By Srinivasan Keshav

“To layout destiny networks which are valuable of society’s belief, we needs to placed the ‘discipline’ of computing device networking on a miles more desirable origin. This booklet rises above the significant trivia of today’s networking applied sciences to stress the long-standing mathematical underpinnings of the field.”

*–Professor Jennifer Rexford, division of machine technological know-how, Princeton University*

“This ebook is strictly the single i've been looking ahead to the final couple of years. lately, i made a decision so much scholars have been already very conversant in the best way the web works yet weren't being taught the fundamentals*–*the math. This e-book comprises the information for those who will create and comprehend destiny communications systems."

*–Professor Jon Crowcroft, the pc Laboratory, college of Cambridge*

**The crucial Mathematical ideas Required to layout, enforce, or assessment complicated machine Networks**

Students, researchers, and pros in computing device networking require a company conceptual realizing of its foundations. ** Mathematical Foundations of machine Networking **provides an intuitive but rigorous creation to those crucial mathematical ideas and techniques.

Assuming a easy clutch of calculus, this booklet bargains enough aspect to function the single reference many readers will desire. every one idea is defined in 4 methods: intuitively; utilizing acceptable mathematical notation; with a numerical instance conscientiously selected for its relevance to networking; and with a numerical workout for the reader.

The first a part of the textual content offers simple thoughts, and the second one half introduces 4 theories in a development that has been designed to steadily deepen readers’ knowing. inside of every one half, chapters are as self-contained as attainable.

The first half covers chance; statistics; linear algebra; optimization; and indications, platforms, and transforms. subject matters diversity from Bayesian networks to speculation trying out, and eigenvalue computation to Fourier transforms.

These initial chapters determine a foundation for the 4 theories coated within the moment a part of the booklet: queueing conception, online game conception, keep watch over idea, and data conception. the second one half additionally demonstrates how mathematical recommendations may be utilized to concerns resembling rivalry for constrained assets, and the optimization of community responsiveness, balance, and throughput.

**Read or Download Mathematical Foundations of Computer Networking PDF**

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**Extra info for Mathematical Foundations of Computer Networking**

**Sample text**

Therefore, if we were to generate a random number u with uniform probability in the range [0,1], the probability that u lies in the range > F x F x + G @ is f x G , which means that x = F – 1 u is distributed according to the desired density function f(Xc). Therefore, the procedure to generate values from the continuous distribution f(Xc) is as follows: First, generate a random variable u uniformly in the range [0,1]; second, compute x = F – 1 u . 15) ³ xf x dx –f Intuitively, the expected value of a random variable is the value we expect it to take, knowing nothing else about it.

Therefore, as the number of endpoints grows, and if we can assume the endpoints to be independent, the sum of their loads will be well modeled by a Poisson random variable. This is heartening because systems subjected to a Poisson load are mathematically tractable, as we will see in our discussion of queueing theory. Unfortunately, over the last two decades, numerous measurements have shown that actual traffic can be far from Poisson. Therefore, this modeling assumption should be used with care and only as a rough approximation to reality.

Instead, the best we can do is to sample the values it takes on by observing its behavior over some period of time. We can estimate the variance of the random variable by keeping running counters for ¦ x i and ¦ x i2 . 4. The following properties of the variance of a random variable can be easily shown for both discrete and continuous random variables. 1. 20) 2. 21) 3. 4 Moments and Moment Generating Functions Thus far, we have focused on elementary concepts of probability. To get to the next level of understanding, it is necessary to dive into the somewhat complex topic of moment generating functions.