Little's Law

Introduction to Little's Law

Little's Law is a widely recognized theorem in queuing theory. It relates the number of items ( L ) in a queuing system to the average arrival rate ( λ ) and the average time ( W ) an item spends in the system. Mathematically, it's expressed as L = λW. It is applicable for stable systems where the average number in the system or in the queue, average arrival rate, and average waiting time remain constant over time.

Parameter usage:

• L (Average number of items in the system)
• λ (lambda) (Average arrival rate of items)
• W (Average time an item spends in the system)

Output:

• The function returns true if L equals lambda multiplied by W, otherwise returns an error message if parameters are invalid.

Data validation

L, and W should be greater or equal to zero and λ should be greater than zero.

Summary

The formula is crucial in designing and understanding processes and systems that involve waiting lines or queues, such as customer service desks, manufacturing processes, and computer networks.