By Fayez Gebali
Analysis of machine and verbal exchange Networks offers the tutorial and study groups with mathematical concept and methods priceless for interpreting 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 presents the elemental innovations for modeling and interpreting those final parts. themes lined contain, yet will not be restricted to: Markov chains and queuing research, site visitors modeling, interconnection networks and turn architectures and buffering suggestions. The textual content additionally includes
- a novel and specific description of Markov techniques 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 purposes and a quick creation at the package deal because it is among the extra universal mathematical applications used,
- over 550 homework problems.
Analysis of computing device and verbal exchange Networks is meant for senior and graduate scholars, college researchers and training engineers in communications, community layout and analysis.
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Extra info for Analysis of Computer and Communication Networks
That slot could be occupied or empty when the user is busy or idle, respectively. Assuming the frame consists of 10 slots, how many slot occupancy patterns can be received in a single frame? Each time slot can be treated as an experiment with only two outcomes, busy or idle. The experiment is repeated 10 times to form the frame. 5 Permutations Permutations arise when we are given n objects and we want to arrange them according to a certain order. In other words, we arrange the objects by randomly picking one, then the next, etc.
15 Expected Value and Variance The pdf and pmf we obtained above help us find the expected value E [X ] of a random variable X . 15 Expected Value and Variance 15 The expectation is sometimes referred to as the first moment of the random variable. Sometimes μ is used as another symbol for the expected value. 34) i=1 The mean is not exactly equal to the expected value μ since m changes its value depending on how many samples we take. However, as n → ∞, the two quantities become equal . 35) The variance describes how much of the mass of the distribution is close to the expected value.
1. 6. 95. Find the joint pmf of X and Y . 095 Note that the sum of all the probabilities must add up to 1. 29 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. 2 =0 =3 =7 =9 Find the individual pmf for X and Y . Are X and Y independent RVs? 30 Expected Value The joint pmf helps us find the expected value of one of the random variables.