I am quite surprised that people think this is an odd configuration.
It is simple as pie, and 100% satisfactory. My company runs 4 different locations, with the server in a 5th location. There are no actual handsets anywhere in the facility (or network, for that matter) where the server resides.
Our server is part of a farm of servers that we have at Rackspace. It is a dual-core 2GB machine, also running some additional apps. Our 4 different locations field about 150 calls a day inbound, and place another 40-60 outbound calls. In essence, all the phones are 'external' to the server.
Our services are via Vonage and CallCentric. Our handsets range from Grandstream (GXP2000), Aastra (55i), Cisco (525G), to the VOIP client. No issues. I wish faxing via 3CX were cleaner, but for our configuration we felt the best solution was to 'drop back and punt'.... we use fax.com for that requirement, bypassing 3CX entirely.
Rackspace does a phenomenal job managing uptime and network connectivity to the server. We have experienced zero problems. I don't know how big the pipe at Rackspace is, but it has not been an issue. Each of the 4 remote facilities use business-class cable modems, and in those locations people run a variety of other network apps all consuming bandwidth too. Bandwidth consumption from those remote locations is not excessive.
Honestly, the only pissy part of the configuration has been STUN servers that get flaky. We transfer calls between locations easily, we manage ring groups, etc. with no problems.
Don't believe for one second that an 'external' server is unacceptable. They work just fine.
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