By Fayez Gebali (auth.)

ISBN-10: 331915656X

ISBN-13: 9783319156569

ISBN-10: 3319156578

ISBN-13: 9783319156576

This textbook offers the mathematical concept and strategies invaluable for examining and modeling high-performance international networks, resembling the net. the 3 major construction 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 publication presents the elemental options for modeling and examining those final parts. subject matters coated contain, yet should not restricted to: Markov chains and queuing research, site visitors modeling, interconnection networks and turn architectures and buffering strategies.

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Many systems based on random phenomena are best studied using the concept of multiple random variables. 96) 32 1 Probability Random Experiment Random Outcome Mapping Function Corresponding Numbers: x, y, ... Fig. 16 The sequence of events leading to assigning multiple numerical values to the outcome of a random experiment Incoming digital signals are modulated by assigning different values to a and . In that sense, QAM modulation combines amplitude and phase modulation techniques. The above signal contains two pieces of information: viz, the amplitude a and the phase that correspond to two random variables A and ˆ.

If the order of choosing the objects is not taken into consideration, then combinations are obtained. The number of combinations of n objects taken k at a time is called the binomial coefficient and is given by: ! n k/Š k MATLAB has the function nchoosek(n,k) for evaluating the above equation where 0 Ä k Ä n. 10. Assume 10 packets are received with 2 packets in error. How many combinations are there for this situation? We have n D 10 and k D 2: ! 11. Assume 50 packets are received but 4 packets are received out of sequence.

This random variable could be discrete or continuous depending on the accuracy of the barometer (analog or digital). x/ and is defined as the probability that the random variable is less than or equal to x. 14) The subscript X denotes the random variable associated with the function while the argument x denotes a numerical value. x/ when we are dealing with a single random variable and there is no chance of confusion. x/ is a probability, it must have the same properties of probabilities. x/ has other properties as shown below: F .

### Analysis of Computer Networks by Fayez Gebali (auth.)

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