In an Internet-of-Things system where status data are collected from sensors and actuators for time-critical applications, the freshness of data is vital and can be quantified by the recently proposed age-of-information (AoI) metric. In this paper, we first consider a general scenario where multiple terminals share a common channel to transmit or receive randomly generated status packets. The optimal scheduling problem to minimize AoI is formulated as a restless multi-armed bandit problem. To solve the problem efficiently, we derive the Whittle's index in closed-form and establish the indexability thereof. Compared with existing work, we extend the index policy for AoI optimization to incorporate stochastic packet arrivals and optimal packet management (buffering the latest packet). Inspired by the index policy which has near-optimal performance but is centralized by nature, a decentralized status update scheme, i.e., the index-prioritized random access policy (IPRA), is further proposed, achieving universally near-optimal AoI performance and outperforming state-of-the-arts in the literature.