By Fayez Gebali (auth.)
This textbook provides the mathematical conception and methods important for reading and modeling high-performance international networks, comparable 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 ebook presents the elemental thoughts for modeling and reading those final elements. issues coated comprise, yet should not constrained to: Markov chains and queuing research, site visitors modeling, interconnection networks and turn architectures and buffering strategies.
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Additional resources for Analysis of Computer Networks
For a router or a switch, a packet might arrive at a given time step or no packet arrives. Consider a chance experiment that has two mutually exclusive outcomes A and A that occur with probabilities p and q; respectively. We define the discrete random variable X where X D 1 when A occurs and X D 0 when A occurs. 15a shows the pmf for the binary distribution and Fig. 15b shows the cdf. a b pX(x) PX(x) 1 p q Fig. 17. The 50/50 draw is one of the traditions of a typical minor lacrosse or baseball sports events.
43) 1 There is no closed-form formula for the cdf associated with the Gaussian distribution but that function is tabulated in many textbooks on statistics. The standard or normal random variable is a Gaussian RV with D 0 and D 1 . 9 shows the output of a Gaussian random variable with zero mean and unity variance using the randn function of MATLAB. 1,000 samples were generated in this experiment. 19 Exponential Distribution The exponential distribution applies for the case of a continuous random variable X that is allowed to have the values ranging from 0 to +1.
The quadrants are assigned the numerical values 1, 2, 3, and 4. Thus the random variable Q will have the values q D 1, 2, 3, or 4. q D 1/ D The CDF for this experiment is shown in Fig. 5. 13 Probability Density Function 13 Fig. x/ will never be negative. It can, however, be zero or even bigger than 1. x/. 14 Probability Mass Function For the case of a discrete random variable the cdf is discontinuous in the shape of a staircase. Therefore, its slope will be zero everywhere except at the discontinuities where it will be infinite.