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Unformatted text preview: Chapter 5 Little's Law John D.C. Little and Stephen C. Graves Massachusetts Institute of Technology The average waiting time and the average number of items waiting for..a service in a service system are important measurements for a manager. Little's Law relates these two metrics via the average rate of arrivals to the system. Thisfunda- mental law has found numerous uses in operations management and managerial decision making. Introduction Caroline is a wine buff and bon vivant. She likes to stop at her local wine store, Transcendental Tastings, on the way home from work. She browses the aisles look- ing for the latest releases from her favorite vineyards. Occasionally she picks up a few bottles. She stores these in a rack in a cool corner of her cellar. She and her partner eat out frequently but when they are at home they usually split a bottle of wine at dinner. Sometimes they have friends over and that puts a bigger ,dentin the wine inventory. They have been doing this for some time. Her wine rack holds 240 bottles. She notices that she seldom fills the rack to the top but sometimes after a good party the rack is empty. On average it seems to be about 2/3rds full, which would equate to 160 bottles. Many wines improve with age. After reading an article about this, Caroline starts to wonder how long, on average, she has been keeping her wines. She went back through a few months of wine invoices from Transcendental and estimates that she has bought, on average, about eight bottles per month. But she certainly doesn't know when she drank which bottle and so there seems to be no way she can find out, even approximately, the average age of the bottles she has been drinking. This is a good task for Little's Law. D. Chhajed and TJ. Lowe (eds.) Building Intuition: Insights From Basic Operations Management Models and Principles. doi: 10.1007/978-0-387-73699-0, <9Springer Science + Business Media, LLC 2008 81 82 J.D.C. Little, S.c. Graves Little's Law Deals with Queuing Systems A "queuing system" consists of discrete objects we shall call "items" that "arrive" at some rate to the "system." Within the system the items may form one or more queues and eventually receive "service" and exit. Figure 5.1 shows this schematically. Arrivals-~ queuing system: items in 1- Departures queue & items in service I Flow of items through a queuing system Fig. 5.1 Schematic view of a queuing system While items are in the system, they may be in queues ,or may be in service or some in queue and some in service. The interpretation will depend on the applica- tion and the goals of the modeler. For example in the case of the wine cellar, we say that a bottle (an "item") arrives to the system when it is first placed into the wine cellar. Each bottle remains in the system until Caroline selects it and removes it from the cellar for consumption. If 'we view the wine rack as a single channel server, the service time is the time between successive removals. It is interesting to note, however, that we do not know which bottle Caroline will pick and there is no...
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