Fast Collision-Free Acquisition in 1-Persistent Age-Threshold Slotted ALOHA via Role-Protected Counters

RESUMO

Goal-oriented sensing, estimation, and control benefit from prompt, regular access to task-relevant updates. Although 1-persistent age-threshold slotted ALOHA (1-pTSA) can self-organize into a periodic collision-free schedule, its acquisition transient can dominate finite-horizon performance. We propose role-protected counter-threshold slotted ALOHA (RP--CTSA), which separates reservation memory from the age of information (AoI). A scheduled singleton retains its phase after colliding with active contenders, whereas a collision involving multiple scheduled nodes releases them immediately; AoI resets only after a decoded update. The protocol requires individual acknowledgments and a binary RELEASE/HOLD indication, but no centralized phase assignment or identification of colliders. Let $n$ denote the number of nodes and $\Gamma_n$ the counter threshold. Under inverse-population access scaling, the acquisition dynamics admit an exact pure-death representation. When $\Gamma_n=n$, the acquisition time is $O(n^2)$; when $\Gamma_n\sim(1+\theta)n$, with $\theta>0$, it is $O(n\log n)$. Simulations confirm both regimes and show substantial finite-horizon AoI gains over 1-pTSA while preserving every collision-free schedule.