Sparse Outage Control for Wireless Internet of Things Systems Through Virtual Queue and Consecutively Effective Throughput

High reliability is crucial for stable and accurate control in wireless Internet of Things (IoT) systems. Although average outage probability is a widely adopted metric for evaluating the reliability of wireless IoT systems, it does not account for the sparsity of outage occurrences, which can be interpreted as the frequency of outage occurrence within a certain time. Compared to an isolated single outage, clustered outages can significantly impact stability. To address this problem, we introduce the concepts of virtual queue and consecutively effective throughput. The virtual queue treats outage packets as arrivals, with its service rate determined by the desired frequency of the single outage. In contrast to the traditional throughput, consecutively effective throughput measures the effectiveness of consecutive success of transmissions. Based on these concepts, we then consider maximizing the consecutively effective throughput under virtual queue constraints. Theoretical analysis is conducted to derive the optimal rate for this problem. Specifically, we explore two scenarios: 1) outages caused by packet decoding errors and 2) outages due to packet decoding errors and latency violations. Considering the nonasymptotic property of the virtual queue, queueing theory is utilized to provide closed-form expressions for virtual queue constraints. Based on the theoretical analysis, efficient and effective algorithms are proposed to obtain the optimal rate based on the above analysis. Numerical comparisons between grid searches and our algorithms validate the correctness of our theoretical analysis. This study underscores the importance of specific scheduling designs to control clustered outages, rather than merely enhancing throughput in wireless IoT systems.