By Fayez Gebali (auth.)
This textbook provides the mathematical concept and methods valuable for examining and modeling high-performance international networks, resembling the net. the 3 major construction blocks of high-performance networks are hyperlinks, switching gear connecting the hyperlinks jointly and software program hired on the finish nodes and intermediate switches. This ebook presents the elemental ideas for modeling and interpreting those final parts. issues coated comprise, yet aren't restricted to: Markov chains and queuing research, site visitors modeling, interconnection networks and turn architectures and buffering strategies.
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Each outcome is assigned a numerical value. Assigning a numerical value to the outcome of a random experiment allows us to develop uniform analysis for many types of experiments independent of the nature of their specific outcomes . We denote a random variable by a capital letter (the name of the function) and any particular value of the random variable is denoted by a lowercase letter (the value of the function). Examples of random variables, and their numerical values, could be: 1. Number of arriving packets at a given time instance is an example of a discrete random variable N with possible values n D 0; 1; 2; .
Number of arriving packets at a given time instance is an example of a discrete random variable N with possible values n D 0; 1; 2; . 2. Tossing a coin and assigning 0 when a tail is obtained and 1 when a head is obtained is an example of a discrete random variable X with values x 2 f0; 1g. 3. The weight of a car in kilograms is an example of a continuous random variable W with values in the range 1; 000 Ä w Ä 2; 000 kg typically. 4. The temperature of a day at noon is an example of random variable T .
3 Counting Sample Space Points In many discussions of probability, we need to determine the number of possible outcomes of a given experiment or trial. The multiplication principle, permutations, and combinations, to be discussed in the following sections, will prove useful. 4 The Multiplication Principle The fundamental principle of counting is useful in finding the number of points in the sample space. Suppose that the number of outcomes for doing experiment E1 is x and the number of outcomes for doing experiment E2 is y.
Analysis of Computer Networks by Fayez Gebali (auth.)