By Fayez Gebali (auth.)

ISBN-10: 331915656X

ISBN-13: 9783319156569

ISBN-10: 3319156578

ISBN-13: 9783319156576

This textbook provides the mathematical concept and strategies useful for reading and modeling high-performance international networks, similar to the web. the 3 major development blocks of high-performance networks are hyperlinks, switching apparatus connecting the hyperlinks jointly and software program hired on the finish nodes and intermediate switches. This e-book presents the fundamental ideas for modeling and studying those final parts. themes coated contain, 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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**Sample text**

11 shows the output of a Pareto random variable with position parameter a D 2 and shape parameter b D 2:5. 1,000 samples were generated in this experiment using the inversion method as described later in Sect. 2. 21 Rayleigh Distribution The Rayleigh distribution is used to model the phenomenon of fading in a wireless communication channel. 54) where a is the shape parameter. 12a shows the Rayleigh pdf distribution for three different values of the shape parameter a. 2a2 / This can be proven using the formulas in Appendix A.

20. A file is being downloaded from a remote site and 500 packets are required to transmit the entire file. It has been estimated that on the average 5 % of received packets through the channel are in error. Determine the probability that 10 received packets are in error using the binomial distribution and its approximations using DeMoivre–Laplace and Poisson approximations approximation. The parameters for our binomial distribution are: N D 500 a D 0:05 b D 0:95 The probability that 5 packets are in error is: !

Y/ is the pmf of the target random variable. 25. 26. t where the signal has a random frequency ! 1 Ä ! 2 . The frequency is represented by the random variable . 2 ! d! 133) We need to find fX and EŒX . For that we use the fundamental law of probability. x/ D 0 for jxj > 1: Now we can write: ˇ ˇ ˇ d! 135) and: ˇ ˇ ˇ d! 138) due to the odd symmetry of the function being integrated. 27. 139) Derive Y as a function of X: This example is fundamentally important since it shows how we can find the transformation that allows us to obtain random numbers following a desired pdf given the random numbers for the uniform distribution.

### Analysis of Computer Networks by Fayez Gebali (auth.)

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