Little's Law

Little’s Law states that in a stable system, L = λW, where: L = mean number of customers in the system λ = mean arrival rate W = mean time a customer spends in the system The law holds regardless of arrival or service distributions, number of servers, or scheduling discipline. Why It Is Surprising Little’s Law holds without any assumptions about the distribution of arrival rates or service times. It does not matter whether arrivals are Poisson, deterministic, or correlated, whether service times are exponential, constant, or heavy-tailed, whether there is one server or a hundred, or what scheduling discipline is used (FIFO, LIFO, random, or priority). As long as the system is stable and stationary, $L = \lambda W$. This universality is remarkable because almost every other formula in queueing theory does depend on distributional assumptions. Practical Use Because $L = \lambda W$ is universal, it can be used to measure hard-to-observe quantities from easy-to-observe ones. For example,…