Have to ask: do you have a Network Analyst License for ArcGIS Server?
If yes, I'm sure one of the Silverlight fans can provide the info.
If no, you are out of luck with Silverlight or any other web bsed app.
Jamal, there is no support widget-wise for using a map service with Network Analysis capability. If you want to integrate routing function within ArcGIS Viewer for Silverlight, you need to write own widget. Another worth considering alternative is to use GP services for routing/service area/VRP solvers. They are very easy to publish since 10.1 and there is no special configuration required.
Geoprocessing service example: Shortest route on a street network
Jamal, hope you understand that the tools you have mentioned are in ArcMap and cannot be reached directly from the SL Viewer. Just fyi, some of the tools do exist as GP tools. You cannot create a new network dataset from scratch, but you are able to create a network dataset and then use GP tools to modify some of its properties and then run Build Network Dataset tool.
Make Route Layer
Add Locations
Look at the overview of the GP tools available in NA.
Jamal, start simple and go through the tutorial using the ArcTutor data: http://resources.arcgis.com/en/help/main/10.2/index.html#/Shortest_Route/00570000009q000000/. When your model works fine in Desktop, you will be able to publish it successfully as a GP service, but first make sure you understand the model logic. It may take some time since you are working with a fairly complex business process.