How to manage HikariCP connections when they leak?

Question

We have a Java web application that gets a connection from Hikari connection pool (ver. 3.2.0) in an HttpServlet as soon as it receives a request and closes it when the response is returned. We set the leakDetectionThreshold and the connectionTimeout so we can identify the connections that leaks.

In "pseudocode" it looks like this:

public class MyServlet extends HttpServlet {

    @Override
    protected void service(HttpServletRequest request, HttpServletResponse response) {
        try {
            Connection connection = dataSource.getConnection();
            String htmlResponse = doStuff(request, connection);
            response.write(htmlResponse);
        } catch (Exception exception) {
            //handle exception
        } finally {
            connection.close();
        }
    }

    private String doStuff(HttpServletRequest request, Connection connection) {
        //...
    }

}

In doStuff we call an external service to get some data and sometimes it takes long to answer (>30 seconds), or we get no answer at all.

This (and the high traffic on the servlet) causes the pool to fill up and so we start getting the Connection leak detection warning and once there are no more idle connections the SQLTransientConnectionException is thrown with this message: Connection is not available, request timed out after 30000ms.

This is the behaviour expected form Hikari and is totally fine.

My quesiton is: how can we handle this situation? Are there other solutions than just intercept the leaked connections and close them?