ArcGIS API for JavaScript ^3.29

routeParams.attributeParameterValues = [
  {
    attributeName: "Time",
    parameterName: "25 MPH",
    value: "2.5"
  },
  {
    attributeName: "Time",
    parameterName: "35 MPH",
    value: "5.0"
  }
];

require([
  "esri/tasks/RouteParameters", "esri/tasks/FeatureSet", "esri/graphic", 
  "esri/tasks/DataFile", ... 
], function(RouteParameters, FeatureSet, Graphic, DataFile, ... ) {
  var routeParams = new RouteParameters();

  //Add barriers as a FeatureSet
  routeParams.barriers = new FeatureSet();
  routeParams.barriers.features.push(
    map.graphics.add(
      new Graphic(
        evt.mapPoint,
        barrierSymbol
      )
    )
  );

  //Requires ArcGIS Server 10.1 or greater
  var networkServiceUrl = 'http://sampleserver3.arcgisonline.com/ArcGIS/rest/services/Network/USA/MapServer/'
  routeParams.barriers = new DataFile({
    url: networkServiceUrl + "/1/query?where=1%3D1&outFields=Name,RouteName&f=json"}
  );
  ...
});

require([
  "esri/map", "esri/tasks/RouteParameters", "esri/tasks/FeatureSet", "esri/symbols/SimpleFillSymbol",
  "esri/toolbars/Draw", "dojo/_base/connect", "esri/graphic", "esri/tasks/DataFile", ... 
], function(Map, FeatureSet, SimpleFillSymbol, Draw, connect, Graphic, DataFile, ... ) {
  var map = new Map( ... );
  var routeParams = new RouteParameters();
  routeParams.polygonBarriers = new FeatureSet();

  //Create a symbol for the barriers
  var polygonBarrierSymbol = new SimpleFillSymbol();

  //Use the draw toolbar to generate polygons to add as barriers.
  drawToolbar.activate(Draw.POLYGON);
  var drawEnd_connect = connect.connect(drawToolbar, "onDrawEnd", function(geometry) {
    routeParams.polygonBarriers.features.push(
    map.graphics.add(new Graphic(geometry, polygonBarrierSymbol))
  );

  //Requires ArcGIS Server 10.1 or greater
  var networkServiceUrl = 'http://sampleserver3.arcgisonline.com/ArcGIS/rest/services/Network/USA/MapServer/';
  routeParams.polygonBarriers = new DataFile({
    url: networkServiceUrl + "/7/query?where=1%3D1&outFields=Name,RouteName&f=json"}
  );
  ...
});

require([
  "esri/map", "esri/tasks/RouteParameters", "esri/tasks/FeatureSet", "esri/symbols/SimpleFillSymbol",
  "esri/Color", "esri/toolbars/Draw", "dojo/_base/connect",
  "esri/graphic", "esri/tasks/DataFile", ... 
], function(Map, RouteParameters, FeatureSet, SimpleFillSymbol, Color, Draw, connect, Graphic, DataFile, ... ) {
  var map = new Map( ... );
  var routeParams = new RouteParameters();
  routeParams.polylineBarriers = new FeatureSet();

  //Create a symbol for the barriers
  var polylineBarrierSymbol = new SimpleLineSymbol().setColor(new Color([255,0,0]));

  //Use the draw toolbar to generate polylines to add as barriers.
  drawToolbar.activate(Draw.POLYLINE);
  var drawEnd_connect = connect.connect(drawToolbar, "onDrawEnd", function(geometry) {
    routeParams.polylineBarriers.features.push(
    map.graphics.add(new Graphic(geometry, polylineBarrierSymbol))
  );

  //Requires ArcGIS Server 10.1 or greater
  var networkServiceUrl = 'http://sampleserver3.arcgisonline.com/ArcGIS/rest/services/Network/USA/MapServer/';
  var lineBarriers = new DataFile({
    url: networkServiceUrl + "/6/query?where=1%3D1&outFields=Name,RouteName&f=json"}
  );
  ...
});

require([
  "esri/tasks/RouteParameters", "esri/tasks/FeatureSet", "esri/graphic", 
  "dojo/dom", "esri/tasks/DataFile", ... 
], function(RouteParameters, FeatureSet, Graphic, dom, DataFile, ... ) {
  var routeParams = new RouteParameters();

  //Add stops as a FeatureSet
  routeParams.stops = new FeatureSet();
  routeParams.stops.features.push(
    map.graphics.add(
      new Graphic(
        evt.mapPoint,
        stopSymbol,
        { RouteName: dom.byId("routeName").value }
      )
    )
  );

  //Requires ArcGIS Server 10.1 or greater
  var networkServiceUrl = 'http://sampleserver3.arcgisonline.com/ArcGIS/rest/services/Network/USA/MapServer/';
  routeParams.stops = new DataFile({
    url: networkServiceUrl + "/1/query?where=1%3D1&outFields=Name,RouteName&f=json"}
  );
  ...
});

You set time windows as attributes on the stops. Here's an example of three stops with time windows:

routeParams.useTimeWindows = true;

var stop1 = new esri.Graphic(new esri.geometry.Point(-117.21,  34.065), stopSymbol);
stop1.attributes = new Object();
stop1.attributes.Name = "A";
stop1.attributes.TimeWindowStart = "8:00 AM";
stop1.attributes.TimeWindowEnd = "8:05 AM";

var stop2 = new esri.Graphic(new esri.geometry.Point(-117.185, 34.05 ), stopSymbol);
stop2.attributes = new Object();
stop2.attributes.Name = "B";
stop2.attributes.TimeWindowStart = "8:10 AM";
stop2.attributes.TimeWindowEnd = "8:15 AM";

var stop3 = new esri.Graphic(new esri.geometry.Point(-117.19,  34.062), stopSymbol);
stop3.attributes = new Object();
stop3.attributes.Name = "C";
stop3.attributes.TimeWindowStart = "8:20 AM";
stop3.attributes.TimeWindowEnd = "8:25 AM";