By Fayez Gebali (auth.)

This textbook offers the mathematical thought and methods valuable for examining and modeling high-performance international networks, similar to the net. the 3 major development 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 offers the fundamental thoughts for modeling and examining those final elements. themes lined contain, 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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**Sample text**

13 shows the pmf for a random variable consisting of six samples which are assumed to take the values 0, 1, , 5. 16. Study the statistical distribution of rounding errors in computer arithmetic. The truncation or rounding operation is required after fixed and floating point number multiplication and also after floating point number addition. Rounding or truncation is employed to reduce the number of bits back to their original size n; say. 14 shows the location of the binary point for the fixed-point number and also shows the bits that will be truncated or rounded.

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. 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.

This type of traffic is described as being self-similar (fractal) [6–8]. Self-similar traffic has distributions with very high variance. Sometimes such distributions are described as being heavy-tailed since the pdf has large values for x far away from the mean . This type of distribution might then prove more accurate in describing the pdf for the rate of data produced by a bursty source. The Pareto distribution could be made to be a heavy-tailed distribution by proper choice of its parameters.