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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)
Where
• 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.

### Conclusion

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

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