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Original Articles

Propagation of epistemic uncertainty in queueing models with unreliable server using chaos expansions

ORCID Icon, ORCID Icon, ORCID Icon & ORCID Icon
Pages 1039-1061 | Received 26 Apr 2018, Accepted 18 Jan 2019, Published online: 11 Mar 2019

References

  • Abate, J., G. L. Choudhury, and W. Whitt. 2000. An introduction to numerical transform inversion and its application to probability models. In: Computational probability, ed. W. K. Grassmann, Kluwer Academic Publishers.
  • Abbas, K., J. Berkhout, and B. Heidergott. 2016. A critical account of perturbation analysis of markov chains. Markov Processes And Related Fields. 522 (2):227–65.
  • Aleti, A., C. Trubiani, A. van Hoorn, and P. Jamshidi. 2018. An efficient method for uncertainty propagation in robust software performance estimation. Journal of System Software 138:222–35. doi: 10.1016/j.jss.2018.01.010.
  • Avi-Itzhak, B., and P. Naor. 1963. Some queuing problems with the service station subject to breakdown. Operations Research 11 (3):303–20. doi: 10.1287/opre.11.3.303.
  • Baccelli, F., and T. Znati. 1981. Queueing systems with breakdowns in data base modeling. In Proceedings of performance 81 (8 th IFIP international symposium on comp. Perf. Model. North Holland: Amsterdam.
  • Cacuci, D. G. 2003. Sensitivity and uncertainty analysis. Vol. I. Boca Raton, FL: Chapman & Hall/CRC.
  • Cao, J. H., and K. Cheng. 1982. Analysis of an M/G/1 queueing system with repairable service station. Acta Mathematicae Applicatae Sinica 5 (2):113–27.
  • Chauvière, C., J. S. Hesthaven, and L. Lurati. 2006. Computational modeling of uncertainty in time-domain electromagnetics. SIAM Journal on Scientific Computing 28 (2):751–75. doi: 10.1137/040621673.
  • Dhople, S. V., Y. C. Chen, and A. D. Domínguez-García. 2013. A set-theoretic method for parametric uncertainty analysis in Markov reliability and reward models. IEEE Transactions on Reliability 62 (3):658–69. doi: 10.1109/TR.2013.2270421.
  • Dhople, S. V., and A. D. Domínguez-García. 2012. A parametric uncertainty analysis method for Markov reliability and reward models. IEEE Transactions on Reliability 61 (3):634–48. doi: 10.1109/TR.2012.2208299.
  • Gautschi, W. 2004. Orthogonal polynomials: computation and approximation. Numerical Mathematics and Scientific Computation. Oxford University Press, New York. Oxford Science Publications.
  • Ghanem, R. G., and P. D. Spanos. 1991. Stochastic finite elements: a spectral approach. New York: Springer-Verlag.
  • Gottlieb, D., and S. A. Orszag. 1977. Numerical analysis of spectral methods: theory and applications. CBMS-NSF Regional Conference Series in Applied Mathematics, No. 26. Philadelphia, PA Society for Industrial and Applied Mathematics.
  • Granger, M., and M. Henrion. 1993. Uncertainty: A guide to dealing with uncertainty in quantitative risk and policy analysis. pp. 332. Cambridge, MA: Cambridge University Press.
  • Helton, J. C. 1993. Uncertainty and sensitivity analysis techniques for use in performance assessment for radioactive waste disposal. Reliability Engineering and System Safety 42 (2–3):327–67. doi: 10.1016/0951-8320(93)90097-I.
  • Helton, J. C. 1994. Treatment of uncertainty in performance assessments for complex systems. Risk Analysis 14 (4):483–511. doi: 10.1111/j.1539-6924.1994.tb00266.x.
  • Helton, J. C. 1997. Uncertainty and sensitivity analysis in the presence of stochastic and subjective uncertainty. Journal of Statistical Computation and Simulation. 57 (1-4):3–76. doi: 10.1080/00949659708811803.
  • Helton, J. C., J. D. Johnson, C. J. Sallaberry, and C. B. Storlie. 2006. Survey of sampling-based methods for uncertainty and sensitivity analysis. Reliability Engineering and System Safety 91 (10-11):1175–209. doi: 10.1016/j.ress.2005.11.017.
  • Homma, T., and A. Saltelli. 1996. Importance measures in global sensitivity analysis of nonlinear models. Reliability Engineering and System Safety 52 (1):1–17. doi: 10.1016/0951-8320(96)00002-6.
  • Iman, R. L., and J. C. Helton. 1988. An investigation of uncertainty and sensitivity analysis techniques for computer models. Risk Analysis 8 (1):71–90. doi: 10.1111/j.1539-6924.1988.tb01155.x.
  • Ionescu-Bujor, M., and D. G. Cacuci. 2004. A comparative review of sensitivity and uncertainty analysis of large-scale system, I: Deterministic methods. Nuclear Science and Engineering· 147 (3):189–203. doi: 10.13182/NSE03-105CR.
  • Li, W., D. Shi, and X. Chao. 1997. Reliability analysis of M/G/1 queueing systems with server breakdowns and vacations. Journal of Applied Probability 34 (2):546–55. doi: 10.2307/3215393.
