Queuing Theory and Telecommunications

Giambene, Giovanni

doi:10.1007/978-1-4614-4084-0

Cited by 55 publications

(28 citation statements)

References 22 publications

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“…The probability p(B) that there will be no collision of random demands on the time interval 0, L is given by (8) where p(B|A k ) is the conditional probability that there will be no collision of random demands given that exactly k random demands occur during the time interval (0, L). p(B|A k ) can be determined considering that if the homogeneous Poisson process is conditioned on the number of random demands, the random demands will be uniformly distributed along the time interval (0, L).…”

Section: Determining the Optimal Number Of Users Served By A Single Smentioning

confidence: 99%

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Evaluating the risk of unsatisfied random demand on a time interval

Todinov

2015

AIR

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This paper focuses on an important and very common problem and presents a theoretical framework for solving it: "determining the risk of unsatisfied request from users placing random demands on a time interval". For the common case of a single source servicing a number of consumers, a closed-form solution has been derived for the risk of collision of random demands. Based on the closed-form solution, an efficient optimisation method has been developed for determining the optimal number of consumers that can be serviced by a single source, such that the probability of unsatisfied demand remains below a maximal tolerable level. A central part of the proposed theoretical framework is a general equation evaluating the risk of unsatisfied demand by the expected fraction of time of unsatisfied demand. The derived equation covers multiple sources servicing multiple consumers. Finally, the conducted parametric studies revealed an unexpected finding: the risk of collision of random demands on a time interval is practically insensitive to the standard deviations of the durations of demands. This surprising result provides the valuable opportunity to work with random demand times characterised by their means only, without supplying their probability distributions or variances.

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Section: Determining the Optimal Number Of Users Served By A Single Smentioning

confidence: 99%

“…[2][3][4][5][6] Neither of these classical comprehensive texts nor more recent comprehensive texts devoted to various problems in probability and queuing theory [7][8][9][10][11][12] treats the question related to risk of unsatisfied demand from random requests on a time interval.…”

Section: Introductionmentioning

confidence: 99%

Evaluating the risk of unsatisfied random demand on a time interval

Todinov

2015

AIR

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“…Queuing theory systems are classified according to various characteristics, which are often summarized using Kendall`s notation [7,9]. The basic parameters of queuing theory systems are as following…”

Section: Background Of Analytical Modelsmentioning

confidence: 99%

Unified Analytical Models of Parallel and Distributed Computing

Hanuliak¹

2014

AJNC

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Abstract:The optimal resource allocation satisfies the needed capacity of the used resources. To such analysis we can use both analytical and simulation methods. Principally analytical methods (AM) belong to the preferred method in comparison to the simulation method, because of their potential ability of more general analysis and also of ability to analyze massive parallel computers. This article goes further in developing AM based on queuing theory results in relation to our published paper in [9]. The extensions are in extending derived AM to whole range of parallel computers and also to sum up public acceptance of our published paper. The article therefore describes deriving of correction factor of standard AM based on M/M/m and M/M/1queuing theory systems. In detail the paper describes derivation of a correction factor for standard AM to study more precise their performance. The paper contributions are in unified AM and in deriving correction factor in order to take into account real non-exponential nature of the inputs to the computing nodes and node's communication channels. The derived analytical results were compared with performed simulation results in order to estimate the magnitude of improvement. Likewise the corrected AM were tested under various ranges of parameters, which influence the architecture of the parallel computers and its communication networks too. These results are very important in practical use.

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“…In such model, jobs arrive at some rate, queue for service on a first-come first-served basis, receive service, and exit the system. This kind of model, with jobs entering and leaving the system, is called an open queuing system model [7,27].…”

Section: Application Of Queuing Theorymentioning

confidence: 99%

Modeling of Parallel Computers Based on Network of Computing

Hanuliak¹

2014

AJNC

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Abstract:The optimal resource allocation to satisfy such demands and the proper settlement of contention when demands exceed the capacity of the resources, constitute the problem of being able to understand and to predict system behavior. To this analysis we can use both analytical and simulation methods. Modeling and simulation are methods, which are commonly used by performance analysts to represent constraints and to optimize performance. Principally analytical methods represented first of all by queuing theory belongs to the preferred method in comparison to the simulation method, because of their potential ability of general analysis and also of their ability to potentially analyze also massive parallel computers. But these arguments supposed to develop and to verify suggested analytical models. This article goes further in applying the achieved analytical results in queuing theory for complex performance evaluation in parallel computing [9,14]. The extensions are mainly in extending derived analytical models to whole range of parallel computers including massive parallel computers (Grid, meta computer). The article therefore describes standard analytical model based on M/M/m, M/D/m and M/M/1, M/D/1 queuing theory systems. Then the paper describes derivation of the correction factor for standard analytical model, based on M/M/m and M/M/1 queuing systems, to study more precise their basic performance parameters (overhead latencies, throughput etc.). All the derived analytical models were compared with performed simulation results in order to estimate the magnitude of improvement. Likewise they were tested under various ranges of parameters, which influence the architecture of the parallel computers and its communication networks too. These results are very important in practical use.

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Queuing Theory and Telecommunications

Abstract: Additional material to this book can be downloaded from http://extras.springer.com ISBN 978-1-4614-4083-3 ISBN 978-1-4614-4084-0 (eBook)

Cited by 55 publications

References 22 publications

Evaluating the risk of unsatisfied random demand on a time interval

Evaluating the risk of unsatisfied random demand on a time interval

Unified Analytical Models of Parallel and Distributed Computing

Modeling of Parallel Computers Based on Network of Computing

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