It isn't often that a business model becomes the subject of a patent violation suit. But according to research reported today in Stanford Knowledgebase, that's exactly what happened in 2006 when Netflix, the pioneer in online video rental, sued Blockbuster, the giant of the brick-and-mortar video rental companies. Granted in 2003, Netflix's 31-page patent details a business model that was a sharp departure from the way video rental companies had operated for years. The conventional model works like this: Customers go to a video rental store and select particular movies to rent. They take the movies home and must return them by a particular due date or be charged a late fee. Netflix, however, patented a subscription model that allows customers to pay a fixed monthly fee, create an online wish list for future rentals, and order them over the Internet. The movies come in the mail and may be kept as long as the customer wants, with no late fee. Depending on the plan selected, customers can keep as many as four DVDs at a time, but cannot rent new movies until the older ones are returned. The suit accused Blockbuster of copying Netflix's business model, including the wish list and the basic subscription model itself. Blockbuster said the patent was so broad, it should not be enforced. Although the patent contains a good deal of detail about the video rental business, it is also quite broad, since it applies to "a method for renting items to customers" and "computer-implemented steps" -- either of which could extend to online rental of non-entertainment items. The novelty of the model and the possibility that it might be applicable to other businesses intrigued Sunil Kumar, the Fred H. Merrill Professor of Operations, information, and Technology at the Stanford Graduate School of Business, whose research focuses on analyzing mathematical models of operations, particularly congestion phenomena. Along with colleagues Achal Bassamboo of Northwestern University and Ramandeep Singh Randhawa of The University of Texas, Austin, he studied the Netflix model with the goal of determining what effect the lack of deadlines has on customers. The researchers also wanted to know the smallest amount of inventory Netflix could carry while still having enough movies on hand to satisfy customers. The answers were straightforward: "Netflix got it right by not imposing deadlines," says Kumar. And the company needs to stock only a small fraction of the total demand for any one video and still provide good service. But the method for calculating those answers was fairly complex. Indeed, nearly all of the 23-page working paper "Dynamics of new product introduction in closed rental systems" is a mathematical proof of those seemingly simple conclusions. Building a model to represent Netflix's business was difficult because of the enormous number of transactions that occur every day. Rather than trying to capture so many events, the researchers used an analogy from engineering -- the behavior of fluids. "Imagine that Netflix is a huge reservoir that drains and refills as people rent and return movies," explains Kumar. "We need to know how a system works with many users, and the alternative (to the fluid model), tracking individual users, is hopeless. The fluid model is a usable approximation that works well as the number of users gets large." The fluid metaphor exists in classical statistics. Proving that it applies in this business case is a contribution of the paper, he notes. The Netflix business model contains an interesting set of tradeoffs. When a customer keeps a movie for an extended period of time, Netflix is deprived of its use, which is a negative. Deadlines help ensure prompt return and thus have the benefit of reducing the number of copies that Netflix needs to stock to provide good service. But because the customer can't rent another movie until it is returned (this is known as "max out" and is included in the patent), deadlines speed up demand for other movies and trigger costs of fulfillment, such as postage, which Netflix pays. Kumar and his co-workers show that there is no tradeoff here at all -- not having deadlines is a win-win. It's important to note that Netflix isn't flying blind. Customer "wish lists" give the company real insight into what movies its customers want. In theory, Netflix could simply stock one movie for every customer who wants to see it. But that, of course, would be a terrible business practice. So the question remains: How many copies of a given movie should the company stock, and is it really better to eschew return deadlines? The researchers realized that customer behavior varies. In fact, it's pretty random. Some people hold movies for a week, others for two or three weeks. And the behavior of each individual customer varies from time to time. The timing of new movie releases is also random. It turns out that those two facts are key to resolving the questions. To demonstrate why, Kumar uses an analogy familiar to many business students, "the inspection paradox." Here's how it works: Suppose we note that taxi cabs pass a given corner on the average of one every 10 minutes. Then assume I show up at a random time, and I'm told that a taxi left the corner eight minutes ago. At first glance, one would assume the next taxi will arrive in two minutes on average. But that's incorrect; the real answer is much longer, and depends on the degree of randomness. That's because the 10-minute interval is an average, so if a customer shows up at a random time, she is less likely to hit a shorter interval and more likely to hit a longer interval between taxis. The release of a new movie is like the appearance of the taxi, and the customer's readiness to rent another DVD is analogous to showing up at the corner. The imposition of deadlines would remove some of the randomness from the equation and push customers to rent faster, resulting in higher costs. Removing deadlines creates a better balance of supply and demand, the researchers conclude. In fact, under the ideal conditions established in Kumar's model, Netflix would only have to stock a small fraction of any given movie to satisfy customers and control its costs. Because the model built by Kumar and his colleagues is just a model, and not reality, it would be useful to compare the results of the researchers' simulation to the company's actual results. But Netflix did not provide the data, citing costs of data collection and data cleaning, says Kumar. Even so, the results of the paper raise an interesting question: If the no-deadline model works for Netflix, would it work for another type of business? The answer is maybe, says Kumar. For example, it would not work for a car rental business, since people tend to rent a car and return it without renting another. But consider the customers of an equipment rental business. One might rent, say, an air compressor, at the beginning of a job, and then return it and rent a backhoe, suitable for a later stage of the job. And that could mean that a no-deadline policy would work. "It's worth examining," says Kumar. And the suit? It was settled out of court in 2007, with the terms kept under wraps.