Many of us would like to enjoy a remote SIP phone to connect on our Asterisk PBX server from a remote location. Unfortunatly connecting SIP phones over firewall is not an obvious task.
The gateways (also called ADSL router, broadband router, home gateway, ...) simply require the capablity to route incoming traffic (from the public internet to the private domain) from a given port to a predefined private address. We will use these gateways as firewall and NAT devices at the local and remote sites.
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.
When SIP was designed it was expected that IP V.6 would be widely available by the time of first services deployment. Unfortunatly this is not the case and the concept of NAT (Network Address Translation ) had to be added to SIP.
When you run a phone service over the public internet there is not much that you can do to optimise the service. The quality of the phone service will be dictated by the IP packet loss, the IP latency and the time require to dial.