Little’s law
Hospital Operations
Definition. Little’s law states that, in a stable system, the average number of items in the system equals the average arrival rate multiplied by the average time each item spends in the system (L = λW).
Explanation
Little (1961) gave the first general proof of the relation, which holds under very broad conditions and does not depend on the distribution of arrivals or service times. Looking back fifty years later, Little (2011) showed that the relation also holds over a finite observation period, which makes it directly usable with the records that managers already keep.
In hospitals the law links three numbers that are usually monitored separately: how many patients are present (occupied beds, chairs or waiting places), how many arrive per unit of time, and how long they stay or wait. When two are known, the third follows. A day treatment unit that receives five patients an hour who each stay five hours needs space, chairs and nurses for about 25 patients at the same time, an example worked through in the chapter on oncology capacity management. Because the law is an identity of averages, it does not reveal the variability that creates peaks, so it is combined with queueing models and simulation when capacity is sized.
Related concepts
Queueing theory Waiting time Length of stay Bed occupancy
Read on The Health Topics
- Workforce, Workload and Capacity Management in the Oncology Hospital: An Introduction (101)
- Bottleneck Management 101: An Interdisciplinary Introduction with a Focus on Healthcare
- The Capacity Problem in Oncology and How to Solve It
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
Cite this entry: Kurutkan, M. N. (2026). Little’s law. In The Health Topics glossary. https://healthtopic.org/glossary/littles-law/
Articles that discuss this concept
3 articles on The Health Topics use this concept. The list updates as new articles are published.