try this?

synapse/federation/sender/per_destination_queue.py

@@ -178,6 +178,7 @@ class PerDestinationQueue(object):
 
     @defer.inlineCallbacks
     def _transaction_transmission_loop(self):
+        acquired_lock = None
         pending_pdus = []
         try:
             self.transmission_loop_running = True
@@ -267,9 +268,12 @@ class PerDestinationQueue(object):
 
                 # END CRITICAL SECTION
 
+                acquired_lock = yield self._transaction_manager.limiter.acquire()
                 success = yield self._transaction_manager.send_new_transaction(
                     self._destination, pending_pdus, pending_edus
                 )
+                acquired_lock = acquired_lock.release()
+
                 if success:
                     sent_transactions_counter.inc()
                     sent_edus_counter.inc(len(pending_edus))
@@ -331,6 +335,8 @@ class PerDestinationQueue(object):
         finally:
             # We want to be *very* sure we clear this after we stop processing
             self.transmission_loop_running = False
+            if acquired_lock:
+                acquired_lock.release()
 
     def _get_rr_edus(self, force_flush):
         if not self._pending_rrs:

synapse/federation/sender/transaction_manager.py

@@ -40,6 +40,8 @@ class TransactionManager(object):
         # HACK to get unique tx id
         self._next_txn_id = int(self.clock.time_msec())
 
+        self.limiter = defer.DeferredSemaphore(50)
+
     @measure_func("_send_new_transaction")
     @defer.inlineCallbacks
     def send_new_transaction(self, destination, pending_pdus, pending_edus):