Pretty much the only way to increase the Alexa ranking of your service is installing the toolbar yourself and making sure you visit your own site every day. You can also get your friends, partners and customers to install it, but I don't think they would visit every day just to help you out, unless there is a clear value for them.
What you shouldn't do is try to hack the sytem. That would be something like install the Toolbar on all machines on your office and create a script that hits your website. Not only that might not work (because you are coming from the same IP address), but the Alexa server processing might decide to permanently exclude data coming from those machines / IP, so it pretty much back-fired on you.