# John D.C. Little

IFORS Distinguished Lecture

IFORS President Nelson Maculan (left) presents the IFORS award to IDL John D.C. Little.
26th European Conference on Operational Research
Rome, Italy
July 2013

Abstract

Applications of Little’s Law
Queues are everywhere. We shall show pictures of them. Some queues contain people, others contain things, and still others elephants. Generically, we call them all items. Some pictures of queues are particularly interesting, or display obvious difficulties, or are funny. Little’s Law (LL) is a property of queues. LL’s simple equation contains three parameters. Expressed in words: (the average number of items in the queuing system (usually denoted, L) = the arrival rate of items to the system (denoted by the Greek letter, lambda) x (the average time an item spends in the system (denoted W ). Thus, L = (lambda) W, is Little’s Law.

You can tell that Little’s Law is useful and possibly important. Otherwise it would have no name at all. I did not name it myself. On the other hand, I haven’t objected to it.

After showing pictures of various styles of queues, we shall prove Little’s Law in a simple but important case. Not only do we prove it, we give a physical intuition as to why it is true. Notice also that it is exactly true. That’s the law.

LL has many applications, mostly unreported. This spring I ran a course with the title of this talk “Applications of Little’s Law.” I sought out several guests who had applied it themselves. My colleague, Richard Larson, told how he used LL to analyze the MIT appointment process with its input of assistant professors and output of faculty retirements. He sought and found policy implications. John Carrier, a consultant in the Boston area, analyzed a medium sized furniture maker in Kentucky who was in financial trouble. He amazed me by finding the LL parameters from the financial statements of the company. He used these values to argue for cutting down the number of line items, thereby saving setup costs, shortening product lead times, and overcoming the cost advantages of foreign competitors by providing faster service. Profits increased. Mike George, a long time entrepreneur and advocate of building a manufacturing operation centered on LL, had sold his consulting firm, which did this, to Accenture for over \$100 million. He has now bought two manufacturing companies to run himself. He has already made them more profitable and we shall explain how. His firms specialize in the precision machining of jet engine parts. This a growing market because new materials permit more efficient engines, which will be snapped up by the airlines.

Finally, I shall try to make generalizations about what makes Little’s Law useful so that it can work for you.