Little’s Law

Little’s Law

> In queueing theory, the long-term average number L of customers in a stationary system is equal to the long-term average effective arrival rate λ multiplied by the average time W that a customer spends in the system.

L = λW

• L = Items in the queue
• λ = Average arrival rate (throughput)
• W = Average processing time

WIP = Throughput * Response time

Response Time = WIP / Throughput

Throughput = WIP / Response Time

defmodule LittleLaw do
  defstruct unit: nil,
            throughput: nil,
            wip: nil,
            response_time: nil

  def wip(ll) do
    value = ll.throughput * ll.response_time
    value / ll.unit
  end

  def response_time(ll) do
    value = ll.wip / ll.throughput
    value * ll.unit
  end

  def throughput(ll) do
    value = ll.wip / ll.response_time
    value / ll.unit
  end
end

ll = %LittleLaw{
  unit: :timer.seconds(1),
  response_time: :timer.seconds(0.2),
  throughput: 10,
  wip: 2
}

LittleLaw.wip(ll) |> IO.inspect()
# LittleLaw.response_time(ll) |> IO.inspect()
# LittleLaw.throughput(ll) |> IO.inspect()