Internet Public address
The address A1 is publicly visible from the Internet which means that you can reach it by a name that does not change over the time. The address B1 is visible from Internet but does not require to get an associated host name.
If these two addresses are not fixed, then some level of stability is required as you can potentially lose calls when established during an IP address change. In practice most of ISP will leave you with the same IP address for at least 24 hours, if you have some traffic running on the interface, what will be the case with the SIP signalling.

Internet visiblity of A1
The address A1 (local site internet connection) must be reachable by a host name lookup. If you use an ISP who sells fixed IP address for no (or little extra money) then you are on the easy side of the fence (e.g. demon.net in UK or free in France).
If your ISP does not provide fixed IP at a reasonable cost, then you will use a dynamic DNS registration from a provider such as DynDNS. DyncDNS provides free services for private users. DynDNS will let you create a dedicated host name in one of their special domain (e.g. mysiphomeasterisk.homelinux.net). Your ISP gateway (e.g. Linksys) will report to DynDNS any IP address change and DynDNS will keep the name lookup up to date. In practice, as it take quite a while to relay hostname/IP addresses over the Internet, it will only work if you have some stability on your IP address. DynDNS normally works well with most ISP.
Domain Da1 and Db1
These two address domains are controled by the ISPs used to connect to the internet the local an the remote sites. You have no control over them.
Domain Da2
This is your home DMZ. Many people directly connect their home LAN at that level. I personnaly always use a DMZ because the quality of the firewalling provided by Iptable under Linux is far more reliable than the simple port filtering offered by consumer broadband gateways. In that zone you want to manage your IP addresses staticly.
If you are paranoid (like me), you can declare a DHCP server to reject any dynamic connexion by allocating the IP value 0.0.0.0 to any host trying to get an IP address via DHCP. If you do not use a DMZ, you can still use the concepts presented in this application but you will have to merge the NAT functions from the 1st and 2nd level home firewalls.
A range such as 10.44.160.xxx/24 or 192.198.40.xxx/24 would do
Domain Da3
This is your home LAN address will typically dynamicaly allocated via DHCP. There is no need to use static address for your SIP phone(s) in that domain.
A range such as 10.44.161.xxx/24 or 192.168.41.xxx/24 would do
Domain Db2
This is the domain of the University housing facility. You have no control over it. The B2 address is generaly allocated by DHCP based on your remote gateway MAC address.
You will most likely discover a private IP range supporting many addresses such as 10.10.0.0/16.
Domain Db3
This is the domain in the student room, it is purely local.
Due to the lack of fine control of the DHCP server provided by the remote gateway, it is required to configure a static IP address on the SIP phone. Feel free to use DHCP for other devices.
The Lynksys gateway DHCP server will allocate the IP addresses in the order of discovery of connected devices after each power cycle. As long as the gateway is not powered off there is no visible problem, but after the first power cut, you will have no control of what IP address your SIP phone will receive while you need that knowledge to configure the NAT.
The DHCP server will configure the other connected devices in the student room (e.g. PC, printer, visiting friend, ...). If you activate the Wireless function of the gateway, don't forget to activate all the security facilities.
A range such as 10.44.170.xxx/24 or 192.168.50.xxx/24 would do.
Please note that the range in Da3 and Db3 can technically be the same, but I do not advise that type of configuration, as you are likely going to confuse yourself and missconfigure something somewhere.


