Visually arranges tickets. People are good at seeing geometric patterns.
Seeing issues cropping up in "urgent and important" quadrant is a clear call to action. Seeing issues dangerously creeping to the edges is a visual clue, too.
Every ticket has importance and due as required parameters;
the very geometry of the chart shows / sets them.
A task may (and generally should) specify an expiration date, later than the due date.
A task past expiration date silently drop off the square into the archive.
This shows the opportunity window closing beyond user's control.
Four quadrants, each divided into its own four (nine?) quadrants. (One more level of subrivision / zoom to be considered.)
Most urgent are on the left, most important are on the top.
The horizontal sequence:
Past due but not expired | Due today | Due tomorrow | Due later.
Possibly each subdivision has its own user-settable division line, into
hot zone and cold zone. E.g. in due today, hot zone may be within 1
hour of due time, and in due later, hot zone may be those tasks with narrow
opportunity windows.
The vertical sequence:
Most important (maybe come up with nicer level names)
---
...
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Least important
The vertical sequence and the horizontal sequence each change background color in a predictable way. E.g. left is 100% red, 0% green and right is 100% green, 0% red, while top to bottom is transparent to 50% blue.
There's no smooth gradient; color levels jump to show quadrant borders.
TBD. Gutter on the left goes to the band / list of archived tasks, all past due.
Separate / split view of completed and failed tasks.
Some analysis tools (e.g. how much past due).