Part of our improvements to the Transactional Pro capability in eVSM included an enhancement to our line thickness visualization gadget. Each green arrow in our transactional map now carries a variable for the demand flowing through it. The gadget uses this data to determine the line thickness.
So, the practical upshot is that it's easy to see how much demand is flowing through a system, even when there rework and splits/merges are involved. When this was shown to an improvement team, they ended up naming this the 'demand river', as it is somewhat akin to water flowing, splitting off, and flowing back together.
Below is an example future state map for a clinical approval process. The goal of the future state design was to make most of the requests finish with the shortest total lead time possible. We used the demand river to help show the improvement in routings. The big fat lines upstream flow quickly through some decision processes, and split off so that the less-common long-lead items are identified early, and the quick/easy items get approved as quickly as possible.
The underlying data is of course of great interest, but it's absolutely necessary to be able to show it to people visually. Great visualizations like the demand river really help people to understand what the map is showing, which makes it easier for people to reconcile that with the real world. This includes being able to point out mistakes in the map (and in the author's conception of the system) much easier than if you had to try and understand a bunch of data points.