remote access via internet

Hi all,
I guess this MUST be a faq, but, I couldnt find an answer so far, so I
try it here..
I have a small device (heating/cooling control for some large facility).
It is connected to a device server. The device server has an ethernet
interface, so it can present the data from the heating/cooling control
device as html-pages, viewable with a browser on the lan to which the
device server is connected.
Now, of course, my boss said "this should be accessable via internet",
i.e. our customers want to see the said html-pages via remote access,
but not by direct dialing in; instead they want a standard internet
connection between browser and device server.
I can connect a router to the described lan, but how do I ensure the
router is online if someone wants to see the data?
One solution would be to set up a dsl connection and choose a flat rate,
so the (dsl-)router would simply stay online.
But are there other possibilities? Maybe there could be some router
which can be "triggered" remotely to establish a connection if need arises?
Any ideas are welcome.

Yours
Dirk


Dirk Zabel