Little's Law

Definition

Little’s Law is a fundamental theorem in queuing theory that relates the average number of items in a stationary system ($L$) to the average arrival rate ($\lambda$) and the average time an item spends in the system ($W$).

$L = \lambda W$

• How to read: “The average number L equals lambda times W.”
• Meaning: In steady state, average inventory equals throughput rate times average time in system—works regardless of arrival/service distribution.

Why It Matters

Little’s Law proves that lead time is a direct function of work-in-progress; ignoring this relationship causes systems—from manufacturing lines to software development teams—to choke under their own weight regardless of individual effort.

Core Concepts

• L (Mean Queue Length): The expected number of customers in the system.

• $\lambda$ (Mean Service/Arrival Rate): The number of arrivals per unit of time.

  • How to read: “The symbol lambda.”
  • Meaning: Customers (or items) entering the system per unit time.

• W (Mean Wait Time): The expected amount of time each customer remains in the system.

• Distribution Independence: A critical feature of Little’s Law is that it holds regardless of the specific probability distribution of arrivals or service times.

Connected Concepts

• Queuing Systems (M&S)
• Kendall’s Notation
• Discrete Event Simulation (DES)