In First Contact, Picard says the Federation is 8,000 light years across
In VOY:Relativity, the Class 9 warp core could go 3 years without refueling.
And considering the fire power of Deep Space Nine...
It would be prudent to construct these stations as cities of refugee for trade routes and outlining exploration vessels like the USS Titan to refuel as well as to direct Flight Control and Early Threat Detection control centers. I wouldn't place one in every sector but one Orbital City could control a 3D Grid of 200-500 light years. I assume this was how the Borg Cube in First Contact was detected even though it was beyond the Federation Border.
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Bashir,
Is this all done in Bridge Commander?