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

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

 // Copyright 2015 The Chromium Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
 // This Polymer element shows information from media that is currently cast
 // to a device.
 Polymer({
   is: 'route-details',
 
   properties: {
@@ skipping 38 matching lines @@
     /**
      * Whether the custom controller extensionview is ready to be shown.
      * @type {boolean}
      */
     isExtensionViewReady: {
       type: Boolean,
       value: false,
     },
 
     /**
+     * The timestamp for when the route details view was opened. We initialize
+     * the value in a function so that the value is set when the element is
+     * loaded, rather than at page load.
+     * @private {number}
+     */
+    openTime_: {
+      type: Number,
+      value: function() {
+        return Date.now();
+      },
+    },
+
+    /**
      * The route to show.
      * @type {?media_router.Route|undefined}
      */
     route: {
       type: Object,
       observer: 'onRouteChange_',
     },
 
     /**
      * The cast mode shown to the user. Initially set to auto mode. (See
@@ skipping 213 matching lines @@
       this.fire('join-route-click', {route: this.route});
     } else {
       this.fire('change-route-source-click', {
         route: this.route,
         selectedCastMode:
             this.computeSelectedCastMode_(this.shownCastModeValue, this.sink)
       });
     }
   },
 });