TULIP Triangulation Algorithm
minRTT = propagation delay + extra delay (due to extra circular routes , congestion and router delays)
?T measured= ?t + ?t0
(Pseudo-distance)
PD = ?T measured . ?
(Actual distance)
D = ?t . ?
PD = (?t + ?t0). ?
PD = D + ?t0 . ? .................................(1)
D = actual distance from the landmark.
C = speed of light
? = X(c) i.e. Speed of digital info in fiber optic cable
X = factor of c with which digital info travels in fiber optic cable.
?t = actual propagation delay along the greater circle router/paths.
?t0 = the extra delay causing overestimation.
PD = pseudo distance
Graphically,
H: host
L1: Landmark 1
L2: landmark 2
L3: landmark 3
Using distance farmula:
D1= ?¯ (XL1 - XH )² + (YL1 - YH)² ............................................. (2)
FROM (1) & (2)
PD1= ?¯ (XL1 - XH )² + (YL1 - YH)² + ?t0 . ? .................... (A)
Similarly for other 2 landmarks:
PD2 = ?¯ (XL2 - XH )² + (YL2 - YH)² + ?t0 . ? .................... (B)
PD3 = ?¯ (XL3 - XH )² + (YL3 - YH)² + ?t0 . ? .....................(C)
We need to linearize (A), (B) & (C) to solve them
Using Taylor Series:
f(x0) . ( x- x0) f ' (x0) . (x - x0)
f = f (x0) + ---------------- + --------------------
1! 2!
Considering the simplified part first
f = f (x0) + f(x0)(x - x0)
put (x-x0) = ?x