Not a simple one answer fits all scenario.
First, the actual physical move: Most nation-wide moving companies offer business moving services. These usually include specialized moving materials for computer-type items. Browsing through the Yellow Pages will probably net you several companies that specialize in business moving services or in moving electronics. Get some quotes and ask for references of other businesses that moved utilizing each movers services.
Second, the methodology: many factors here. Obviously a short distance move can usually be completed over a weekend, minimizing the amount of potential down-time for your servers.
With a long distance move, obviously time is a factor. At a minimum, it will be a 2-step process. Long-haul drivers are usually legally limited to either the distance or number of hours travelled in a day. With a 3000-mile move, you are probably talking 5+ days just in travel time, plus loading/unloading time at each end.
Assuming yourservers are hosting some sort of business critical operations that can't afford to be down for a week or more, you are looking at needing the capability to mirror critical operations at both the old and the new site. Obviously you need infrastructure available at both sites simultaneously. Only you can answer how much reconfiguration you will have to do on the front end to ensure half your servers can handle all business-critical operations. Then you will need time in the middle to set-up the other half of your servers once they are moved and ensure they are all working properly, before you can shut down the servers still at your old site. Then once the old site is shut down there will be time involved in the move of those servers and then reintegration of those servers into your operation once the move is complete.
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