# Little’s Law Is Big For Startups

Editor’s note: Matt Oguz is managing director of Palo Alto Venture Science.

Traffic, traction, growth. We all know that these terms are prerequisites to success. As we launch our startups we hope for initial customer acceptance, which would lead to traffic, traction and growth (TTG). In some cases, we’re willing to pay for traffic. In most other cases, we work around the clock to ignite organic TTG.

When we read about the successful co-founders of a Yelp, Pinterest, or WhatsApp, we find ourselves inspired by their drive and intellect, but we often leave wondering what it really was that gave these startups the astronomical TTG that we all want. There’s certainly no shortage of ideas and opinions about how one startup achieved success, but as analytical founders, the prescribed path from “good to great” often does not satisfy us. We crave more mathematical guidance.

One discipline to turn to in order to understand the underlying mechanics of business is operations research (OR).

OR principles not only guide us to optimize and run our businesses smoothly but also provide us with statistical analysis of underlying business concepts via modeling and simulation. One of the most interesting studies in OR which provides relevant guidance to today’s applications is queuing theory. And inside queuing theory, Little’s law is a hidden gem that gives us profound hints on where to focus to achieve superior traffic, traction and growth.

Queuing theory in its simplest terms tackles problems within the context of the following flow in a store:

Arrival –> Service–> Departure

In a queuing system, there are items that arrive at some rate to the system. Then they depart. An item can be a customer or inventory. When we think about it, this is exactly what we have on a website or app. Visitors arrive, they stick around for a while, then they leave. The most valuable company is the one with the most visitors that stay the longest.

Little’s Law says that, under steady state conditions, the average number of items in a queuing system equals the average rate at which items arrive multiplied by the average time that an item spends in the system.

## Letting

L =average number of items in the queuing system,

W = average waiting time in the system for an item, and

λ =average number of items arriving per unit time, the law states the following:

“The long-term average number of customers in a stable system is equal to the long-term effective arrival rate multiplied by the average time a customer spends in the store.”

This statement sounds trivial. Its magic, however, lies in the simplicity that the relationship is not influenced by the service distribution, service order or anything else. It’s not influenced by the color of the site, the distribution of the content or the price of the product. The only thing that matters is how fast the visitors are coming and how long they’re staying. Everything else is secondary. Little’s law doesn’t only apply to queues in physical stores; it applies to networks and to any system where there’s a flow of items.

To examine a real-life situation, it’s safe to claim that Google, as a search engine, has the highest arrival rate of visitors, namely λ. But the visitors don’t stick around much. They quickly click through to another site via organic or paid links. Then they come back later for another search only to leave quickly. Google has done a phenomenal job at building up that arrival rate that made the company what it is today. But take a look at the acquisitions, research or any other top initiative at Google, and you’ll easily see that all of them target the second part of Little’s law: W, the average time a customer spends at a Google property, whether that’s email, phone, calendar or web browser.

According to Comscore, Google received about 13 billion search queries in March 2014. This translates to 433.3 million queries per day, 18 million per hour, 300 thousand per minute and only 5,000 per second. A quick comparison to Bing looks like this:

 Number of search queries Timeframe Microsoft Google Per month 3,600,000,000.00 13,000,000,000.00 Per day 120,000,000.00 433,333,333.33 Per hour 5,000,000.00 18,055,555.56 Per minute 83,333.33 300,925.93 Per second 1,388.89 5,015.43 Per millisecond 1.4 5

One wonders if Bing at any point exceeded Google’s 5,000 per second search rate. If yes, that’s good for Bing and bad for Google and it’s crucial to figure out why that jolt happened at that particular second. Investigating short bursts of higher-than-usual traffic leads to significant hints versus observing daily or monthly numbers.

Now consider Facebook. Facebook has both great arrival rate and time spent in “store.” But its customer arrival rate (λ) is not as high as Google’s. This is why all the top acquisitions and projects at Facebook target increasing the arrival rate. We visit Facebook a few times a day and stick around a little bit but then we quickly jump to a Google search.

Operation managers and entrepreneurs are more concerned with the throughput rate rather than the arrival rate. But the throughput rate is important only if there is arrival. Arrival is certainly a binary function without which there’s no usefulness. Once visitors arrive, the key metric to monitor is how fast they arrive, not how many.

Here are three implications of Little’s law as it applies to startups:

1. For investors evaluating startups, it’s best to examine traffic figures at the lowest level of granularity possible. Even if the monthly uniques are low, surges in traffic at much smaller time intervals provide traces of higher value. The reverse is also true. Dips in arrival rates may suggest potential problems.
2. For an entrepreneur, instead of focusing on the monthly stats, working on how to increase the searches per second is a healthier effort — particularly for those wanting to disrupt a certain market. The traffic numbers may be up and down and all over the place throughout the month, but it is the peaks of high traffic per second (or millisecond) that deserves the attention.
3. It’s important to focus on why and how the influx of visitors surged in the smallest time frame available. Work to figure out ways to sustain that instead of focusing on monthly uniques.

Little’s law provides hints for social or viral growth, too, because in both cases, influence is spread out in short bursts as people visit the site/page/app almost all at the same time. Viral influx is the dream of a startup and after that, some level of stickiness is required to keep people around. But early traction trumps great content. Normalizing your metrics over time and looking at meaningful windows of time are a lot more useful than just looking at long-term averages.

If you’re hungry for analytical insights on traffic, traction and growth, look no further than queuing theory and particularly Little’s law. For those of you interested in the mathematical proof of Little’s law, here’s the link to Professor Little’s 2011 paper celebrating the 50th anniversary of his theory.