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

chrome/browser/media/router/media_router_metrics.h

Index: chrome/browser/media/router/media_router_metrics.h
diff --git a/chrome/browser/media/router/media_router_metrics.h b/chrome/browser/media/router/media_router_metrics.h
index fddfd45884c5ead60a46990ce5a1e1a8219bc4d4..b5c9c7dfff7cce204663235d4596ee0933f2d60c 100644
--- a/chrome/browser/media/router/media_router_metrics.h
+++ b/chrome/browser/media/router/media_router_metrics.h
@@ -5,6 +5,8 @@
 #ifndef CHROME_BROWSER_MEDIA_ROUTER_MEDIA_ROUTER_METRICS_H_
 #define CHROME_BROWSER_MEDIA_ROUTER_MEDIA_ROUTER_METRICS_H_
 
+#include "base/time/time.h"
+
 namespace media_router {
 
 // NOTE: Do not renumber enums as that would confuse interpretation of
@@ -52,6 +54,16 @@ class MediaRouterMetrics {
   // Records why the media route provider extension was woken up.
   static void RecordMediaRouteProviderWakeReason(
       MediaRouteProviderWakeReason reason);
+
+  // Records the duration it takes for the Media Router dialog to open and
+  // finish painting after a user clicks to open the dialog.
+  static void RecordMediaRouterDialogInitialPaint(

[mark a. foltz, 2015/12/09 22:20:13]

Or maybe just "RecordMediaRouterDialogPaint".  If we want to record subsequent
rendering we can call them "Repaint."

[apacible, 2015/12/09 23:19:55]

Done. Also updated histogram name.

+      const base::TimeDelta& delta);
+
+  // Records the duration it takes for the Media Router dialog to load its
+  // initial data after a user clicks to open the dialog.
+  static void RecordMediaRouterDialogInitializedWithData(

[mark a. foltz, 2015/12/09 22:20:13]

RecordMediaRouterDialogLoaded?

[apacible, 2015/12/09 23:19:55]

Done. Also updated histogram name.

+      const base::TimeDelta& delta);
 };
 
 }  // namespace media_router