How Long Wait? Little's Law

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[The App]

Sometimes we have to wait in the queue…

Have you ever thought it would be nice if I could estimate how long I have to wait?

The app calculates estimate waiting time using Little's law in queuing theory.

The requirements are the length of the queue does not change with time and non-preemptive.

Hope this app cures your discontent a bit :-)

[Features]

Easy and intuitive to use, big buttons and swiping

Comprehensible progress display for waiting time with gradation

Timer function for counting the number of people/pairs in time

Multiple choices of progress time format

Update wallpaper during waiting time with animation

Notification when the waiting time is complete.

Share the estimate waiting time with your friends!

Tablet support, portrait and landscape

No advertisement (for paid version)

Offline available (for paid version)

[Little's law]

L = The number of people/pairs

λ = Arrival rate of people/pairs

W = Estimate waiting time

The formula of Little's law is

L = λ x W

λ is also called the effective arrival rate.

It shows how many people/pairs will come per unit time

and the higher the value, the more people/pair will come.

In Poisson distribution, it is equivalent to the average rate.

The law or formula is a theorem by Professor John Little (MIT) in 1961.

The law is fairly universal because it is not influenced by the arrival process distribution,

the service distribution, the service order.

[Little's law example 1]

- 10 people are waiting at a shop

- 4 people arrived in 1 minute

By Little's law、

L = 10

λ = 4

W = L / λ = 10 / 4 = 2.5

Answer: 2min 30sec to wait

[Little's law example 2]

- 8 people are waiting at a cash desk

- 2 people arrived in 10 seconds

By Little's law、

L = 8

λ = 2

W = L / λ = 8 / 2 (10sec unit time)

Answer: 40sec to wait