By Fayez Gebali
Analysis of machine and communique Networks provides the tutorial and study groups with mathematical thought and strategies worthy for studying and modeling high-performance worldwide networks, reminiscent of the Internet.
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 paintings offers the elemental ideas for modeling and reading those final parts. subject matters lined comprise, yet aren't constrained to: Markov chains and queuing research, site visitors modeling, interconnection networks and turn architectures and buffering techniques. The textual content additionally includes
- a novel and specific description of Markov approaches in addition to a whole bankruptcy devoted to fixing Markov chains in equilibrium,
- appendices are supplied as a convenient reference for cloth and formulation mentioned within the book,
- a dialogue at the use of MATLAB® in engineering functions and a quick creation at the package deal because it is likely one of the extra universal mathematical applications used,
- over 550 homework problems.
Analysis of machine and communique Networks is meant for senior and graduate scholars, collage researchers and training engineers in communications, community layout and analysis.
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Extra resources for Analysis of Computer and Communication Networks
Well, we can do that through transforming random variables, which is the subject of this section. 35 will show how to actually generate the random numbers using the techniques of this section. 115) X is named the source random variable and Y is named the target random variable. We are interested in finding the pdf and cdf of Y when the pdf and cdf of X are known. 116) But this probability must equal the probability that Y lies in the range y and y + dy. 117) where f Y (y) is the pdf for the random variable Y and it was assumed that the function g was monotonically increasing with x.
The Gaussian distribution applies for the case of a continuous random variable X that is allowed to have the values ranging from −∞ to +∞. 42) where μ is the mean and σ is the standard deviation of the distribution. 43) −∞ 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 μ = 0 and σ = 1 . 9 shows the output of a Gaussian random variable with zero mean and unity variance using the randn function of MATLAB.
The parameter a in the above formula is usually expressed as a=λt where λ is the rate of event A and t is usually thought of as time. Because we talk about rates, we usually associate Poisson distribution with time or with average number of occurrences of an event. So let us derive the expression for Poisson distribution based on this method of thinking. Consider a chance experiment where an event A occurs at a rate λ events/second. In a small time interval (⌬t), the probability that the event A occurs is p = λ⌬t.