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can be summed by any dimension and provide a valid value Other facts, such as inventory levels, are semi-additive, meaning they cannot simply be summed across all dimensions The ending inventory for the first quarter cannot be added to the ending inventory for the second quarter to give a valid inventory level for the first half of the year Instead, an average can be used, or simply the ending inventory for the second quarter Facts, also called measures, reside in a fact table The fact table is actually fully normalized by nature, unlike the denormalized dimension tables Typically, dimension tables have single-field primary keys, often of an integer data type Each fact represents a unique combination of items for the lowest level of detail for each dimension As an example, assume three simple dimensions: Time, Product, and Customer The Time dimension goes to the Day level, the Product dimension goes to the SKU level, and the Customer dimension goes to the Customer level This means that the level of detail, or granularity, of the fact table is by customer, day, and product Therefore, a single record contains a particular item sold to a particular customer on a particular day If the customer ordered the same item on the same day in two or more different orders, the products will be summed to a single record Each fact record will contain a foreign key back to the dimension tables, and these foreign keys make up the primary key of the fact table; after the key fields are the measures themselves Thus, the fact table is often made up entirely, or nearly so, of numeric fields This means that the fact table is relatively narrow, since storing numbers requires less space than storing descriptive strings While the fact table may be narrow, it is often extremely large as far as the number of records being held In many cases, the fact table makes up ninety eight percent or more of the total storage used by the relational warehouse To illustrate the sizing of a warehouse, consider the same three dimension tables: Time, Product, and Customer If tracking 10 years of data with a daily grain, this means that the Time table will hold approximately 3652 records The company might have 10,000 products and sell to 100,000 customers While not every customer will buy every product every day, imagine that they did: the fact table will hold 3652 10,000 100,000 records, or 3,652,000,000,000, or 365 trillion records Even at one tenth of one percent of this value, the fact table would still hold almost four billion records These are indeed impressive numbers Because fact tables are often so large, most organizations estimate the storage requirements for their relational data warehouse simply by estimating the number of rows in the fact table, multiplying it by the size of the record, and then adding a percentage for the indexes This typically works well, because the dimension tables are relatively small compared to the fact table, and most warehouse architects tend to overestimate the number of records in order to build in a cushion Strategies for backing up and restoring large fact tables are critical, but are beyond the scope of this book.

The strength of a radio signal falls in proportion to the square of the distance traveled For a satellite link, this distance is very large and so the signal becomes very weak This results in a low, signal-to-noise ratio Typical bit error rates for a satellite link might be on the order of 10 -7 Noise becomes less of a problem as error control coding is used Error performance equal to fiber is possible with proper error control coding

Recently, Sharp started selling a set of infrared range detectors Particular models include the Sharp GP2D02 and GP2D12 These sensors have both the infrared receiver and infrared emitter in the same package The LED is positioned at a slight angle relative to the receiver to use an optical triangulation approach to determine range The output from these sensors is either an analog voltage or a digital signal As with the ultrasonic sensors, the drawback to these sensors is that they have a narrow field of view thus multiple sensors must be used to obtain a wide field of view Many bots have successfully used these sensors to detect objects and detect ranges for these objects

The radio spectrum is a finite resource, and there is only so much bandwidth available Typical carrier frequencies for current point-to-point (fixed) satellite services 6/4 GHz (C band); 14/12 GHz (Ku band); and 30/20 GHz (Ka band) Traditional C and Ku-band transponder bandwidth is typically 36 MHz to accommodate one color television channel (or 1200 voice channels) One satellite may carry two dozen or more transponders New applications, such as personal communications services, may change this picture Bandwidth is limited by nature, but the allocations for commercial communications are limited by international agreements so that the scarce resource can be used fairly Applications that are not bandwidth efficient waste a valuable resource, especially in the case of satellites Scaleable technologies will be more important in the future

Wendy helped drive the book to completion and was always professional and friendly My copy editor, Julie Smith, helped ensure that none of my former English teachers would throw a fit Thanks to Russ Whitney of Microsoft for looking over the chapters and providing feedback; I think his team has done a superb job and I expect great things from them in the future I d also like to thank Mark Souza, Lubor Kollar, and the rest of the SQL Server Customer Advisory Team who gave me a chance to work directly with the Analysis Services team for over a year Naturally there are others who did not have a direct impact on the book, but had to deal with me while I wrote First and foremost is my wife, Linda, who was supportive from start to finish My daughter, Alison, continued to grow into a fine young lady while I was busy My dogs forced me to take breaks every few hours and helped restore some sanity to the late nights of writing Special thanks go out to Greg Clark, Mark Orgel, Jim Walters, and all the other guys at the RCMC Doug Churchman was always there to inject some levity into the situation I d also like to thank Kevin Heine because my wife told me to I cannot say enough about my friends at FPG Unlimited And once again, this book would not have been possible without the help of my good friend, Martha McMahon