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I work in the radio industry. GPS antennas are found at every radio installation for syncronizing the system. If it loses the 10 MHz. sync info, it stops. No cellular, no internet, no broadband, no power from the substation, nothing. Except, HF radio!
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What do you do, roughly ... just finished a stint here with Cisco/BWBU (Broadband Wireless Business Unit, the old Navini startup they in bought late 2007) where we were completing the P4 WiMAX beam-forming basestation that used GPS for system-synchronization and frequency-locking (we did extensive testing of this feature with a couple different vendor's GPS modules as well as pay attention to ultimate phase-noise of the two S-band synthesizers in the product) ... the previous Navini-proprietary over-the-air protocol (for the P3 product line) only used GPS to assure that all basestations were transmitting in/during the TX time slot (a TDD protocol - time division duplexing like WiMAX is) ... loss of GPS would have meant eventual 'wandering' of the TX slot into adjacent basestation's RX timeslots and some degradation of operation ...
I don't know how dependent routers and internet-backbone systems are on GPS, where accurate time and or frequency would intrinsically play a part, but the TCP/IP protocol itself has no requirement for accurate time/time-stamping per se. The generation of accurate clocks for digital transmission on optical links: generally, they have used PLL techniques to lock onto and 'slave' onto the incoming Layer 1 (phys layer) and demodulate that serial data bit stream.
It used to be that Telco systems required accurate timing to prevent phase-slip/loss of synchonization of T1/T3 et al between equipment and adjacent networks they interfaced with, but later technologies don't require the kind of synchronization that a memoryless, phase-synchronized 1.544 MB/s based system did ... even the Ericsson RBS 882 base stations could be 'slaved' (frequency-locked) off a T1 trunk coming in to the cell site ...