We consider a time slotted status update system with an error-free preemptive queue. The goal of the sampler-scheduler pair is to minimize the age of information at the monitor by sampling and transmitting the freshly sampled update packets to the monitor. The sampler-scheduler pair also has a choice to preempt an old update packet from the server and transmit a new update packet to the server. We formulate this problem as a Markov decision process and find the optimal sampling policy. We show that it is optimal for the sampler-scheduler pair to sample a new packet immediately upon the reception of an update packet at the monitor. We also show that the optimal choice for the scheduler is to preempt an update packet in the server, if the age of that packet crosses a fixed threshold. Finally, we find the optimal preemption threshold when the range of the service time of the server is finite, otherwise we find the $\epsilon$-optimal preemption threshold.

翻译：我们考虑一个时隙状态更新系统，其中包含一个无差错的抢占式队列。采样器-调度器对的目标是通过采样并传输最新采样的更新数据包到监视器，来最小化监视器处的信息年龄。采样器-调度器对还可以选择从服务器抢占一个旧的更新数据包，并将一个新的更新数据包传输到服务器。我们将此问题建模为马尔可夫决策过程，并找到最优采样策略。我们证明，对于采样器-调度器对而言，在监视器接收到更新数据包后立即采样一个新数据包是最优的。同时，我们还证明，如果服务器中的数据包年龄超过固定阈值，调度器的最优选择是抢占该数据包。最后，当服务器服务时间的范围有限时，我们找到最优抢占阈值；否则，我们找到ε-最优抢占阈值。