How to solve questions faster : Little's Law

A simple approach for the assessment of the efficiency of queuing systems

Say you own a small patisserie. You want to guess the average number of customers queuing for your pastries to decide if you need more space. Your small patisserie can accommodate up to 4 people.

You know that

• on average, 20 customers arrive at your coffee shop per hour.

• each customer spends about 5 minutes in your store (or, 5/60 = 0.08 hours)

Do you need more space to accommodate more customers?

This is where Little's Law comes in. Little’s Law states that -

The average number of things in the system is the product of the average rate at which things leave the system and the average time each one spends in the system

Or, on average there are 20 * 0.08 = about 2 people in your patisserie. So, you will not need extra space.

Another example can be the case of movie tickets. Say, you wait outside the theater to purchase your tickets. The place holds about 60 people inside and an average person will stay inside for 3 hours. So, you're entering at the rate if 20 people per hour. If there are 20 people waiting in line, you'll have to wait about an hour before you get your tickets.

Another intuitive example is, say you have 100 packets of coffee in stock and you consume 25 packets per year. How long do you hold each packet? Little's Law tells us that we divide 100 by 25 / month to get 4 packets per month.

Little's Law finds application wherever there is any system in which things enter and leave like an emergency department, in business operations research or by software performance testers (to measure throughput and response time). It is pleasantly intuitive and simple to understand.

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