This figure shows the effect of the muffler valve as installed in all XB12:

My mate and I decided to give it a try with our XB9 also, to find out if it might work similar there too.
Pash kindly pointed me to a free engine simulation software, which allows to compute one cylinder only, but this would be fine for just a proof of concept. I modeled one cylinder and an exhaust with the valve opened and closed and started the simulation runs. The figure below shows one of the results:

Apparently the valve increases VE (a indicator of the air mass available for combustion) which in sequence would allow to add fuel and increase torque. With the XB12 muffler and the valve motor installed we made a few rides and ended with the switching points shown below, which are not too far away from the simulated results:

My mate has a Sinus module installed (an early predecessor of the Remus Powerizer, but mapped for the stock silencer), which will provide enough fuel, but I don't have and decided to adjust the fuel maps to cope with the new situation. All enrichments were switched off (WOT, OL, front cylinder temperature correction ...), but I left EGO correction and AFV active as I wanted to watch how these were changing. Next I logged some rides, to adjust the closed loop area first, because I wanted get a stable AFV before adjusting the open loop regions.
That seemed to be a pretty large variation, and it took serveral rides to adjust the map until I ended with this:
That's still not perfect, but more uniform than before and it didn't seem worth any more efforts. Additionally a wideband O2 sensor was installed in each exhaust header, and I tried to adjust the front map to make the front cylinder run slightly rich and the rear cylinder (which is monitord by the o2 sensor) about stoich:
There are apparently some lean spots left, but these numbers are averaged and weighted, so all values must be taken with a grain of salt. With WOT enrichment and open loop correction enabled again, these lean spots will disappear then.

_________________
"It is often said that before you die your life passes before your eyes. It is in fact true. It's called living."
Terry Pratchett

Now, as everything is set up, how did the fuel maps change?

Compared to the VE curves as shown above, most fuel had to be added around the 3400 rpm column, where the change in VE reaches it's maximum also. By default the stock front map is much richer than the rear map at WOT (lambda < 0.8 at some spots), but leaner in closed loop. Although some numbers seem small, fuel differs by 108-115% in the 3400 rpm column, with lambda kept constant.
The following two images show fuel curves for a load of 175 and 255 (WOT), and the appearance is now a bit more of that taken from a XB12 ECM:


In the end rideability is improved in my oppinion because of a bit more grunt (in torque and sound), and our trip to the alps revealed no negative impact.

_________________
"It is often said that before you die your life passes before your eyes. It is in fact true. It's called living."
Terry Pratchett

The front running lean at cruise will probably be an attempt to get fuel consumption down, assuming it was intentionally set up like this. Not sure why you would want to intentionally run the front over-rich at WOT though...

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08 Specialized Langster

It's not my intention to run a front map like the one shown, but first of all I wanted a map providing an even mixture to start with and to get a feeling how to use the averaged data.

The front map can still be shifted using the front cylinder temperatur correction (but I want to know more about temperature distribution between front and rear before I touch that) and changed with open loop or WOT enrichment, and I liked to stay on the safe side of course, so better run it rich than lean.

My current fueling looks like this:

but this took another 6 iterations and I'm not sure if it's worth the effort. And compared to the stock setup

my work seems pretty well done to me.

_________________
"It is often said that before you die your life passes before your eyes. It is in fact true. It's called living."
Terry Pratchett

How stable is your AFV on a run?

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08 Specialized Langster

but I'm using a different setup for AFV: 2% (default: 5%) change after 13 (default: 21) transitions. Gives more, but smaller adjustments.

_________________
"It is often said that before you die your life passes before your eyes. It is in fact true. It's called living."
Terry Pratchett