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We study a scheduling problem for a base-station transmitting status information to multiple user-equipments (UE) with the goal of minimizing the total expected Age-of-Information (AoI). Such a problem can be formulated as a Restless MultiArmed Bandit (RMAB) problem and solved asymptoticallyoptimally by a low-complexity Whittle index policy, if each UE’s sub-problem is Whittle indexable. However, proving Whittle indexability can be highly non-trivial, especially when the value function cannot be derived in closed-form. In particular, this is the case for the AoI minimization problem with stochastic arrivals and unreliable channels, whose Whittle indexability remains an open problem. To overcome this difficulty, we develop a sufficient condition for Whittle indexability based on the notion of active time (AT). Even though the AT condition shares considerable similarity to the Partial Conservation Law (PCL) condition, it is much easier to understand and verify. We then apply our AT condition to the stochastic-arrival unreliablechannel AoI minimization problem and, for the first time in the literature, prove its Whittle indexability. Our proof uses a novel coupling approach to verify the AT condition, which may also be of independent interest to other large-scale RMAB problems.