I would guess the RequestDispatcher is what you're looking for - it's the closest thing towards having one servlet "invoke" another (i.e. pass request handling to another). There's no way (indeed there is no need) to invoke a servlet instance directly. Please clarify for further advice.
Charles Lyons (SCJP 1.4, April 2003; SCJP 5, Dec 2006; SCWCD 1.4b, April 2004)
Author of OCEJWCD Study Companion for Oracle Exam 1Z0-899 (ISBN 0955160340 / AmazonAmazon UK )