Remove delay for the first JumpList top site sync in one session

chrome/browser/win/jumplist.h

Index: chrome/browser/win/jumplist.h
diff --git a/chrome/browser/win/jumplist.h b/chrome/browser/win/jumplist.h
index 30df91991bfc0b51fa63cf55be9b39b04e693a6b..fdcf6f6590ef5813945bdce9c9a20ec30535c034 100644
--- a/chrome/browser/win/jumplist.h
+++ b/chrome/browser/win/jumplist.h
@@ -124,10 +124,9 @@ class JumpList : public sessions::TabRestoreServiceObserver,
   // quiet period, thus avoiding update storms.
   void InitializeTimerForUpdate();
 
-  // Called on a timer after requests storms have subsided. Calls APIs
-  // ProcessTopSitesNotification and ProcessTabRestoreNotification on
-  // demand to do the actual work.
-  void OnDelayTimer();
+  // Processes update notifications. Calls APIs ProcessTopSitesNotification and
+  // ProcessTabRestoreNotification on demand to do the actual work.
+  void ProcessNotifications();
 
   // Processes notifications from TopSites service.
   void ProcessTopSitesNotification();
@@ -282,6 +281,9 @@ class JumpList : public sessions::TabRestoreServiceObserver,
   // A flag indicating if a session has at least one tab closed.
   bool has_tab_closed_ = false;
 
+  // A flag indicating if a session has at least one top sites sync.
+  bool has_topsites_sync = false;
+
   // Number of updates to skip to alleviate the machine when a previous update
   // was too slow. Updates will be resumed when this reaches 0 again.
   int updates_to_skip_ = 0;