comprehensive steady-state analysis of threshold-ALOHA, derives optimal parameters, and confirms conjectures about its scaling behavior and efficiency improvements over standard slotted ALOHA.

Findings

Optimal age threshold scales linearly with network size as 2.2n.

Optimal transmission probability scales inversely with network size as 4.69/n.

Achieves nearly half the minimal AoI of standard slotted ALOHA with less than 1% throughput loss.

Abstract

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.