In this paper, we consider a scenario where the base station (BS) collects time-sensitive data from multiple sensors through time-varying and error-prone channels. We characterize the data freshness at the terminal end through a class of monotone increasing functions related to Age of information (AoI). Our goal is to design an optimal policy to minimize the average age penalty of all sensors in infinite horizon under bandwidth and power constraint. By formulating the scheduling problem into a constrained Markov decision process (CMDP), we reveal the threshold structure for the optimal policy and approximate the optimal decision by solving a truncated linear programming (LP). Finally, a bandwidth-truncated policy is proposed to satisfy both power and bandwidth constraint. Through theoretical analysis and numerical simulations, we prove the proposed policy is asymptotic optimal in the large sensor regime.

中文翻译：

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在具有马尔可夫和易错通道状态的时变网络中优化年龄惩罚

在本文中，我们考虑基站 (BS) 通过时变且容易出错的通道从多个传感器收集时间敏感数据的场景。我们通过一类与信息时代（AoI）相关的单调递增函数来表征终端的数据新鲜度。我们的目标是设计一个最佳策略，以在带宽和功率限制下，将无限范围内所有传感器的平均老化损失最小化。通过将调度问题表述为约束马尔可夫决策过程 (CMDP)，我们揭示了最优策略的阈值结构，并通过求解截断线性规划 (LP) 来逼近最优决策。最后，提出了带宽截断策略来满足功率和带宽约束。通过理论分析和数值模拟，