[Media Router] Add UMA metrics to record the load time for route controls

chrome/browser/resources/media_router/elements/media_router_container/media_router_container.js

Index: chrome/browser/resources/media_router/elements/media_router_container/media_router_container.js
diff --git a/chrome/browser/resources/media_router/elements/media_router_container/media_router_container.js b/chrome/browser/resources/media_router/elements/media_router_container/media_router_container.js
index 4163d7874352a9c66a7defd31fc2ab93e2a42e13..f994f9213b33daae5865b2127ae005dc7e1ffb98 100644
--- a/chrome/browser/resources/media_router/elements/media_router_container/media_router_container.js
+++ b/chrome/browser/resources/media_router/elements/media_router_container/media_router_container.js
@@ -253,6 +253,15 @@ Polymer({
     },
 
     /**
+     * The time at which the route details view was first opened.
+     * @private {?Date}
+     */
+    routeDetailsOpenTime_: {
+      type: Date,
+      value: null,
+    },
+
+    /**
      * The list of current routes.
      * @type {!Array<!media_router.Route>|undefined}
      */
@@ -2310,6 +2319,9 @@ Polymer({
    * @private
    */
   showRouteDetails_: function(route) {
+    if (!this.routeDetailsOpenTime_) {
+      this.routeDetailsOpenTime_ = new Date();

[imcheng, 2017/06/02 23:53:13]

Use Date.now() to get back a number instead of a Date object.

Also, it would be a bit simpler if this could go into the constructor for
route-details. 

[takumif, 2017/06/03 01:31:14]

Done.

+    }
     this.currentRoute_ = route;
     this.currentView_ = media_router.MediaRouterView.ROUTE_DETAILS;
     if (this.useWebUiRouteControls) {