We consider a setting where multiple active sources send real-time updates over a single-hop wireless broadcast network to a monitoring station. Our goal is to design a scheduling policy that minimizes the time-average of general non-decreasing cost functions of Age of Information. We use a Whittle index based approach to find low complexity scheduling policies that have good performance. We prove that for a system with two sources, having possibly different cost functions and reliable channels, the Whittle index policy is exactly optimal. We derive structural properties of an optimal policy, that suggest that the performance of the Whittle index policy may be close to optimal in general. These results might also be of independent interest in the study of restless multi-armed bandit problems with similar underlying structure. We further establish that minimizing monitoring error for linear time-invariant systems and symmetric Markov chains is equivalent to minimizing appropriately chosen monotone functions of Age of Information. Finally, we provide simulations comparing the Whittle index policy with optimal scheduling policies found using dynamic programming, which support our results.

翻译：我们考虑多源活跃终端通过单跳无线广播网络向监测站发送实时更新的场景。目标是设计一种调度策略，以最小化信息年龄一般非递减成本函数的时间平均值。我们采用基于Whittle指数的方法来寻找具有良好性能的低复杂度调度策略。我们证明，在具有可能不同成本函数和可靠信道的双源系统中，Whittle指数策略是严格最优的。我们推导了最优策略的结构性质，表明Whittle指数策略的性能在一般情况下可能接近最优。这些结果对于具有类似底层结构的 restless多臂赌博问题研究也可能具有独立价值。进一步地，我们证明线性时不变系统和对称马尔可夫链的监测误差最小化等价于适当选取的信息年龄单调函数最小化。最后，我们通过仿真比较了Whittle指数策略与使用动态规划求得的最优调度策略，仿真结果支持了我们的理论结论。