Puzzle HN: Throughput and Latency

So here's something to think about on a Monday morning:

What's the relationship between latency and throughput in different systems, perhaps a disk system, perhaps a network system, perhaps a single core CPU system?

We are all used to decreasing latency and increasing throughput.

But can you think of examples where you can increase latency and increase throughput at the same time?

Can you come up with scenarios where you can decrease or increase latency without any impact on throughput?

Can you contrive cases where you can decrease latency but also decrease throughput?