While importing historical Gitter archives into Gitter's homeserver we added a patch to improve performance:

diff --git a/synapse/handlers/message.py b/synapse/handlers/message.py
--- a/synapse/handlers/message.py
+++ b/synapse/handlers/message.py
@@ -502,7 +502,7 @@

         # We arbitrarily limit concurrent event creation for a room to 5.
         # This is to stop us from diverging history *too* much.
-        self.limiter = Linearizer(max_count=5, name="room_event_creation_limit")
+        self.limiter = Linearizer(max_count=1, name="room_event_creation_limit")

         self._bulk_push_rule_evaluator = hs.get_bulk_push_rule_evaluator()

Digging some context out of internal issues:

The idea is to reduce the concurrency of event sends into rooms from 5 -> 1 in order to eliminate state resolution from occurring when sending bursts of events to a local room: matrix-org/synapse@54c012c/synapse/handlers/message.py#L502-L504

For cross-linking, there was an old issue about doing this in #8612.

Unfortunately this changes was applied at the same time as a few other changes (disabling push and increasing the number of workers), so it is unclear how much impact this change had.