Is it possible to host our own TFS server that works in conjunction with Microsoft's hosted TFS service? Asked another way: Can we have some sort of edge server at our location running our source control reposisotry that acts as a local cache to the source control running in Microsoft's TFS environment? The goal is to allow for us to commit code changes, initiate builds, etc all locally but still have the source code stored up in Microsoft's environment as the master controller? We currently host our own build server but when Microsoft's TFS service goes down or is running slowly we're unable to pull the latest code and run builds.
You want TFS Proxy. It's a proxy for source control files. It had been around for a while and was originally designed to save bandwidth at a remote site, but it will do just what you describe with the service. It comes with on premises TFS. Here is the page that describes how to set it up on MSDN:
This page is geared toward a remote installation to save bandwidth, but just consider your local pc the remote site and the TFS service as "headquarters."