By Fayez Gebali (auth.)

ISBN-10: 331915656X

ISBN-13: 9783319156569

ISBN-10: 3319156578

ISBN-13: 9783319156576

This textbook offers the mathematical thought and strategies beneficial for studying and modeling high-performance worldwide networks, reminiscent of 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 presents the fundamental suggestions for modeling and studying those final parts. issues lined contain, yet are usually not restricted to: Markov chains and queuing research, site visitors modeling, interconnection networks and turn architectures and buffering strategies.

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**Example text**

When N is large, it becomes cumbersome to evaluate the above equation. 87) is nonzero and finite. 0 ! N k N a b k k . 88) We can prove the above equation using the following two simplifying expressions. 90) Using the above two expressions, we can write [10]: ! 95) where D N a. This gives the expression for the Poisson distribution. This is especially true when N > 50 and a < 0:1 in the binomial distribution. 21. Packets arrive at a device at an average rate of 500 packets per second. Determine the probability that four packets arrive during 3 ms.

D 0. 3. S / D 1. 4. 7) Event E and its complement E c are mutually exclusive. AjB/ and is sometimes referred to as the probability of A conditioned by B. A/ because the probability of event A taking place will not change whether event B occurs or not. A/ provided that the two events are independent. 11 Random Variables Many systems based on random phenomena are best studied using the concept of random variables. A random variable allows us to employ mathematical and numerical techniques to study the phenomenon of interest.

K/ is given by: ! 86) where b D 1 a. When N is large, it becomes cumbersome to evaluate the above equation. 87) is nonzero and finite. 0 ! N k N a b k k . 88) We can prove the above equation using the following two simplifying expressions. 90) Using the above two expressions, we can write [10]: ! 95) where D N a. This gives the expression for the Poisson distribution. This is especially true when N > 50 and a < 0:1 in the binomial distribution. 21. Packets arrive at a device at an average rate of 500 packets per second.

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

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