In this paper, we introduce a new metric, named Penalty upon Decision (PuD), for measuring the impact of communication delays and state changes at the source on a remote decision maker. Specifically, the metric quantifies the performance degradation at the decision maker's side due to delayed, erroneous, and (possibly) missed decisions. We clarify the rationale for the metric and derive closed-form expressions for its average in M/GI/1 and M/GI/1/1 with blocking settings. Numerical results are then presented to support our expressions and to compare the infinite and zero buffer regimes. Interestingly, comparing these two settings sheds light on a buffer length design challenge that is essential to minimize the average PuD.

翻译：本文提出一种名为“决策惩罚”（PuD）的新指标，用于度量源端通信延迟与状态变化对远端决策者的影响。具体而言，该指标量化了因决策延迟、错误及（可能）遗漏导致的决策者侧性能退化。我们阐明了该指标的理论依据，并在M/GI/1及带阻塞的M/GI/1/1系统中推导出平均PuD的闭式表达式。随后通过数值结果验证表达式，并对比无限缓冲与零缓冲两种场景。有趣的是，这两种场景的对比揭示了最小化平均PuD的关键缓冲区长度设计挑战。