In the old days all Phone Company Customers were connected to the central office via copper wire directly to the switch in the central office and the common battery. The central office had emergency generators with a run time dependent on the fuel supply, usually a week without a refill. When the Bell System began deploying Subscriber Line Carrier Systems they used Commercial Power and Battery Back Up at the remote cabinets. Depending on the age of the batteries the SLC systems could remain up from 12 to 24 Hours.
Some Synchronous Optical Network System have repeaters that are powered by Commercial Power and have 12 to 24 Hours of battery backup. If a Cellular tower is connected via fiber through a optical repeater with battery backup, the tower will drop out as soon as the fiber repeater batteries fail even though the tower has back up generators. There was a Hurricane in South Florida several years ago that was so severe that many Bell South central offices almost ran out of fuel for their emergency generators. Commercial Electric Power was out in many areas for up to 30 Days. Our power came back up in 4.5 days. One of our neighbors had a whole house generator that almost ran out of fuel because the propane supplier did not have an emergency generator, to operate the pump, that transferred propane from the storage tank to the delivery trucks.