Automated Reliability Analysis in Fog Computing Environment
Resumo
This paper introduces the EMA (Expectation Maximization Algorithm) tool, an automated solution designed to fit Hyper-Erlang distributions for reliability analysis, particularly in fog computing environments. Traditional methods for evaluating Time Failure (TTF) distributions are time consuming and do not scale well in complex systems. The EMA tool addresses this limitation by automating the fitting process, significantly reducing computational time. Applying a resampling method across 100 scenarios, the EMA tool captures system variability and efficiently generates key metrics, such as Probability Density Functions (PDFs) and Cumulative Distribution Functions (CDFs). The tool estimates Hyper-Erlang distribution parameters for each scenario and derives critical reliability metrics, including Mean Time to Absorption (MTTA). The fitting process for the 100 scenarios was completed in just 8 minutes and 22 seconds, and subsequent reliability analysis took 24 and 35 seconds. The EMA tool provides essential information on system performance under various conditions, improving the scalability and efficiency of reliability analysis in distributed environments.Referências
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Fernandes, S., Tavares, E., Santos, M., Lira, V., and Maciel, P. Dependability assessment of virtualized networks. In 2012 IEEE International Conference on Communications (ICC) (2012), pp. 2711–2716.
Häggström, O., Nerman, O., and Asmussen, S. EMPHT: A Program for Fitting Phase-type Distributions. Chalmers tekniska högskola, 1992.
Horváth, G., and Telek, M. On the canonical representation of phase type distributions. Performance Evaluation 66, 8 (2009), 396–409.
Horváth, G., and Telek, M. Butools 2: a rich toolbox for markovian performance evaluation. In VALUETOOLS (2016), pp. 135–141.
Horváth, G., and Telek, M. Markovian performance evaluation with butools. In Systems Modeling: Methodologies and Tools. Springer, 2019, pp. 253–268.
Li, X., Duan, C., Cai, J., Zuo, H., Liu, Z., and Liu, Y. Remaining useful life prediction of iiot equipment using hidden semi-markov model with hyper-erlang sojourn time. IEEE Internet of Things Journal (2024).
Maciel, P., Matos, R., Silva, B., Figueiredo, J., Oliveira, D., Fé, I., Maciel, R., and Dantas, J. Mercury: Performance and dependability evaluation of systems with exponential, expolynomial, and general distributions. In 2017 IEEE 22nd Pacific Rim international symposium on dependable computing (PRDC) (2017), IEEE, pp. 50–57.
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Mialaret, M., Pereira, P., Sá Barreto, A., Pinheiro, T., and Maciel, P. Automated phase-type distribution fitting via expectation maximization. Journal of Reliable Intelligent Environments 10 (2024), 339–355.
Okamura, H., and Dohi, T. Ph fitting algorithm and its application to reliability engineering. Journal of the Operations Research Society of Japan 59, 1 (2016), 72–109.
Pereira, P., Araujo, J., Melo, C., Santos, V., and Maciel, P. Analytical models for availability evaluation of edge and fog computing nodes. The Journal of Supercomputing 77, 9 (2021), 9905–9933.
Pereira, P., Araujo, J., Torqato, M., Dantas, J., Melo, C., and Maciel, P. Stochastic performance model for web server capacity planning in fog computing. The Journal of Supercomputing (2020), 1–25.
Pereira, P., Melo, C., Araujo, J., Dantas, J., Santos, V., and Maciel, P. Availability model for edge-fog-cloud continuum: an evaluation of an end-to-end infrastructure of intelligent traffic management service. The Journal of Supercomputing 78, 3 (2022), 4421–4448.
Prados-Garzon, J., Ameigeiras, P., Ramos-Munoz, J. J., Andres-Maldonado, P., and Lopez-Soler, J. M. Analytical modeling for virtualized network functions. In 2017 IEEE International Conference on Communications Workshops (ICC Workshops) (2017), IEEE, pp. 979–985.
Reinecke, P., Krauss, T., and Wolter, K. Hyperstar: Phase-type fitting made easy. In 2012 Ninth International Conference on Quantitative Evaluation of Systems (2012), IEEE, pp. 201–202.
Reinecke, P., Krauss, T., and Wolter, K. Phase-type fitting using hyperstar. In European Workshop on Performance Engineering (2013), Springer, pp. 164–175.
Silva, B., Matos, R., Callou, G., Figueiredo, J., Oliveira, D., Ferreira, J., Dantas, J., Lobo, A., Alves, V., and Maciel, P. Mercury: An integrated environment for performance and dependability evaluation of general systems. In Proceedings of Industrial Track at 45th Dependable Systems and Networks Conference, DSN (2015).
Silva Pinheiro, T. F., Oliveira, D., Matos, R., Silva, B., Pereira, P., Melo, C., Oliveira, F., Tavares, E., Dantas, J., and Maciel, P. The Mercury Environment: A Modeling Tool for Performance and Dependability Evaluation. 06 2021.
Thummler, A., Buchholz, P., and Telek, M. A novel approach for fitting probability distributions to real trace data with the em algorithm. In 2005 International Conference on Dependable Systems and Networks (DSN’05) (2005), IEEE, pp. 712–721.
