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International Conference on Quantitative Evaluation of Systems

QEST 2016: Quantitative Evaluation of Systems pp 19–34Cite as

Optimal Aggregation of Components for the Solution of Markov Regenerative Processes

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9826))

Abstract

The solution of non-ergodic Markov Renewal Processes may be reduced to the solution of multiple smaller sub-processes (components), as proposed in [4]. This technique exhibits a good saving in time in many practical cases, since components solution may reduce to the transient solution of a Markov chain. Indeed the choice of the components might significantly influence the solution time, and this choice is demanded in [4] to a greedy algorithm. This paper presents a computation of an optimal set of components through a translation into an integer linear programming problem (ILP). A comparison of the optimal method with the greedy one is then presented.

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Notes

  1. 1.

    This logic implication is not in standard ILP form. It can be transformed [10] in ILP form as follows. Let U be a constant greater than |V|. Add a new variable \(k_{v,w}\) subject to these constraints: \(0 \le k_{v,w} \le 1\), \(U k_{v,w} - U < x_v -x_w \le U k_{v,w}\) and \(\forall D' \in \varvec{\mathcal {D}}\setminus \{D\}\) add \(y^{D'}_v \le y^{D'}_w + U k_{v,w}\).

References

  1. Amparore, E.G.: A new GreatSPN GUI for GSPN editing and CSL\(^{\!\text{TA}}\) model checking. In: Norman, G., Sanders, W. (eds.) QEST 2014. LNCS, vol. 8657, pp. 170–173. Springer, Heidelberg (2014)

    Google Scholar 

  2. Amparore, E.G., Donatelli, S.: A component-based solution method for non-ergodic Markov regenerative processes. In: Aldini, A., Bernardo, M., Bononi, L., Cortellessa, V. (eds.) EPEW 2010. LNCS, vol. 6342, pp. 236–251. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  3. Amparore, E.G., Donatelli, S.: MC4CSL\(^{\rm TA}\): an efficient model checking tool for CSL\(^{\rm TA}\). In: International Conference on Quantitative Evaluation of Systems, pp. 153–154. IEEE Computer Society, Los Alamitos (2010)

    Google Scholar 

  4. Amparore, E.G., Donatelli, S.: A component-based solution for reducible Markov regenerative processes. Perform. Eval. 70(6), 400–422 (2013)

    Article  Google Scholar 

  5. Amparore, E.G., Donatelli, S.: Improving and assessing the efficiency of the MC4CSL\(^{\rm TA}\) model checker. In: Balsamo, M.S., Knottenbelt, W.J., Marin, A. (eds.) EPEW 2013. LNCS, vol. 8168, pp. 206–220. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  6. Baarir, S., Beccuti, M., Cerotti, D., Pierro, M.D., Donatelli, S., Franceschinis, G.: The GreatSPN tool: recent enhancements. SIGMETRICS Perform. Eval. Rev. 36(4), 4–9 (2009)

    Article  Google Scholar 

  7. Baier, C., Haverkort, B., Hermanns, H., Katoen, J.P.: Model-checking algorithms for continuous-time Markov chains. IEEE Trans. Softw. Eng. 29(6), 524–541 (2003)

    Article  MATH  Google Scholar 

  8. Bondavalli, A., Mura, I.: High-level Petri net modelling of phased mission systems. In: 10th European Workshop on Dependable Computing, pp. 91–95, Vienna (1999)

    Google Scholar 

  9. Bondavalli, A., Filippini, R.: Modeling and analysis of a scheduled maintenance system: a DSPN approach. Comput. J. 47(6), 634–650 (2004)

    Article  Google Scholar 

  10. Brown, G.G., Dell, R.F.: Formulating integer linear programs: a rogues’ gallery. INFORMS Trans. Educ. 7(2), 153–159 (2007)

    Article  Google Scholar 

  11. Cassandras, C.G., Lafortune, S.: Introduction to Discrete Event Systems. Springer, Secaucus (2006)

    MATH  Google Scholar 

  12. Donatelli, S., Haddad, S., Sproston, J.: Model checking timed and stochastic properties with CSL\(^{\rm TA}\). IEEE Trans. Softw. Eng. 35(2), 224–240 (2009)

    Article  Google Scholar 

  13. German, R.: Performance Analysis of Communication Systems with Non-Markovian Stochastic Petri Nets. Wiley, New York (2000)

    MATH  Google Scholar 

  14. German, R.: Iterative analysis of Markov regenerative models. Perform. Eval. 44, 51–72 (2001)

    Article  MATH  Google Scholar 

  15. Mura, I., Bondavalli, A.: Markov regenerative stochastic petri nets to model and evaluate phased mission systems dependability. IEEE Trans. Comput. 50(12), 1337–1351 (2001)

    Article  Google Scholar 

  16. Stewart, W.J.: Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling. Princeton University Press, Princeton (2009)

    MATH  Google Scholar 

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Authors and Affiliations

  1. University of Torino, Corso Svizzera 187, Torino, Italy

    Elvio Gilberto Amparore & Susanna Donatelli

Authors
  1. Elvio Gilberto Amparore
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  2. Susanna Donatelli
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Correspondence to Elvio Gilberto Amparore .

Editor information

Editors and Affiliations

  1. University of Illinois , Urbana, Illinois, USA

    Gul Agha

  2. University of Antwerp , Antwerp, Belgium

    Benny Van Houdt

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Amparore, E.G., Donatelli, S. (2016). Optimal Aggregation of Components for the Solution of Markov Regenerative Processes. In: Agha, G., Van Houdt, B. (eds) Quantitative Evaluation of Systems. QEST 2016. Lecture Notes in Computer Science(), vol 9826. Springer, Cham. https://doi.org/10.1007/978-3-319-43425-4_2

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  • DOI: https://doi.org/10.1007/978-3-319-43425-4_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-43424-7

  • Online ISBN: 978-3-319-43425-4

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