The Age-of-Information is an important metric for investigating the timeliness performance in information-update systems. In this paper, we study the AoI minimization problem under a new Pull model with replication schemes, where a user proactively sends a replicated request to multiple servers to “pull” the information of interest. Interestingly, we find that under this new Pull model, replication schemes capture a novel tradeoff between different values of the AoI across the servers (due to the random updating processes) and different response times across the servers, which can be exploited to minimize the expected AoI at the user’s side. Specifically, assuming Poisson updating process for the servers and exponentially distributed response time, we derive a closed-form formula for computing the expected AoI and obtain the optimal number of responses to wait for to minimize the expected AoI. Then, we extend our analysis to the setting where the user aims to maximize the AoI-based utility, which represents the user’s satisfaction level with respect to freshness of the received information. Furthermore, we consider a more realistic scenario where the user has no prior knowledge of the system. In this case, we reformulate the utility maximization problem as a stochastic Multi-Armed Bandit problem with side observations and leverage a special linear structure of side observations to design learning algorithms with improved performance guarantees. Finally, we conduct extensive simulations to elucidate our theoretical results and compare the performance of different algorithms. Our findings reveal that under the Pull model, waiting does not necessarily lead to aging; waiting for more than one response can often significantly reduce the AoI and improve the AoI-based utility in most scenarios.

中文翻译：

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等待但不老化：在拉动模型下优化信息新鲜度

信息时代是调查信息更新系统中及时性性能的重要指标。在本文中，我们研究了具有复制方案的新Pull模型下的AoI最小化问题，其中用户主动向多个服务器发送复制请求以“提取”感兴趣的信息。有趣的是，我们发现在这种新的Pull模型下，复制方案捕获了跨服务器的不同AoI值（由于随机更新过程）和跨服务器的不同响应时间之间的新颖权衡，可以利用这种折衷来最大程度地减少预期的用户侧的AoI。具体来说，假设服务器的泊松更新过程和响应时间呈指数分布，我们导出了一个用于计算预期AoI的闭式公式，并获得了最佳的响应数，以等待最小化预期AoI。然后，我们将分析扩展到用户旨在最大程度地提高基于AoI的效用的设置，它表示用户对接收到的信息的新鲜度的满意度。此外，我们考虑了一个更现实的情况，即用户没有系统的先验知识。在这种情况下，我们将效用最大化问题重新构造为带有旁观的随机多武装强盗问题，并利用旁观的特殊线性结构来设计具有改进性能保证的学习算法。最后，我们进行了广泛的仿真，以阐明我们的理论结果并比较不同算法的性能。我们的发现表明，在“拉”模型下，等待不一定会导致衰老。在大多数情况下，等待一个以上的响应通常可以显着降低AoI并改善基于AoI的实用程序。