What I take away is

  hc=1.2 does not ever result in any significant routing error (where
  error is failure to match 1.0), of course in the cases you tried.

  hc=1.3 is almost always non-erroneous, and the time saving from 1.5 to
  1.3 is never important


I don't 100% follow the "need 1.2 to be safe for economic route".  Those
routes don't necessarily look better than the 1.3, and you don't have
the "economic cost", because osmand doesn't expose it.  In the second
example, the 1.2 is 164km and the 1.3 is 168km, but at the cost of 15m.
But the economic cost values could be only a factor of 1.0001 apart.  So
I would not be upset with that "error".  But I see your point with the
metric of "did the route at 1.3 exactly match the 1.2 route (which is
exactly the 1.0 route) as something you can say definitively.

In ad hoc networks (computers talking over radio), there is an important
paper that proposes a way to evaluate routing algorithms.  The basic
problem is that if every node has complete, up-to-date state
information, then you can compute routes that are by definition optimal.
But sending that state information takes up capacity.   So the
definition of the best routing algorithm is one that minimizes

  total messages sent to maintain routing state

  +  

  extra hops in delivery (in that a message sent 11 hops when perfect
  information would have sent it 10 hops gets charged as an extra
  message)


This leads to wanting less information if it doesn't hurt accuracy more
than the savings.

So if you think about getting in your car and pushing the calculate
button, and then when there's a route starting to drive (since at least
here you cannot touch the phone to recmopute routes once driving), then
the metrics would be the travel distance and the sum of computation time
and driving time.


>From your research, I think I'll just use 1.3, and maybe save a 1.5
profile for really long routes.

Thanks for doing this work!



As an aside:

long ago I started using shortest rather than fastest on a garmin
handheld for driving, and found that mostly the routes were much shorter
and only slightly more time (not in the city, where you have endless
opportunities to make 3 extra turns and save 2m distance; where I am
there just aren't that many extra roads).  I'm a bit careful about
these, but I found several good ways to travel that I didn't know about
before, compared to usung the ~motorways.

This makes me want a metric which is partly based on time and partly
based on distance.  Essentially, would I want to save 1km in distance at
a cost of 1min in time?  Hard call, but for 1m extra I would want to
save 10km, and I would not want to save 100m.  I might guess at 2km/min
I'd want to save distance and add time.  One could add a blend of fuel
use to this too of course.

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