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Download e-book for iPad: Applied Discrete-Time Queues by Attahiru Alfa

By Attahiru Alfa

ISBN-10: 149393418X

ISBN-13: 9781493934188

This book introduces the theoretical basics for modeling queues in discrete-time, and the fundamental methods for constructing queuing types in discrete-time. there's a concentrate on functions in glossy telecommunication systems.

It presents how such a lot queueing types in discrete-time could be arrange as discrete-time Markov chains. concepts reminiscent of matrix-analytic tools (MAM) that could used to investigate the ensuing Markov chains are incorporated. This e-book covers unmarried node platforms, tandem approach and queueing networks. It indicates how queues with time-varying parameters might be analyzed, and illustrates numerical matters linked to computations for the discrete-time queueing structures. optimum keep watch over of queues can also be covered.

Applied Discrete-Time Queues ambitions researchers, advanced-level scholars and analysts within the box of telecommunication networks. it's appropriate as a reference e-book and will even be used as a secondary textual content ebook in machine engineering and computing device science.  Examples and routines are included.

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Extra resources for Applied Discrete-Time Queues

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Let us briefly mention the characteristics of queueing systems that determine or govern those measures. It is clear that both arrival and service processes have a lot to do with it, and can be used to characterize a queueing system. Common sense tells us that if the arrival rate increases without anything else changing then both the waiting times and number waiting in the system would increase and conversely increasing service rate decreases those measures. Adding servers in parallel would also increase the effective service rate.

7 Example of Discrete Time Concept the time points may or may not represent specific events. We can now observe the system at these points in time. For example, we observe the system at time t1 , t2 , t3 , ... , implying that everything that occurs after time tn and throughout the interval up to time tn+1 , is observable at time tn+1 ; for example all arrivals to a system that occur between the interval (tn , tn+1 ] are observed, and assume to take place, at time epoch tn+1 . Another way to look at it is that nothing occurs between the interval (tn , tn+1 ] that is not observable at time epoch tn+1 .

In this case, for example, X could be the length of time it takes to process a job. If we have two jobs in a system the total time it takes to process the two is given by Y2 . It is easy to show that if we have K jobs then the z-transform of the total time to process all of them will be (p(z))K . 2 Number of renewals Let Zn be the number of renewals in [0, n] then Zn = max{m ≥ 0|Ym ≤ n}. 5) Hence, P{Zn ≥ j} = P{Yj ≤ n} = n ∑ P{Yj = v}. 7) j=1 v=j mn is called the renewal function. It is a well known elementary renewal theorem that the mean renewal rate μ is given by μ = lim|n→∞ mn .

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Applied Discrete-Time Queues by Attahiru Alfa


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