We study the optimal scheduling problem where n source nodes attempt to transmit updates over L shared wireless on/off fading channels to optimize their age performance under energy and age-violation tolerance constraints. Specifically, we provide a generic formulation of age-optimization in the form of a constrained Markov Decision Processes (CMDP), and obtain the optimal scheduler as the solution of an associated Linear Programming problem. We investigate the characteristics of the optimal single-user multi-channel scheduler for the important special cases of average-age and violation-rate minimization. This leads to several key insights on the nature of the optimal allocation of the limited energy, where a usual threshold-based policy does not apply and will be useful in guiding scheduler designers. We then investigate the stability region of the optimal scheduler for the multi-user case. We also develop an online scheduler using Lyapunov-drift-minimization methods that do not require the knowledge of channel statistics. Our numerical studies compare the stability region of our online scheduler to the optimal scheduler to reveal that it performs closely with unknown channel statistics.
翻译:我们研究最佳日程安排问题,即n源节点试图通过L共享的无线上网/脱节频道传送最新消息,以优化其在能源和违反年龄容忍限制下的年龄性能;具体地说,我们以限制的Markov决策程序(CMDP)的形式提供年龄优化通用公式,并获得最佳日程安排作为相关线性规划问题的解决方案;我们调查平均年龄和违反率最小化等重要特殊案例的最佳单一用户多渠道调度器的特点;这导致对有限能源的最佳分配性质的若干关键见解,因为通常的门槛政策并不适用,而且将有益于调度设计师的指导;我们然后调查多用户案件的最佳日程安排程序的稳定区域;我们还利用Lyapunov-drift-minomization方法开发一个不需要了解频道统计数据的在线调度器。我们的数字研究将我们在线调度器的稳定区域与最佳调度器进行比较,以显示它与未知的频道统计数据密切相关。