cc: Limit ManageTiles calls to once per-frame on average

cc/scheduler/scheduler_state_machine.h

Index: cc/scheduler/scheduler_state_machine.h
diff --git a/cc/scheduler/scheduler_state_machine.h b/cc/scheduler/scheduler_state_machine.h
index 2e61224fb284eb9933005a9cd9822227e98d626b..069384bdcccd4585a29e107c1e6f3ee5c3841b3a 100644
--- a/cc/scheduler/scheduler_state_machine.h
+++ b/cc/scheduler/scheduler_state_machine.h
@@ -254,6 +254,7 @@ class CC_EXPORT SchedulerStateMachine {
   bool ShouldCommit() const;
   bool ShouldManageTiles() const;
 
+  void AdvanceCurrentFrameNumber();
   bool HasSentBeginMainFrameThisFrame() const;
   bool HasScheduledManageTilesThisFrame() const;
   bool HasUpdatedVisibleTilesThisFrame() const;
@@ -280,8 +281,12 @@ class CC_EXPORT SchedulerStateMachine {
   int last_frame_number_swap_performed_;
   int last_frame_number_begin_main_frame_sent_;
   int last_frame_number_update_visible_tiles_was_called_;
-  int last_frame_number_manage_tiles_called_;
 
+  // manage_tiles_funnel_ is "filled" each time ManageTiles is called
+  // and "drained" on each BeginImplFrame. If the funnel gets too full,
+  // we start throttling ACTION_MANAGE_TILES such that we average one
+  // ManageTile per BeginImplFrame.
+  int manage_tiles_funnel_;
   int consecutive_failed_draws_;
   bool needs_redraw_;
   bool needs_manage_tiles_;