# Little's Law Little's Law is a result from queuing theory, proved by John Little in 1961: L = λW. In plain terms, the average number of items in a system (L) equals the average rate at which items arrive (λ) multiplied by the average time each item spends in the system (W). Applied to knowledge work, it's usually written as: **average work in progress = average throughput × average [[Cycle time]]** or, rearranged, **average cycle time = average WIP ÷ average throughput**. The consequence is counterintuitive and important. If your throughput stays the same (you finish, say, four tasks a week) and you double the number of things you have in progress, each item takes twice as long on average to get done. Starting more work does not make work finish faster; it makes everything finish later. This is the mathematical basis for the advice to [[Limit Work In Progress]] in [[Kanban Methodology]]. Two caveats. First, the law holds for long-run averages in a reasonably stable system, where roughly as much work leaves as enters. Daniel Vacanti stresses that it describes what happened rather than forecasting what will happen, and that its assumptions break when work is abandoned or arrivals keep exceeding departures. Second, it says nothing about individual items: a single task can still take far longer than the average. ## References - Little, J. D. C. (1961). A proof for the queuing formula: L = λW. Operations Research, 9(3), 383-387. https://doi.org/10.1287/opre.9.3.383 - Little, J. D. C. (2011). Little's Law as viewed on its 50th anniversary. Operations Research, 59(3), 536-549. https://doi.org/10.1287/opre.1110.0940 - Vacanti, D. S. (2015). Actionable Agile Metrics for Predictability (book) - https://en.wikipedia.org/wiki/Little%27s_law - https://concepts.dsebastien.net/concept/littles-law/ ## Related - [[Cycle time]] - [[Lead time]] - [[Work In Progress (WIP)]] - [[Limit Work In Progress]] - [[Kanban Methodology]] - [[System trashing]]