Little's shopping basket

We've all been there. Waiting. Waiting. Looking at the queue ahead of us. Waiting. Glancing at our watches. Wondering when we're going to get our turn...

In the 1960s, Dr. John Little famously provided the Mathematical proof for the following helpful formula (which later became known as Little's Law).

L = ⅄W

Where, in this instance:
L is the average number of customers at the checkout.
W is the average time the customer waits.
⅄  is the average rate of new arrivals.



Now, crucially, in a stable system - where no customers are created or destroyed on their way through the checkout process(!) - the Departure rate will equal the Arrival rate.

Therefore, in a stable system, we can happily equate these to queuing theory terms. Such that:
L ≡ average W.I.P. (Work in Process)
W ≡ average Cycle time
⅄ ≡ average Throughput

E.g. if there are 5 of us queuing at the checkout, 4 people ahead of us, and the cashier is processing on average 1 person every 2 minutes, we are likely - remember it's only an average (not a fool-proof predicting tool!) - to be waiting 8 minutes before we are seen, and for it to be 10 minutes before we are leaving the store...

What this simple, Mathematical relationship explains to us is why when we double the average WIP, we double the average Cycle Time (i.e. the average time it takes to get work finished).

This is why 'Single-Piece Flow' (i.e. Limiting the WIP to working upon 1 item at a time) is the ideal... And why, when given the choice of two checkouts - all other things being equal - we'd choose the checkout with the shorter line...

Location: England, UK

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