  • Limbourg, P. 2008. Dependability modelling under uncertainty: An imprecise probabilistic approach. Studies in Computational Intelligence, 148, Berlin, Heidelberg: Springer.
  • Mattia, P., C. M. Sergio, and G. M. Dimitrov. 2007. Comparative analysis of uncertainty propagation methods for robust engineering design. In: Proceedings of the international conference on engineering design, ICED’07. 28–31 August, Cité Des Sciences et de l’industrie, Paris.
  • Mishra, K., and K. S. Trivedi. 2011. An unobtrusive method for uncertainty propagation in stochastic dependability models. IJRQP 3 (1):49–65.
  • Mitrany, I., and B. Avi-Itzhak. 1968. A Many-Server queue with service interruptions. Operation Research 16 (3):628–38. doi: 10.1287/opre.16.3.628.
  • Moore, R. 1979. Methods and applications of interval analysis. Philadelphia, PA: SIAM Studies in Applied Mathematics.
  • Neuts, M. F. 1981. Matrix-geometric solutions in stochastic models, Volume 2 of johns hopkins series in the mathematical sciences. An algorithmic approach. Baltimore, MD: Johns Hopkins University Press.
  • Neuts, M. F., and D. M. Lucantoni. 1979. A markovian queue with N servers subject to breakdowns and repairs. Management Science. 25 (9):849–61. 1980. doi: 10.1287/mnsc.25.9.849.
  • Ouazine, S., and K. Abbas. 2016. A functional approximation for retrial queues with two way communication. Annals of Operations Research 247 (1):211–227. doi: 10.1007/s10479-015-2083-2.
  • Pettersson, M. P., G. Iaccarino, and J. Nordström. 2015. Polynomial chaos methods for hyperbolic partial differential equations. Mathematical engineering. Numerical techniques for fluid dynamics problems in the presence of uncertainties. Cham: Springer.
  • Rahman, S. 2009. Extended polynomial dimensional decomposition for arbitrary probability distributions. Journal of Engineering Mechanics 135 (12):1439–1451. doi: 10.1061/(ASCE)EM.1943-7889.0000047.
  • Rocco, C. M., and W. Klindt. 1998. Distribution systems reliability uncertainty evaluation using an interval arithmetic approach. In: Proceedings of the second IEEE international CARACAS conference on devices, circuits and systems., Isla de Margarita, Venezuela.
  • Ronen, Y. 1988. Uncertainty analysis. Boca Raton, FL: CRC Press.
  • Sepahvand, K., S. Marburg, and H. J. Hardtke. 2010. Uncertainty quantification in stochastic systems using polynomial chaos expansion. International Journal of Applied Mechanics 02 (02):305–53. doi: 10.1142/S1758825110000524.
  • Shooman, M. 1990. Probabilistic reliability: An engineering approach. Second edition. Malabar, FL: R. Krieger Pub. Co.
  • Shortle, J. F., M. J. Fischer, and P. H. Brill. 2007. Waiting-time distribution of M/DN/1 queues through numerical laplace inversion. INFORMS Journal of Computing 19 (1):112–20. doi: 10.1287/ijoc.1050.0148.
  • Shuxing, Y., F. Xiong, and F. Wang. 2017. Polynomial chaos expansion for probabilistic uncertainty propagation. Uncertainty Quantification and Model Calibration, Jan Peter Hessling, IntechOpen. doi: 10.5772/intechopen.68484. Available from: https://www.intechopen.com/books/uncertainty-quantification-and-model-calibration/polynomial-chaos-expansion-for-probabilistic-uncertainty-propagation.
  • Sobol, I. M. 1993. Sensitivity estimates for nonlinear mathematical models. Mathematcis Modeling Computing Experiment 1 (4):407–14.
  • Sudret, M. 2008. Global sensitivity analysis using polynomial chaos expansion. Reliability Engineering and System Safety 93 (7):964–79. doi: 10.1016/j.ress.2007.04.002.
  • Takhedmit, B., and K. Abbas. 2017. A parametric uncertainty analysis method for queues with vacations. The Journal of Computational and Applied Mathematics. 312:143–55. doi: 10.1016/j.cam.2016.02.031.
  • Thiruvengadam, K. 1963. Queuing with breakdowns. Operation Research 11 (1):62–71. doi: 10.1287/opre.11.1.62.
  • Wang, J., J. Cao, and Q. Li. 2001. Reliability analysis of the retrial queue with server breakdowns and repairs. Queueing Systems 38 (4):363–80. doi: 10.1023/A:1010918926884.
  • Winkler, R. L. 1996. Uncertainty in probabilistic risk assessment. Reliability Engineering System Safety 54 (2/3):127–32. doi: 10.1016/S0951-8320(96)00070-1.
  • Winkler, R. L. 2004. A comparative review of sensitivity and uncertainty analysis of Large-Scale Systems - II: Statistical methods. Nuclear Science Engineering 147 (3):204–17.
  • Xiu, D., and G. E. Karniadakis. 2002. The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM Journal on Scientific Computing 24 (2):619–44. doi: 10.1137/S1064827501387826.
  • Yang, D. H., Y. C. Chiang, and C. Tsou. 2013. Cost analysis of a finite capacity queue with server breakdowns and threshold-based recovery policy. Journal of Manufacturing System 32 (1):174–9. doi: 10.1016/j.jmsy.2012.06.002.

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