Incoming events over federation can be slow to process

*This issue was originally created by [**@neilalexander**](https://github.com/neilalexander) at .*

This is a combination of:

1. The federation API needing to round-trip to the roomserver to find out if auth events or prev events are missing;
2. Possibly having to then go and fetch them from a pool of servers which takes time;
3. Sending the events into the input API of the roomserver can block on per-room mutexes;
4. Calculating the state might not be terribly fast either.

Trace the federation API through the roomserver lookup and input API, including missing auth or prev-event fetching, per-room mutex waits, and state calculation. Establish which stage causes the delay and define done as incoming federated events being processed faster without losing the required event and state handling.

Written by the indexing model from the issue text.