We consider the problem of real-time remote monitoring of a two-state Markov process, where a sensor observes the state of the source and makes a decision on whether to transmit the status updates over an unreliable channel or not. We introduce a modified randomized stationary sampling and transmission policy where the decision to perform sampling occurs probabilistically depending on the current state of the source and whether the system was in a sync state during the previous time slot or not. We then propose two new performance metrics, coined the Version Innovation Age (VIA) and the Age of Incorrect Version (AoIV) and analyze their performance under the modified randomized stationary and other state-of-the-art sampling and transmission policies. Specifically, we derive closed-form expressions for the distribution and the average of VIA, AoIV, and Age of Incorrect Information (AoII) under these policies. Furthermore, we formulate and solve three constrained optimization problems. The first optimization problem aims to minimize the average VIA subject to constraints on the time-averaged sampling cost and time-averaged reconstruction error. In the second and third problems, the objective is to minimize the average AoIV and AoII, respectively, while considering a constraint on the time-averaged sampling cost. Finally, we compare the performance of various sampling and transmission policies and identify the conditions under which each policy outperforms the others in optimizing the proposed metrics.

翻译：我们研究一个两状态马尔可夫过程的实时远程监控问题，其中传感器观测源状态并决定是否通过不可靠信道传输状态更新。我们引入一种改进的随机化稳态采样与传输策略，其中执行采样的决策依据当前源状态以及系统在前一时隙是否处于同步状态而概率性地作出。随后，我们提出两个新的性能指标——版本创新年龄（VIA）与错误版本年龄（AoIV），并在改进的随机化稳态策略及其他先进采样传输策略下分析其性能。具体而言，我们推导了这些策略下VIA、AoIV及错误信息年龄（AoII）的分布与平均值的闭式表达式。此外，我们构建并求解了三个约束优化问题：首个优化问题旨在最小化平均VIA，同时约束时间平均采样成本与时间平均重构误差；第二与第三个问题则分别以最小化平均AoIV和平均AoII为目标，并考虑时间平均采样成本的约束。最后，我们比较了多种采样传输策略的性能，并确定了各策略在优化所提指标时优于其他策略的条件。