The idea behind the recently introduced "age of information" performance measure of a networked message processing system is that it indicates our knowledge regarding the "freshness" of the most recent piece of information that can be used as a criterion for real-time control. In this foundational paper, we examine two such measures, one that has been extensively studied in the recent literature and a new one that could be more relevant from the point of view of the processor. Considering these measures as stochastic processes in a stationary environment (defined by the arrival processes, message processing times and admission controls in bufferless systems), we characterize their distributions using the Palm inversion formula. Under renewal assumptions we derive explicit solutions for their Laplace transforms and show some interesting decomposition properties. Previous work has mostly focused on computation of expectations in very particular cases. We argue that using bufferless or very small buffer systems is best and support this by simulation. We also pose some open problems including assessment of enqueueing policies that may be better in cases where one wishes to minimize more general functionals of the age of information measures.

中文翻译：

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消息处理系统的信息年龄性能度量分布

最近引入的网络消息处理系统的“信息时代”性能度量背后的想法是，它表明我们对最新信息的“新鲜度”的了解，这些信息可以用作实时控制的标准。在这篇基础论文中，我们研究了两种这样的措施，一种在最近的文献中得到了广泛研究，另一种从处理器的角度来看可能更相关。将这些度量视为静止环境中的随机过程（由无缓冲系统中的到达过程、消息处理时间和准入控制定义），我们使用 Palm 反演公式来表征它们的分布。在更新假设下，我们为他们的拉普拉斯变换推导出明确的解决方案，并展示了一些有趣的分解特性。以前的工作主要集中在非常特殊情况下的期望计算。我们认为最好使用无缓冲或非常小的缓冲系统，并通过模拟支持这一点。我们还提出了一些开放性问题，包括对排队策略的评估，如果人们希望最小化信息时代更一般的功能，则可能会更好。