论文标题

控制信息时代的动态定价和平均现场分析

Dynamic Pricing and Mean Field Analysis for Controlling Age of Information

论文作者

Wang, Xuehe, Duan, Lingjie

论文摘要

如今,许多区域中的许多移动用户都被邀请感知并寄回实时有用信息(例如,流量观察和传感器数据),以保持此类区域中内容更新的新鲜感。但是,由于感应和传输的采样成本,用户可能没有动机来贡献实时信息以帮助降低信息的年龄(AOI)。我们建议每个区域都提供动态定价,以提供与年龄相关的货币回报,并鼓励用户随着时间的推移以不同的速度采样信息。这个动态的定价设计问题需要很好地平衡货币支付作为向用户和AOI演变的奖励,尤其是在有关用户的到达及其私人抽样成本的不完整信息下解决的挑战。在将问题提出为非线性约束动态程序之后,为了避免维数的诅咒,我们首先提议将动态AOI降低近似为时间平均项,并成功地在封闭形式中成功解决了近似动态定价。此外,通过为无限时间范围提供稳态分析,我们表明定价方案(尽管以封闭形式)可以进一步简化为$ \ varepsilon $ - 最佳版本,而无需随着时间的推移递归计算。最后,我们将AOI控件从单个区域扩展到具有异质用户到达率和初始年龄的许多区域,每个区域不仅关心其自己的AOI动力学,而且还关心平均场游戏系统中所有区域的平均AOI,以提供整体服务。因此,我们通过使用平均野外项来估算所有区域的平均年龄动态,甚至不需要许多区域来彼此交换其本地数据,因此我们建议每个区域的分散平均现场定价以自动攻击。

Today many mobile users in various zones are invited to sense and send back real-time useful information (e.g., traffic observation and sensor data) to keep the freshness of the content updates in such zones. However, due to the sampling cost in sensing and transmission, a user may not have the incentive to contribute the real-time information to help reduce the age of information (AoI). We propose dynamic pricing for each zone to offer age-dependent monetary returns and encourage users to sample information at different rates over time. This dynamic pricing design problem needs to well balance the monetary payments as rewards to users and the AoI evolution over time, and is challenging to solve especially under the incomplete information about users' arrivals and their private sampling costs. After formulating the problem as a nonlinear constrained dynamic program, to avoid the curse of dimensionality, we first propose to approximate the dynamic AoI reduction as a time-average term and successfully solve the approximate dynamic pricing in closed-form. Further, by providing the steady-state analysis for an infinite time horizon, we show that the pricing scheme (though in closed-form) can be further simplified to an $\varepsilon$-optimal version without recursive computing over time. Finally, we extend the AoI control from a single zone to many zones with heterogeneous user arrival rates and initial ages, where each zone cares not only its own AoI dynamics but also the average AoI of all the zones in a mean field game system to provide a holistic service. Accordingly, we propose decentralized mean field pricing for each zone to self-operate by using a mean field term to estimate the average age dynamics of all the zones, which does not even require many zones to exchange their local data with each other.

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