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The procedure is similar to finding the shortest path through a network with no time-dependent travel cost (go there first).

First calculate the path(s) from origin to the cutoff-point(s), where the new time interval starts. In other words spread until the available time in time interval 1, depending on your starting time, has been used up. From the cutoff-point(s) in time interval 1, calculate the shortest path(s) to the destination through time interval 2. The path with the lowest value is the sought path. Join the paths.

The cell value at the cutoff-point for time interval 1added to the cell values of the shortest path in time interval 2 is the total cost for the joined path.

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Creating proximity surfaces for path(s) in time interval 2 and adding these together yield the shortest path(s) through time interval 2.

SpreadFromCutoff1_Time2 = Spread Cutoff_Point1
To 600
In costoftravel_time2
Outof direction
;

SpreadFromCutoff2_Time2 = Spread Cutoff_Point2
To 600
In costoftravel_time2
Outof direction
;

SpreadFromCutoff3_Time2 = Spread Cutoff_Point3
To 600
In costoftravel_time2
Outof direction
;

SpreadFromCutoff4_Time2 = Spread Cutoff_Point4
To 600
In costoftravel_time2
Outof direction
;

SpreadFromStop_Time2 = Spread stopTo 600
In costoftravel_time2
Outof direction
;

ShortestPath1_InNetwork_time2 =
SpreadFromCutoff1_Time2 + SpreadFromStop_Time2
;

ShortestPath2_InNetwork_time2
= SpreadFromCutoff2_Time2 + SpreadFromStop_Time2
;

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Now, the shortest path(s) can be extracted as follows:

ShortestPath_time2 = Recode ShortestPath4_InNetwork_time2
Assigning 999 To 83…85
;

For time interval 1, first add proximity surfaces, then extract path.
SpreadFromCutoff4_time1 = Spread Cutoff_Point4
To 600
In costoftravel_time1
Outof direction
;

ShortestPath_InNetwork_time1 = SpreadFromStart_Time1
+ SpreadFromCutoff4_time1
;

ShortestPath_time1 = Recode ShortestPath_InNetwork_time1
Assigning 999 To 169…171;

The extracted paths can now be joined and overlayed over the study area map for visualization.

ShortestPath_time = Cover ShortestPath_time1 With ShortestPath_time2
;

ShortestPath_OverMap_time = Cover BrownsPond With ShortestPath_time
;

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