By Fayez Gebali (auth.)

This textbook offers the mathematical concept and methods precious for examining and modeling high-performance worldwide networks, reminiscent of the net. 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 ebook offers the fundamental suggestions for modeling and interpreting those final parts. issues lined comprise, yet should not restricted to: Markov chains and queuing research, site visitors modeling, interconnection networks and turn architectures and buffering strategies.

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**Example text**

30 Individual pmf from a Given Joint pmf Sometimes we want to study an individual random variable even though our random experiment generates multiple RVs. 23. Assume a random experiment that generates two random variables X and Y with the given joint pmf. 32 Correlation 35 Find the individual pmf for X and Y . Are X and Y independent RVs? 31 Expected Value The joint pmf helps us find the expected value of one of the random variables. 24. 23 above, find the expected values for the random variables X and Y .

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. 2 0 0 0 2 4 6 8 10 0 x 2 4 6 8 10 x Fig. 12 The Rayleigh distribution for three different values of the shape parameter a.

In other words, small variance means that the pdf is large only in regions close to the expected value . For an archery target practice experiment, this might mean that most of the arrows were clustered together and landed very close at some spot on the target (not necessarily dead center). Conversely, a large variance means that the pdf is large for values of X far away from . Again for the archery experiment, this means that most of the arrows were not clustered together and landed at different spots on the target.