A Funny Thing Happened on the Way to the Priority Queue

Suppose two workloads $W_a$ and $W_b$ access a common resource, e.g., the CPU. They each have response times $R_a$ and $R_b$, respectively. The response time $R_a$ is longer than you would like. A common way to try and improve $R_a$ is to give $W_a$ a higher priority at the CPU. That's what the Unix nice command is all about. For example, if $W_a$ were a Unix process then: nice -15 Wa, would give a higher priority than the default already assigned by the Unix scheduler. But how much better will it's response time be? Nice can't tell you that.