Analysis of Slotted ALOHA with an Age Threshold
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We present a comprehensive steady-state analysis of "threshold-ALOHA", a distributed age-aware modification of slotted ALOHA proposed recently in [1]. In threshold-ALOHA each terminal suspends its transmissions until the age of its status flow exceeds a certain threshold Γ, and once age exceeds Γ, it attempts transmission with some constant probability τ, as in standard slotted ALOHA. We analyze the time-average expected Age of Information (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 in the network and use this to optimize the parameters Γ and τ, resolving the conjectures in [1] 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 using slotted ALOHA, while the loss from the maximum achievable throughput of e^-1 remains below 1%.
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