By Fayez Gebali (auth.)

This textbook provides the mathematical conception and strategies worthy for reading and modeling high-performance international networks, equivalent to the web. 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 e-book presents the fundamental recommendations for modeling and studying those final elements. themes coated contain, yet aren't constrained to: Markov chains and queuing research, site visitors modeling, interconnection networks and turn architectures and buffering strategies.

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**Example text**

So let us derive the expression for Poisson distribution based on this method of thinking. Consider a chance experiment where an event A occurs at a rate events/second. In a small time interval (t ) the probability that the event A occurs is p D t . We chose t so small so that event A occurs at most only once. For example, might indicate the average number of packets arriving at a link per unit time. In that case the variable t will indicate time. might also refer to the average number of bits in error for every 1,000 bits, say.

The CDF for a discrete random variable will be a staircase as illustrated in the following example. 13. Consider again the case of the spinning pointer experiment but define the discrete random variable Q which identifies the quadrant in which the pointer rests in. The quadrants are assigned the numerical values 1, 2, 3, and 4. Thus the random variable Q will have the values q D 1, 2, 3, or 4. q D 1/ D The CDF for this experiment is shown in Fig. 5. 13 Probability Density Function 13 Fig. x/ will never be negative.

In a small time interval (t ) the probability that the event A occurs is p D t . We chose t so small so that event A occurs at most only once. For example, might indicate the average number of packets arriving at a link per unit time. In that case the variable t will indicate time. might also refer to the average number of bits in error for every 1,000 bits, say. In that case, the variable t would indicate the number of bits under consideration. In these situations we express the parameter a in the form a D t where expresses the rate of some event and t expresses the size or the period under consideration.