The speed of light in fibre is roughly 0.66*c where c is the velocity of light in vacuum. The speed of light in a vacuum is 299,792,458km/sec exactly or roughly 300km/sec. Thus:
RTD[km] = Alpha * min_RTT[ms] * 100 [km/sec]
where RTD = Round Trip Distance.
Thus if we know the RTD (e.g. by knowing the latitude and longitudes of the source and destination) and have measured the min_RTT then we can derive Alpha as:
Alpha = RTD[km] / (min_RTT[ms] * 100 [km/sec])
Thus assuming no queuing (which is why we use min_RTT) and negligible network device delays: large values of Alpha close to one indicate a very direct path (i.e. a great circle route); smaller values usually indicate a very indirect path.
The approximations can mean that Alpha can be > 1. Besides the approximation of the speed of light in vaccum, there is the approximation that the speed of light in fibre is 0.66c. However if the refractive index of the fibre is 1.4 then the speed of light in the fibre is not 200,000km/sec but 214,000km/sec. For more on the refractive index see John E. Midwinter, “Optical Fibers for Transmission”, John Wiley & Sons, NY, 1979. There is states:
For multimode and single mode step index fibers operating at wavelengths near 850 nm a typical cladding would have a refractive index of 1.518 and the core would have a refractive index of 1.538 which is 1.3% greater. The velocity of propagation in the multimode step index fiber would be near the speed of light (c) divided by 1.538.
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