连续时间马尔可夫链推式和拉式采样中的AoII建模
Modeling AoII in Push- and Pull-Based Sampling of Continuous Time Markov Chains
AI总结：
本文针对连续时间马尔可夫链过程，分别建立推式和拉式采样传输的AoII分析模型，利用吸收CTMC和相位型分布推导平均AoII与采样率，并给出最优采样策略见解。
摘要：
错误信息年龄（AoII）最近被提出，作为现有信息新鲜度指标的替代方案，用于涉及由远程监视器跟踪的信息源的实时采样和估计问题。与现有指标不同，只要信息源和监视器失去同步，AoII就会随时间线性增加以惩罚错误信息，并在它们重新同步时重置。虽然AoII通常针对离散时间信息源进行研究，但本文针对连续时间马尔可夫链（CTMC）过程的推式和拉式采样与传输，开发了一种新颖的分析模型。在拉式模型中，传感器仅在收到来自监视器的拉取请求时才开始传输所观测CTMC的信息。另一方面，在推式场景中，传感器了解AoII过程，当AoII过程超过一个随机阈值时进行采样和传输。针对这两种场景所提出的分析模型均基于离散时间马尔可夫链（DTMC）的构造，该DTMC在同步点的嵌入时刻进行状态转移，并利用了吸收CTMC理论，特别是相位型分布。对于给定的采样策略，开发了用于获得平均AoII和平均采样率的分析模型。给出了数值结果以验证分析模型，并为采样率约束下的最优采样策略提供见解。
英文摘要：
Age of incorrect information (AoII) has recently been proposed as an alternative to existing information freshness metrics for real-time sampling and estimation problems involving information sources that are tracked by remote monitors. Different from existing metrics, AoII penalizes the incorrect information by increasing linearly with time as long as the source and the monitor are de-synchronized, and is reset when they are synchronized back. While AoII has generally been investigated for discrete time information sources, we develop a novel analytical model in this paper for push- and pull-based sampling and transmission of a continuous time Markov chain (CTMC) process. In the pull-based model, the sensor starts transmitting information on the observed CTMC only when a pull request from the monitor is received. On the other hand, in the push-based scenario, the sensor, being aware of the AoII process, samples and transmits when the AoII process exceeds a random threshold. The proposed analytical model for both scenarios is based on the construction of a discrete time MC (DTMC) making state transitions at the embedded epochs of synchronization points, using the theory of absorbing CTMCs, and in particular phase-type distributions. For a given sampling policy, analytical models to obtain the mean AoII and the average sampling rate are developed. Numerical results are presented to validate the analytical model as well as to provide insight on optimal sampling policies under sampling rate constraints.
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