Since timeouts are dynamic (e.g. controllable via header values), it is difficult to observe how close requests are to hitting the timeout in production.

A histogram of remaining timeout budget would allow the user to identify latencies that are trending towards the timeout cliff as well as identify poorly tuned timeouts.

Likely a percentage histogram would be the most useful stat, i.e. p95 of requests to upstream are within 80% of their timeout budget.

Also see #6121: add computed-timeout header.