In one of my recent teaching trips to St. Louis, MO the discussion came up as to how to use the network analyst extension capabilities in the web mapping application. While looking through the Web ADF Java Doc surprisingly I did find the Routing task and an associated taskinfo class. Java Web ADF has a ready to use Routing Task but is not configurable through the manager.
Out of curiosity and with help of fellow employee (Thanks Lloyd) we figured out that if you have ArcGIS Server Service with Network Analysis capability enabled and a Geocode service then you can use these services with the Routing task in your web mapping application. The only thing missing is documentation on how to configure and use the task. Here are the steps to add this task to your application :