Efficient Generators of the Generalized Fractional Gaussian Noise and Cauchy Processes
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 h...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/6/455 |
| _version_ | 1797594754063532032 |
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| author | María Estrella Sousa-Vieira Manuel Fernández-Veiga |
| author_facet | María Estrella Sousa-Vieira Manuel Fernández-Veiga |
| author_sort | María Estrella Sousa-Vieira |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T02:27:59Z |
| format | Article |
| id | doaj.art-b97c0791c5d2481798876f8a241f1127 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T02:27:59Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-b97c0791c5d2481798876f8a241f11272023-11-18T10:29:32ZengMDPI AGFractal and Fractional2504-31102023-06-017645510.3390/fractalfract7060455Efficient Generators of the Generalized Fractional Gaussian Noise and Cauchy ProcessesMaría Estrella Sousa-Vieira0Manuel Fernández-Veiga1atlanTTic Research Center, Universidade de Vigo, 36310 Vigo, SpainatlanTTic Research Center, Universidade de Vigo, 36310 Vigo, SpainIn 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.https://www.mdpi.com/2504-3110/7/6/455generalized fGn processgeneralized Cauchy processM/G/∞ processWhittle estimatorefficient online generation |
| spellingShingle | María Estrella Sousa-Vieira Manuel Fernández-Veiga Efficient Generators of the Generalized Fractional Gaussian Noise and Cauchy Processes Fractal and Fractional generalized fGn process generalized Cauchy process M/G/∞ process Whittle estimator efficient online generation |
| title | Efficient Generators of the Generalized Fractional Gaussian Noise and Cauchy Processes |
| title_full | Efficient Generators of the Generalized Fractional Gaussian Noise and Cauchy Processes |
| title_fullStr | Efficient Generators of the Generalized Fractional Gaussian Noise and Cauchy Processes |
| title_full_unstemmed | Efficient Generators of the Generalized Fractional Gaussian Noise and Cauchy Processes |
| title_short | Efficient Generators of the Generalized Fractional Gaussian Noise and Cauchy Processes |
| title_sort | efficient generators of the generalized fractional gaussian noise and cauchy processes |
| topic | generalized fGn process generalized Cauchy process M/G/∞ process Whittle estimator efficient online generation |
| url | https://www.mdpi.com/2504-3110/7/6/455 |
| work_keys_str_mv | AT mariaestrellasousavieira efficientgeneratorsofthegeneralizedfractionalgaussiannoiseandcauchyprocesses AT manuelfernandezveiga efficientgeneratorsofthegeneralizedfractionalgaussiannoiseandcauchyprocesses |