[Media Router] Add UMA metrics for Media Router Dialog WebUI performance.

chrome/browser/ui/webui/media_router/media_router_ui.h

Index: chrome/browser/ui/webui/media_router/media_router_ui.h
diff --git a/chrome/browser/ui/webui/media_router/media_router_ui.h b/chrome/browser/ui/webui/media_router/media_router_ui.h
index 958b5bb7bcde0bdba2726f17880ab118646c0e9a..ce675aa533471f98bffc23697160c129d0309325 100644
--- a/chrome/browser/ui/webui/media_router/media_router_ui.h
+++ b/chrome/browser/ui/webui/media_router/media_router_ui.h
@@ -121,6 +121,11 @@ class MediaRouterUI : public ConstrainedWebDialogUI,
   // Marked virtual for tests.
   virtual const std::string& GetRouteProviderExtensionId() const;
 
+  // Called to track UI metrics.
+  void SetUIInitializationTimer(const base::Time& start_time);
+  void OnUIInitiallyLoaded();
+  void OnUIInitialDataReceived();
+
  private:
   FRIEND_TEST_ALL_PREFIXES(MediaRouterUITest,
                            UIMediaRoutesObserverFiltersNonDisplayRoutes);
@@ -243,6 +248,10 @@ class MediaRouterUI : public ConstrainedWebDialogUI,
   // Timer used to implement a timeout on a create route request.
   base::OneShotTimer route_creation_timer_;
 
+  // The start time for UI initialization metrics timer. When a dialog has been
+  // been painted and initialized with initial data, this should be cleared.
+  base::Time start_time_;
+
   // NOTE: Weak pointers must be invalidated before all other member variables.
   // Therefore |weak_factory_| must be placed at the end.
   base::WeakPtrFactory<MediaRouterUI> weak_factory_;