# Knowledge Base & Community Wiki

## Little’s Law

John Dutton Conant Little, is an Institute Professor at the Massachusetts Institute of Technology, best known for his result in Operations Research, Little’s Law. Little’s law is truly amazing in its simplicity and can be used to describe the most complex of systems including resources within those systems.

Let’s take for example the system described above. The notations used include:

- N – Number of users present within the system
- C – Number of completions
- X – Throughput or Rate of Departure
- A – Number of Arrivals
- λ – Rate of Arrival
- R
_{t}– Time spent by Customers within the system

Little’s Law basically states that the long-term average number of customers in a stable system N is equal to the long-term average effective arrival rate, λ, multiplied by the average time a customer spends in the system, W or Rt, or expressed algebraically:

- N = λ * R
_{t}……………….. [ N = Number of Users in the System, R_{t}= Response Time, λ = Arrival Rate ]

Little’s Law can also be stated as:

- N = R
_{t}* X ……………….. [ N = Number of Users in the System, Rt = Response Time, X = Throughput ]

For a system where Zt (Think Time is Non Zero) Little’s Law can be stated as:

- N = [R
_{t}+ Z_{t}] * X ……………….. [ N = Number of Users in the System, Rt = Response Time, Zt = Think Time, X = Throughput ]

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