S=sampling interval
I=time between two packets to the same route
O=offered load

1) convergence event instant
first sampling interval where received rate < offered load
we can observe to all routes (instantaneous loss for all routes)
a) best case (smallest deviation between real and measured value)
T0-S+2dT: sample (received rate == offered load)
T0-1/O+dT: packet, received
T0: convergence event instant
T0+dT: packet, dropped
T0+2dT: sample (received rate < offered load)
 
real - measured = (T0) - (T0+2dT) ~ 0
 
b) worst case (largest deviation between real and measured value)
T0-dT: packet, received
T0: convergence event
T0+1/O-2dT: sample (received rate == offered load)
T0+1/O-dT: packet, dropped
T0+1/O+S-2dT: sample (received rate < offered load)
 
real - measured = (T0) - (T0+1/O+S-2dT) ~ -(S+1/O)
Note: for ECMP member failures, less traffic is sent on preferred egress interface (in extremis only traffic to one route) it can become -(S+I)

=> measured - (S+1/O) < real < measured



2) first route convergence event instant
first sampling interval where received rate starts increasing
we can focus the observation to the first route x (yet unknown) converging
a) best case
T0: first route convergence event instant
T0+dT: packet to x, received
T0+2dT: sample (received rate increased)
 
real - measured = (T0) - (T0+2dT) ~ 0
 
b) worst case
T0-dT: packet to x, dropped
T0: first route convergence event instant
T0+I-2dT: sample (received rate not increased)
T0+I-dT: packet to x, received
T0+I+S-2dT: sample (received rate increased)
 
real - measured = (T0) - (T0+I+S-2dT) ~ -(S+I)

=> measured - (S+I) < real < measured


 
3) convergence recovery instant
first sampling interval where received rate == offered load
we can focus on the last route y (yet unknown) converging
a) best case
T0-I+dT: packet to y, dropped
T0-I+dT: sample (received rate < offered load)
T0: convergence recovery instant
T0+dT: packet to y, received
T0-I+S+dT: sample (received rate == offered load)
 
real - measured = (T0) - (T0-I+S+dT) ~ -(S-I)
 
b) worst case
T0-I-dT: packet to y, dropped
T0-2dT: sample (received rate < offered load)
T0-dT: packet to y, received
T0: convergence recovery instant
T0+S-2dT: sample (received rate < offered load)
T0+2S-2dT: (received rate == offered load)
 
real - measured = (T0) - (T0+2S-2dT) ~ -2S

=> measured - 2S < real < measured - (S-I)



Derived metrics
===============

convergence event instant: [-(S+1/O), +0]
first route convergence event instant: [-(S+I), +0]
convergence recovery instant: [-2S, -(S-I)]

first route convergence time
= first route convergence event instant - convergence event instant
accuracy interval: [-(S+I)-0, 0-(-(S+1/O))] = [-(S+I), +(S+1/O)]

full convergence time
= convergence recovery instant - convergence event instant
accuracy interval: [-2S-0, -(S-I)-(-(S+1/O))] = [-2S, +(I+1/O)]