By Fayez Gebali (auth.)
This textbook provides the mathematical concept and strategies precious for examining and modeling high-performance worldwide networks, similar to the web. 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 offers the fundamental options for modeling and interpreting those final elements. subject matters 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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Assume 50 packets are received but 4 packets are received out of sequence. How many combinations are there for this situation? We have n D 50 and k D 4: ! 8 Probability We define probability using the relative-frequency approach. Suppose we perform an experiment like the tossing of a coin for N times. We define event A is when the coin lands head up. Define NA as the number of times that event A occurs when the coin tossing experiment is repeated N times. 1 NA N This equation defines the relative frequency that event A happens.
A uniform distribution is characterized by a random variable that spans the range a to b such that a < b. 39) Typically a D 0 and b D 1. 7a shows the pdf for the uniform distribution and Fig. 7b shows the corresponding cdf. 18 Gaussian Distribution a 17 b fX(x) FX(x) 1 1 0 1 x 0 1 x Fig. 7 The uniform distribution for a continuous random variable. (a) The pdf; and (b) is the corresponding cdf The following MATLAB code generates and plots a random variable having a uniform distribution in the range 0 Ä x < 1.
The pdf in the discrete case is called the Probability Mass Function (pmf) . x/. 29) where the expression on the right-hand side indicates the probability that the random variable X has the value x. x/. 14. 13), plot the pdf for the continuous random variable ‚ and the corresponding pmf for the discrete random variable Q. 6a shows the pdf for the continuous case where the random variable ‚ measures the angle of the pointer. 6b shows the pmf for the discrete case where the random variable Q measures the quadrant where the pointer is located.
Analysis of Computer Networks by Fayez Gebali (auth.)