Tomcat is just a servlet container. It launches web applications. The SPARQL endpoint is a special kind of web application that you can run on Tomcat.
Fuseki ( Joseki's successor and, like Tomcat, the Apache Software Foundation project) is the most popular choice.
You say your RDF model is "big." Depending on how big it is (that is, whether it fits comfortably in memory or not), you may also need a permanent RDF repository such as Apache TDB (which is designed to work with Fuseki) or OpenLink Virtuoso (which is its own web server, so you wonβt use it with Tomcat and Fuseki, but as a standalone server).
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