Fernandes, S., Tavares, E., Santos, M., Lira, V., and Maciel, P. Dependability assessment of virtualized networks. In 2012 IEEE International Conference on Communications (ICC) (2012), pp. 2711–2716.
Häggström, O., Nerman, O., and Asmussen, S. EMPHT: A Program for Fitting Phase-type Distributions. Chalmers tekniska högskola, 1992.
Horváth, G., and Telek, M. On the canonical representation of phase type distributions. Performance Evaluation 66, 8 (2009), 396–409.
Horváth, G., and Telek, M. Butools 2: a rich toolbox for markovian performance evaluation. In VALUETOOLS (2016), pp. 135–141.
Horváth, G., and Telek, M. Markovian performance evaluation with butools. In Systems Modeling: Methodologies and Tools. Springer, 2019, pp. 253–268.
Li, X., Duan, C., Cai, J., Zuo, H., Liu, Z., and Liu, Y. Remaining useful life prediction of iiot equipment using hidden semi-markov model with hyper-erlang sojourn time. IEEE Internet of Things Journal (2024).
Maciel, P., Matos, R., Silva, B., Figueiredo, J., Oliveira, D., Fé, I., Maciel, R., and Dantas, J. Mercury: Performance and dependability evaluation of systems with exponential, expolynomial, and general distributions. In 2017 IEEE 22nd Pacific Rim international symposium on dependable computing (PRDC) (2017), IEEE, pp. 50–57.
Maciel, P. R. M. Performance, Reliability, and Availability Evaluation of Computational Systems, Volume I: Performance and Background. Chapman and Hall/CRC, 2023.
Maciel, P. R. M. Performance, Reliability, and Availability Evaluation of Computational Systems, Volume II: Performance and Background. Chapman and Hall/CRC, 2023.
Mialaret, M., Pereira, P., Sá Barreto, A., Pinheiro, T., and Maciel, P. Automated phase-type distribution fitting via expectation maximization. Journal of Reliable Intelligent Environments 10 (2024), 339–355.
Okamura, H., and Dohi, T. Ph fitting algorithm and its application to reliability engineering. Journal of the Operations Research Society of Japan 59, 1 (2016), 72–109.
Pereira, P., Araujo, J., Melo, C., Santos, V., and Maciel, P. Analytical models for availability evaluation of edge and fog computing nodes. The Journal of Supercomputing 77, 9 (2021), 9905–9933.
Pereira, P., Araujo, J., Torqato, M., Dantas, J., Melo, C., and Maciel, P. Stochastic performance model for web server capacity planning in fog computing. The Journal of Supercomputing (2020), 1–25.
Pereira, P., Melo, C., Araujo, J., Dantas, J., Santos, V., and Maciel, P. Availability model for edge-fog-cloud continuum: an evaluation of an end-to-end infrastructure of intelligent traffic management service. The Journal of Supercomputing 78, 3 (2022), 4421–4448.
Prados-Garzon, J., Ameigeiras, P., Ramos-Munoz, J. J., Andres-Maldonado, P., and Lopez-Soler, J. M. Analytical modeling for virtualized network functions. In 2017 IEEE International Conference on Communications Workshops (ICC Workshops) (2017), IEEE, pp. 979–985.
Reinecke, P., Krauss, T., and Wolter, K. Hyperstar: Phase-type fitting made easy. In 2012 Ninth International Conference on Quantitative Evaluation of Systems (2012), IEEE, pp. 201–202.
Reinecke, P., Krauss, T., and Wolter, K. Phase-type fitting using hyperstar. In European Workshop on Performance Engineering (2013), Springer, pp. 164–175.
Silva, B., Matos, R., Callou, G., Figueiredo, J., Oliveira, D., Ferreira, J., Dantas, J., Lobo, A., Alves, V., and Maciel, P. Mercury: An integrated environment for performance and dependability evaluation of general systems. In Proceedings of Industrial Track at 45th Dependable Systems and Networks Conference, DSN (2015).
Silva Pinheiro, T. F., Oliveira, D., Matos, R., Silva, B., Pereira, P., Melo, C., Oliveira, F., Tavares, E., Dantas, J., and Maciel, P. The Mercury Environment: A Modeling Tool for Performance and Dependability Evaluation. 06 2021.
Thummler, A., Buchholz, P., and Telek, M. A novel approach for fitting probability distributions to real trace data with the em algorithm. In 2005 International Conference on Dependable Systems and Networks (DSN’05) (2005), IEEE, pp. 712–721.
Publicado
26/11/2024
Como Citar
MIALARET, Marco; PINHEIRO, Thiago; NETO, Antonio; PESSOA, Pablo Philipe; PEREIRA, Paulo; DANTAS, Jamilson Ramalho; MACIEL, Paulo Romero Martins.
Automated Reliability Analysis in Fog Computing Environment. In: WORKSHOP SOBRE ENGENHARIA DE RESILIÊNCIA EM SISTEMAS DE COMPUTAÇÃO (RECS), 1. , 2024, Recife/PE.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2024
.
p. 19-24.
DOI: https://doi.org/10.5753/recs.2024.35965.
