Question : Suggestions for dumb terminal connection to internet

I have a remote office with several dumb wyse terminals. They currently use a multiplexor and leased line to access the data center computer. I want to switch to using the internet instead of the leased line. At the data center I have a Pix 501 and a linux server. Does anyone have any recommendations for the type of hardware I would need at both sites?

Answer : Suggestions for dumb terminal connection to internet

Where I have "T1" in my last diagram you can replace that with the Internet.
 
You need to look at what the host, the host OS, and the application used by the Wyse terminals can and can not do.

Obviously the host and the application right now exepct to see a serial connection to the remote terminals.  If it requires this, there is nothing you can do.  

If the application supports telnet clients, then you can get a standard PC and a Wyse terminal emulator that support telnet and get rid of the dumb terminals, mux's and the dedicated T1.