Can adding a "via" make for a shorter trip?

A few times just ignoring the route has resulted in a quicker time. I don't know why though.

I can think of one way in theory that this could happen and also be correct:

If you GPS has some Avoidance set (Tolls, ferries, unpaved roads, etc.), it could be that it's correctly planning the fastest route with that chosen avoidance, the 5:30 arrival time.

But I can conceive of a situation where adding a via point forces the GPS to ignore some Avoidance if ignoring the avoidance is the only way to reach the via point. And in some cases, the forced path through that Avoidance could result in a shorter trip timewise, hence your 5:13 arrival.

On the other hand, a GPS not offering a 17-minute quicker route over a lengthy trip may just be showing us that a GPS can't be expected to calculate every possible combination or routes before giving you a "fastest route" and your example may be a case in which this is being demonstrated. What was the overall distance and elapsed time for this trip? I expect that the longer the total travel time, the more likely it will be that a GPS will miss properly calculating the true fastest route.

If memory serves, this was around 135 miles, and three hours.

I "avoid" toll roads, dirt roads and U-turns. Don't think any of these applied here.

I do know this area is difficult for the GPS. I'd tried to plan a route on Basecamp, to include "Tail of the Dragon", and it wanted to go way out of the way, like Knoxville, to Chattanooga, to Atlanta.

There didn't seem to be anyway to mix "fastest time" and "shortest distance".

Roy

I've also had the routing changed, when I recalculated the same trip in the middle of the route. There are a bunch of quirks to the routing algorithms.

I haven't experience any of these problems with my TomTom

You really can't do that. While the shortest distance may result in the fastest time, often is doesn't. Your case seems a bit extreme, and I would agree that maybe there is an avoidance that is hanging up the unit. Maybe on that faster route, it thinks a section is coded as a dirt road so it rejects the route?

When I got my Nuvi and was playing with the functions, I plotted a route using fastest time, then canceled and rerouted using shortest distance. It was about 1/2 mile shorter (on a 10 or 15 mile trip) but the travel time was about 4 times longer, and would have routed me down 87 little side streets to make up that 1/2 mile, rather than taking me a marginally longer distance onto a highway.

I have seen this happen occasionally. For instance, I put a via point on the way to and from my airport.

Some family enjoys seeing how much time and how much mileage they save when they turn off the route.

I have been on a road. It is`the only road between two points in North Dakota and have the GPS (Nuvi 350) have a screen pop up telling me there is a better way to go. If I let it show me the "better way" it comes up with the same road.
It can't be avoidances, there is no other way to go.

When I leave my home going north or south i alway get a route to take me to the freeway by putting in a wia. it will take me on a diffeent road and shorten the driveing distance. I use it all the time when traveling.

I live in Albuquerque New Mexico and we don't have toll roads around here. Somewhere among the three Garmin models that I have used I thought I think I have observed behaviors that avoiding toll roads seemed to cause it to be less likely to use the interstate.

Can others comment on whether that relationship is possible?

Whether that is true or not, it certainly is true that it is absolutely impossible for the GPS to compute all possible routes and choose the fastest one In the cases where the distance between beginning and end involves a nontrivial number of route networks. This is the kind of question for which quantum computing is reputed to offer an enormous speed up in that the quasi-parallel processing aspect of such computers, if they ever come to exist, can actually handle such optimization problems fully in reasonable amounts of time. The algorithms used in your GPS come pretty close, most of the time. But they definitely give what should be considered a pretty good guess, not full optimization.

I never question the route. Regardless of what way it takes you It will always get you there. To me that is the most important thing. My 255 of 1490 have never failed me yet.

Obviously, adding a via should never give a shorter route (when shortest is selected, or faster when fastest is selected) but in real life the Nuvi often makes mistakes that are hard to explain. In the area near my home, (with no toll roads or other avoidances) my Nuvi frequently wants to take me out of my way when routing me to home. The route it selects is more "major" but is longer and includes three long traffic lights (and the Nuvi doesn't even factor red light delays into its calculations). I make a right turn off the Nuvi's route, hear "recalculating" and watch the dashboard jump to a shorter route and a faster ETA, and as a bonus I also get two less traffic lights on this route. Clearly the Nuvi knows these roads (they are paved, show on the map. and it can calculate the time and distance once I force the choice), but it just doesn't consider the shorter route.

I've seen this many times with the Nuvi. So I generality trust my route over the Nuvi, and often enjoy using the dashboard when it confirms that I made a better choice.

I certainly have used my Nuvi when taking unfamiliar backs roads in a different state on a very enjoyable trip to see an old friend. And it got me there. It might have even routed me there efficiently, but I'm not foolish enough to say that I'm certain it did. And whenever I have the Nuvi select a long route I always look it over to see if I can spot any place where it is taking me greatly out of my way just to stay on more traveled (and potentially busier and so slower) roads.

The routes sometimes are not optimal. On 95 N. the nuvi gets me off the interstate too early when my destination is in Fayetteville, so I have a via route to mark the exit that is more optimal. While the distance is longer staying on the interstate with the time being about the same, I prefer to stay on the interstate. This is with fastest time selected.

Maybe this has already been mentioned but my Garmin 2460 and my Garmin 765 both have sent me out of the way just so I would arrive at a destination on the right hand side of the road.

That happens to me too! There seems to be a road attribute in the maps for "median" or "no left turns" so that you can't make a left turn into a destination for some roads. Unfortunately the map may not know about a break in the median designed for just such a turn to that location and you get routed around Robin Hood's barn to return to the location on the opposite side of the street.