I have the war file of my application. I need to deploy this at the root level. The current URL is http://localhost:8080/war_name/application_name.
You have a couple of options:
Remove the out-of-the-box ROOT/ directory from tomcat and rename your war file to ROOT.war before deploying it.
Deploy your war as (from your example) war_name.war and configure the context root in conf/server.xml to use your war file :
The first one is easier, but a little more kludgy. The second one is probably the more elegant way to do it.