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Applying the Queueing Theory to Kanban

22 January 2016

Kaushik Saha
Infinite Computer Solutions (Client Place : Verizon Data Services India Ltd.)

Queuing Theory: Little's Law

According to the Queueing Theory (Little's Law), if the average number of customers in the queue = L, the average arrival rate = A, and the average time a customer spends in the queue = W, then Little's Law says that L = A * W.

If we apply this same theory to Kanban software development, then we can say:
  • WIP (work in progress) = Throughput * Cycle Time
  • Or, Throughput = WIP/Cycle Time
  • Or, Throughput ∞ 1/ Cycle Time (when WIP is constant)
  • WIP = The average number of work items in the process
  • Throughput = The average number of work items that are in the "done" state (i.e., average departure rate)
  • Cycle Time = The average time a work item spends in the process (delivery date – start date)
That means that if we would like to increase the Throughput in our system, we'd have to reduce the Cycle Time of a work item.

Scenario 1: Calculation of WIP limit

Suppose that Throughput = 3 work items per day and Cycle Time per work item = 2 days, then WIP = 3 * 2 = 6. That means that only a maximum of 6 items are allowed to stay in the work-in-process field. This is called "limiting WIP."

Scenario 2: Comparison of Throughput based on constant WIP

Suppose the WIP is constant and equals to 2, and we observe that the Cycle Time we have per work item is 8 days, then Throughput = 2/8 or 0.25.

The team decides that it needs to increase its throughput from 0.25 to 0.5 to make a faster delivery. Then the "Cycle Time" calculation would be 2/0.50 = 4 days per work item.


Kanban provides greater visibility, perfect measurement, and faster feedback for improvements in the pull system by using this process.

Opinions represent those of the author and not of Scrum Alliance. The sharing of member-contributed content on this site does not imply endorsement of specific Scrum methods or practices beyond those taught by Scrum Alliance Certified Trainers and Coaches.

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