Here is the existing situation explained:

I have 4 DOS PCs and 2 Dumb Terminals which I have connected to an Intel 486 machine running AT&T Unix SVR 4.2. The two Dumb Terminals are connected to the serial ports (RS 232) of the Unix machine. The Unix machine also has a 4 port (RJ-45) terminal card. The 4 DOS PCs are connected thru serial ports to the 4 port terminal card of the Unix machine. The serial ports and the 4 port terminal card of the 486 Unix system are configured in Unix through port monitor and port service utilities of Unix. I directly get the login prompt of the Unix system on the Dumb Terminals. While in the 4 DOS PCs I run a terminal emulation software (beeline.exe) that helps me get the login prompt of the Unix system. I can now log into the Unix system from the 2 Dumb Terminals as well as the 4 DOS PCs, now acting as terminals.

Here is the desired situation explained:

I would like to replace the Intel 486 Unix system with an Intel Pentium P-4 system running Linux (Red Hat 8.0). How can I retain the connectivity with the Linux machine that I had with the 486 Unix system as explained above?