Avoiding timeout on container-managed EntityManager

I have an J2EE application whose beans have container-managed EntityManager's. In long running method calls, trying to merge data throws a

RollbackException (Timed out)

I have tried using an EntityManagerFactory but it doesn't seem to be allowed:

Cannot use an EntityTransaction while using JTA

How can I run arbitrarily long processes without setting an unreasonable timeout? Can't JTA create a new transaction when needed?

Following the comments to my question, this question and the documentation here, I solved the problem using a container-managed EntityManager and TransactionAttributeType annotations.

The bean method that caused the timeout now does multiple calls to a different method that handles a subtask, such as each method call executes within a different transaction. I use NOT_SUPPORTED attribute type since:

If the client is not associated with a transaction, the container does not start a new transaction before running the method.

With this arrangement, only the smaller processDoc method creates transactions that shouldn't timeout.

public class MyBean {
    @EJB
    private DocsBean docsBean;

    /**
     * This method transaction risks a timeout
     * so no transaction is created with NOT_SUPPORTED
     */
    @TransactionAttribute(TransactionAttributeType.NOT_SUPPORTED)
    public void longRunning(List<Document> docs) {
        for (Document doc : docs) {
            // a different transaction is used for each element
            docsBean.processDoc(doc);
        }
    }
}

public class DocsBean {
    /** Runs within a new transaction */
    @TransactionAttribute(TransactionAttributeType.REQUIRES_NEW)
    public void processDoc(Document document) {
        // takes some time but under the timeout
        // ...
    }
}

.