We consider a slotted-time system with a transmitter-receiver pair. In the system, a transmitter observes a dynamic source and sends updates to a remote receiver through a communication channel. We assume that the channel is error-free but suffers a random delay. Moreover, when an update has been transmitted for too long, the transmission will be terminated immediately, and the update will be discarded. We assume the maximum transmission time is predetermined and is not controlled by the transmitter. The receiver will maintain estimates of the current state of the dynamic source using the received updates. In this paper, we adopt the Age of Incorrect Information (AoII) as the performance metric and investigate the problem of optimizing the transmitter's action in each time slot to minimize AoII. We first characterize the optimization problem using Markov Decision Process and evaluate the performance of some canonical transmission policies. Then, by leveraging the policy improvement theorem, we prove that, under a simple and easy-to-verify condition, the optimal policy for the transmitter is the one that initiates a transmission whenever the channel is idle and AoII is not zero. Lastly, we take the case where the transmission time is geometrically distributed as an example. For this example, we verify the condition numerically and provide numerical results that highlight the performance of the optimal policy.
翻译:我们考虑的是带有发报机接收器配对的定时系统。 在系统中, 发报机会观察动态源, 并通过通信频道向远程接收器发送更新信息。 我们假设频道没有错误, 但是会受到随机延误。 此外, 当更新传输时间过长, 传输会立即终止, 更新会被丢弃。 我们假设最大传输时间是预先设定的, 并且不受发射机控制。 接收机会使用收到的更新信息来维持动态源当前状态的估计。 在本文中, 我们采用错误信息时代( AoII) 作为性能衡量标准, 并调查每个时段优化发报机行动以尽量减少 AoII 的问题。 我们首先使用马尔科夫 决策程序来描述优化问题, 并评估某些可控传输政策的性能。 然后, 我们通过利用政策改进标尺来证明, 在一个简单和容易核实的条件下, 发报机的最佳政策是当频道闲置时即启动传输信号的时代( AoII ) 。 最后, 我们用最优的时则以数字列表来验证数据传输结果。