# Chapter 1Introduction

## 1.1 Motivation

Computer scientists and engineers need powerful techniques to analyze algorithms and computer systems. Similarly, networking engineers need methods to analyze the behavior of protocols, routing algorithms, and congestion in networks. Computer systems and networks are subject to failure, and hence methods for their reliability and availability are needed. Many of the tools necessary for these analyses have their foundations in probability theory. For example, in the analysis of algorithm execution times, it is common to draw a distinction between the *worst-case* and the *average-case* behavior of an algorithm. The distinction is based on the fact that for certain problems, while an algorithm may require an inordinately long time to solve the least favorable instance of the problem, the average solution time is considerably shorter. When many instances of a problem have to be solved, the probabilistic (or average-case) analysis of the algorithm is likely to be more useful. Such an analysis accounts for the fact that the performance of an algorithm is dependent on the distributions of input data items. Of course, we have to specify the relevant probability distributions before the analysis can be carried out. Thus, for instance, while analyzing a sorting algorithm, a common assumption is that every permutation of the input sequence is equally likely to occur.

Similarly, if the storage is dynamically allocated, a probabilistic analysis of the storage ...

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