By Randolph Nelson

ISBN-10: 1441928464

ISBN-13: 9781441928467

ISBN-10: 1475724268

ISBN-13: 9781475724264

We will sometimes footnote a section of textual content with a "**,, to point Notes at the that this component might be at first bypassed. the explanations for bypassing a textual content component to the textual content contain: the topic is a unique subject that may not be referenced later, the cloth might be skipped on first studying, or the extent of arithmetic is larger than the remainder of the textual content. In situations the place a subject matter is self-contained, we prefer to gather the fabric into an appendix that may be learn through scholars at their relaxation. the cloth within the textual content can't be absolutely assimilated till one makes it Notes on "their personal" by means of making use of the cloth to express difficulties. Self-discovery difficulties is the simplest instructor and even though they're no alternative for an inquiring brain, difficulties that discover the topic from varied viewpoints can frequently support the scholar to contemplate the fabric in a uniquely in step with sonal means. With this in brain, now we have made difficulties an essential component of this paintings and feature tried to cause them to attention-grabbing in addition to informative.

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**Additional info for Probability, Stochastic Processes, and Queueing Theory: The Mathematics of Computer Performance Modeling**

**Example text**

Disks). The random event "system down" corresponds to A = {(O, 2), (1,2), (2, 2), (3,0), (3, 1), (3, 2)}. The event "one more processor failure causes system down" corresponds to 8 = {(2, 0), (2, I)} and the event "one more disk failure causes system down" corresponds to C = {(O, 1), (1, 1), (2, I)}. The family F generated by A, 8, and C is given by F = {n,0,A,8,C, A+8,A+C,8+C,A+8+C,8C,Ac,8c,Cc, (A + 8)C, (A + C)C, (8 + C)C, (A + 8 + cy}. When n is finite the family of sets F can be easily generated by simply forming all possible subsets of elements of n.

For some coins, however, there is the remote chance that the coin lands upright on its side. For practical purposes, however, the occurrence of such an event is so rare, perhaps occurring 1 time out of 109 tosses, that it is not included in a model. For a model of the reliability of a highly reliable computer system, however, it is exactly these "rare events" that are modeled. For such systems, failures often occur at rates of 10- 9 per second (this implies that the average time between failures is 109 seconds or about 31 years).

3; they form the foundation that supports all of our results. 4 we summarize the results of the chapter. 20 2. Randomness and Probability We close this introductory section by pointing out the hierarchy of models typically used to analyze complex systems. In the example of a computer system we first model events, such as arrivals and service times, using probability theory. That is, much like the hidden assumptions in Laplace's equiprobable assumption, we assume, without explicit statement, that these events are random, and then we assign probabilities to them.

### Probability, Stochastic Processes, and Queueing Theory: The Mathematics of Computer Performance Modeling by Randolph Nelson

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