Study on estimating probabilities of buffer overflow in high-speed communication networks

Lokshina, Izabella

doi:10.1007/s11235-015-0055-0

Cited by 8 publications

(7 citation statements)

References 16 publications

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“…. Traffic modeling at small time scales is needed in applications, such as queuing, buffer design, traffic delay, anomaly detection, see e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. From the point of view of the study of network infrastructure for network management, design planning, and simulation, however, traffic modeling at a large time scale is particularly needed.…”

Section: Introductionmentioning

confidence: 99%

Long-range dependence and self-similarity of teletraffic with different protocols at the large time scale of day in the duration of 12 years: Autocorrelation modeling

2020

Phys. Scr.

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Teletraffic (traffic in short) modeling is crucial in the analysis and design of the infrastructure of cyber-physical network systems from a view of traffic engineering. However, reports regarding traffic modeling at the large time scale of day in the duration of years are rarely seen. This paper addresses our finding in autocorrelation function modeling in the closed form of traffic at the time scale of day (daily traffic for short) in the duration of 12 years with different protocols. We shall show that the autocorrelation function of daily traffic takes the autocorrelation function form of the generalized Cauchy process based on studying the autocorrelation function modeling of daily traffic with real traffic data. Thus, the long-range dependence and local self-similarity of daily traffic are in general uncorrelated according to the theory of the generalized Cauchy process. In addition, we will exhibit that the concrete values of long-range dependence measure and local self-similarity one of daily traffic may relate to protocol types.

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Section: Introductionmentioning

confidence: 99%

Long-range dependence and self-similarity of teletraffic with different protocols at the large time scale of day in the duration of 12 years: Autocorrelation modeling

2020

Phys. Scr.

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“…Since, in the past, complex correlation structures were empirically observed both in aggregated and individual traffic traces, including long-range dependence (LRD) and large-timescale self-similarity (SS) [3][4][5][6][7][8][9][10][11][12][13][14], it is reasonable to expect that novel or modified flexible stochastic processes have to be analyzed for teletraffic and simulation analysis of such advanced communication services. A similar research effort was made when queuing models with fractal correlated input and the analysis of that on network performance [15][16][17][18][19][20][21][22][23][24][25][26] were thoroughly studied. These works demonstrated that second-order statistics, and their extreme manifestations as LRD and SS, lead to very slow decay of the queue backlogs, thus having a huge impact on loss and delay.…”

Section: Introductionmentioning

confidence: 99%

Efficient Generators of the Generalized Fractional Gaussian Noise and Cauchy Processes

Sousa-Vieira

Fernández‐Veiga

2023

Fractal Fract

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In the last years of the past century, complex correlation structures were empirically observed, both in aggregated and individual traffic traces, including long-range dependence, large-timescale self-similarity and multi-fractality. The use of stochastic processes consistent with these properties has opened new research fields in network performance analysis and in simulation studies, where the efficient synthetic generation of samples is one of the main topics. Nowadays, networks have to support data services for traffic sources that are poorly understood or still insufficiently observed, for which simple, reproducible, and good traffic models are yet to be identified, and it is reasonable to expect that previous generators could be useful. For this reason, as a continuation of our previous work, in this paper, we describe efficient and online generators of the correlation structures of the generalized fractional noise process (gfGn) and the generalized Cauchy (gC) process, proposed recently. Moreover, we explain how we can use the Whittle estimator in order to choose the parameters of each process that give rise to a better adjustment of the empirical traces.

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“…Markovprocessesprovideflexible,powerful,andefficientmeansforevaluationandanalysisof dynamicsystems.Performanceandreliabilitymeasuresofaqueueingnetworkcanbederivedand evaluatedwiththesteady-stateanalysisofDiscrete-TimeMarkovChains(DTMC)andContinuous-TimeMarkovChains(CTMC).Generally,eachqueueingsystemcanbeconsideredasaspecific caseofMarkovprocess,andthenmathematicallyevaluatedintermsoftheprocess (Hassinand Haviv, 2003;Liu, Ma and Li, 2012;Lokshina, 2016;Lokshina and Bartolacci, 2012;Zhang, 2009).Directanditerativemethodscanbeusedtoobtainnumericalsolutionsinthesteady-state analysisofMarkovchains (Bhalai,2002;Liu,MaandZhang,2015;Lokshina,2016;Lokshina andBartolacci,2012;LokshinaandBartolacci,2007;Radev,LokshinaandDenchev,2007;Radev, LokshinaandRadeva,2007).…”

Section: Introductionmentioning

confidence: 99%

“…final (or, exact) values. The main advantage of iterative methods, compared with direct methods,isbecauseiterativemethodsmaintaintheparametermatrix (Stewart,1994;Lokhina, 2016;Radev,LokshinaandDenchev,2007),sinceefficientsparsestorageschemesandefficient sparsity-preservingalgorithmsareapplied.Ontheotherhand,themaindisadvantageofiterative methodsisthatconvergenceisnotalwaysguaranteed (RubinsteinandMelamed,1998;Lokshina, 2016), and it is highly dependent on the applied method (Hassin and Haviv, 2003;Krieger, Muller-ClostermannandSczittnick,1990;Lokshina,2016;LokshinaandBartolacci,2012).The rateofconvergenceisverysensitiveforentryvaluesintheparametermatrix (Trivedi,2001;Lokshina,2016;Radev,LokshinaandDenchev,2007). Theimportanttaskhereistoobtainexactorapproximatenumericalsolutionsforglobaland localbalanceequationsofqueueingsystemswithMarkovchains (HassinandHaviv,2003;Hayesand GaneshBabu,2004;Lokshina,2016;LokshinaandBartolacci,2012;LokshinaandBartolacci,2007;Radev,LokshinaandDenchev,2007).Thisisafocalpointformodelingclosedandopenqueueing networks,especiallywithheavytailedtraffic.…”

Section: Introductionmentioning

confidence: 99%

“…Developingcomputationalprocedurestoobtainthesteady-stateprobabilitiesforallpossiblestates inaqueueingnetworkisacentralissueinthequeueingtheory.Themeansformanyotherimportant network performance measures can be easily obtained after having these algorithms developed (Dugas,Chapados,Ducharme,Saint-MleuxandVincent;2011;HassinandHaviv,2003;Lokshina, 2016;LokshinaandBartolacci,2012;LokshinaandBartolacci,2007).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analysis of Queueing Networks in Equilibrium

Lokshina

Lanting²

2020

International Journal of Interdisciplinary Telecommunications and Networking

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Equilibria of queueing networks are a means for performance analysis of real communication networks introduced as Markov chains. In this paper, the authors developed, evaluated, and compared computational procedures to obtain numerical solutions for queueing networks in equilibrium with the use of direct, iterative, and aggregative techniques in steady-state analysis of Markov chains. Advanced computational procedures are developed with the use of Gaussian elimination, power iteration, Courtois' decomposition, and Takahashi's iteration techniques. Numerical examples are provided together with comparative analysis of obtained results. The authors consider these procedures are also applicable to other domains where systems are described with comparable queuing models and stochastic techniques are sufficiently relevant. Several suitable domains of applicability are proposed.

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Study on estimating probabilities of buffer overflow in high-speed communication networks

Cited by 8 publications

References 16 publications

Long-range dependence and self-similarity of teletraffic with different protocols at the large time scale of day in the duration of 12 years: Autocorrelation modeling

Long-range dependence and self-similarity of teletraffic with different protocols at the large time scale of day in the duration of 12 years: Autocorrelation modeling

Efficient Generators of the Generalized Fractional Gaussian Noise and Cauchy Processes

Analysis of Queueing Networks in Equilibrium

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