itely ad- justable set of values. The height of a tower or the angle of an antenna are continuous 2Operations research is the art of getting bad answers to problems that otherwise would have had even worse answers. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Capacity and Quality Tradeoffs Capacity and Quality Principles variables. The combination of discrete and continuous variables makes a problem very difficult to solve in a mathematically closed form. 3 Often our choice of discrete or con- tinuous variables depends more on the practical aspects of our model than on the phys- ical reality. A radio power level might have 128 discrete decibel choices in the actual system, but we can model it as a continuous variable and round it off at the end of optimization because it makes the calculations easier. Or we might take a set of base station antenna heights and model them as integer heights in half-meter increments SO that we can use a search algorithm to find better solutions. 22.3 Tradeoff So we have a system on the drawing board, in a computer model, or in physical reality, and we consider a change to that system and ask how the goal factors will change as a result. For any given change, some of the factors may improve, some may get worse, and others stay the same. If we are lucky, then the change will make some improve- ments and degrade nothing, a universally good change. Of course, we will execute any change that does nothing but good to our system. 4 Once we make all the changes we can find that are unequivocal improvements, we come upon changes that are more ambiguous in their results. Most of the changes we think about for a system, wireless or otherwise, are good for some things and bad for other things. They may improve capacity but cost money, or they may improve quality of service at the expense of reliability. We can anticipat