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[sumo-user] update of travel time

Hi everyone,
In the ~.alt.rou file of iteration i, there are two routes r and s. In the next iteration, the r route is chosen and in ~.alt.rou of iteration i+1, we will update the travel time of these routes. According to what Gawron says, for not remembering the routes which have not used for a long time, the updated travel time of the route s will be: 
image.png
I want to know:
1- The difference between the underlined variables.
2- The meaning of "how long". Does is it refer to any specific number of iterations? 

Best regards,
Ali

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