flow = speed x density

I attended the ALE conference in Berlin last week. It was excellent in many many ways. Lots of participants have written blog entries and I thought I would write a short one about just one of the many things I thought was really great. It was the above graph which Karl Scotland drew in his talk, The Science of Kanban.

Karl used this graph in the context of traffic.
  • The green line is traffic Speed and it rises (to the right) from zero at the bottom left.
  • The red line is traffic Density and it rises (to the left) from zero at the bottom right.
  • The black line is traffic Flow and equals Speed x Density.
Speaking to Karl afterwards we discussed the analogy:
  • Speed = cycle time. The time it takes from the moment a piece of work enters the system to the time it gets to Done.
  • Density = work in progress. The amount of work that has entered the system but hasn't yet got to Done.
Karl also pointed out two feedback loops.
  • Start on the density line (red) at zero (bottom right) and increase the density (move up and to the left). For a while increasing the density increases the flow. Increasing the flow causes the density to reduce. Thus you have a stabilizing feedback loop helping to increase the flow.
  • As you continue to increase the density you drop over the top of the flow-curve.
  • Now as the density increases the flow decreases. And decreasing the flow causes the density to further increase. Thus you have a different destabilizing feedback loop helping to decrease the flow.
Simple and effective. Thank you Karl.


  1. Hi Jon,

    nice post thanks. I am just wondering about wording in last bullet: this is in my opinion not a stabilizing feedback loop, as we are trying to get as high flow as possible, or? So I would rather say it is destabilizing feedback loop. The analogy in development: if number of WIPs reach certain level, system destabilizes and it will be very hard to keep feature completion speed.

    So keeping the number of WIP small is relative peaceful but as soon as they cross certain level, we need to add an extra energy to keep the speed.


  2. Thanks for your comment Ivan.
    I agree and have changed it you suggested.