Download Computer Networks and Systems: Queueing Theory and by Thomas G. Robertazzi PDF

By Thomas G. Robertazzi

Statistical functionality evaluate has assumed an expanding quantity of significance as we search to layout an increasing number of refined conversation and knowledge processing structures. the facility to foretell a proposed system's according to­ formance earlier than one constructs it truly is a really reasonably-priced layout instrument. This ebook is intended to be a first-year graduate point creation to the sphere of statistical functionality assessment. it really is meant for those who paintings with sta­ tistical functionality evaluate together with engineers, computing device scientists and utilized mathematicians. As such, it covers non-stop time queueing thought (chapters 1-4), stochastic Petri networks (chapter 5), discrete time queueing conception (chapter 6) and up to date community site visitors modeling paintings (chapter 7). there's a brief appendix on the finish of the booklet that stories easy likelihood thought. This fabric may be taught as a whole semester lengthy path in functionality evalua­ tion or queueing idea. on the other hand, one might train merely chapters 2 and six within the first half an introductory computing device networking path, as is finished at Stony Brook. the second one half the path may use a extra protocol orientated textual content comparable to ones through Saadawi [SAAD] or Stallings [STALl what's new within the 3rd version of this publication? as well as the good bought fabric of the second one variation, this version has 3 significant new features.

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Extra resources for Computer Networks and Systems: Queueing Theory and Performance Evaluation

Example text

43) But this is just the same differential equation that we found using difference equation arguments in the last section! The equation for dP o(t)ldt can be derived in a similar manner. So for the MIMl1 queueing system we have a set of differential equations to describe the evolution of the state probabilities as a function of time. As with electric circuits, this is useful if one wants a transient analysis of the queueing system. This is the study of the queueing system over a limited time period.

99) P (X (t)=j)P (X (t+t)=i IX (t)=j) or PiP(X (t+t)=j IX (t)=i)=PjP(X (wc)=i I X (t)=j). 101) which is the desired result. Proving the converse is a little more involved. We start by assuming that the Pi exist which satisfy the detailed balance equations. 102) 2. 103) jcS which is just a form of global balance equation. We will look now at the interval t I: [- T, Tj. Suppose that the process is in state i 1, at time -T and stays in this state for a period k 1 and then jumps to state i 2 which it stays in for a period k 2 and so on, until the state is im for a period km until time T.

One would naturally like to answer one minute, and this would be true if trains arrived deterministically exactly twenty minutes apart. However. we are dealing with a Poisson arrival process. The answer is twenty minutes! To see that this is true, we have to go back to our coin flipping explanation of the Poisson process. An event is the result of a positive outcome of a "coin flip" in an infinitesimally small interval. As time proceeds there are a very large number of such flips. When we put the Poisson process in this context it is easy to see that the distribution until the next positive outcome does not depend at all on 2.

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