Abstract
Multiple-Phased Systems (MPS) are systems whose behaviour can be split in a set of successive periods, called phases, and the system behaviour typically depends on the current phase. Previous work has modelled MPS as Deterministic Stochastic Petri Nets (DSPN) composed of two parts: a Phase net (PhN) that describes the progress of the phases and a System Net (SN) that describes the system behaviour, typically influenced by the current phase. By imposing certain restrictions on the net, the authors were able to devise an ad-hoc technique, implemented in the tool DEEM, that reduces the computation of the mission performances to a sequence of transient solutions of Markov chains. In this paper we define X-PPN, an extension of the PPN formalism that allows the modeller more freedom in the structure and in the stochastic distribution of the phases (from deterministic to general) and in the definition of the dependencies among the system and the phase net. X-PPN are solved using the solvers of the GreatSPN tool for Markov Regenerative Processes (MRgP). The GreatSPN solution can solve X-PPN with millions of state and, when the net is actually only a PPN, the computational cost in time reduces to that of the ad-hoc technique of PPN.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
M. Ajmone Marsan, G. Chiola, On Petri nets with deterministic and exponentially distributed firing times, in Advances in Petri Nets. Lecture Notes in Computer Science, vol. 266 (Springer, Berlin, 1987), pp. 32–145
M. Ajmone Marsan, G. Conte, G. Balbo, A class of generalized stochastic Petri nets for the performance evaluation of multiprocessor systems. ACM Trans. Comput. Syst. 2, 93–122 (1984)
E.G. Amparore, S. Donatelli, A component-based solution method for non-ergodic Markov Regenerative Processes, in Computer Performance Engineering. Lecture Notes in Computer Science, vol. 6342 (Springer, Berlin, 2010), pp. 236–251
E.G. Amparore, S. Donatelli, MC4CSLTA: an efficient model checking tool for CSLTA, in International Conference on Quantitative Evaluation of Systems (IEEE Computer Society, Los Alamitos, 2010), pp. 153–154
E.G. Amparore, S. Donatelli, Revisiting the matrix-free solution of Markov regenerative processes, in Numerical Linear Algebra with Applications. Special Issue on Numerical Solutions of Markov Chains, vol. 18 (Wiley, New York, 2011), pp. 1067–1083
E.G. Amparore, S. Donatelli, A component-based solution for reducible Markov regenerative processes. Perform. Eval. 70(6), 400–422 (2013)
E.G. Amparore, S. Donatelli, Efficient solution of extended Multiple-Phased Systems, in 10th Valuetools Conference (EAI, 2016), pp. 125–132
E.G. Amparore, S. Donatelli, Optimal aggregation of components for the solution of Markov regenerative processes, in Quantitative Evaluation of Systems: 13th International Conference, QEST 2016, Quebec City, August 23–25, Proceedings (Springer International Publishing, Cham, 2016), pp. 19–34
E.G. Amparore, S. Donatelli, alphaFactory: a tool for generating the alpha factors of general distributions, in Proceedings of Quantitative Evaluation of Systems (QEST) 2017 (Springer, Berlin, 2017), pp. 36–51
E. Amparore, S. Donatelli, Efficient solution of extended multiple-phased systems, in Proceedings of 10th VALUETOOLS Conference (ICST, Brussels, 2017), pp. 125–132
E.G. Amparore, G. Balbo, M. Beccuti, S. Donatelli, G. Franceschinis, 30 Years of GreatSPN, in Principles of Performance and Reliability Modeling and Evaluation: Essays in Honor of Kishor Trivedi (Springer, Cham, 2016), pp. 227–254
A. Bondavalli, I. Mura, K.S. Trivedi, Dependability Modelling and Sensitivity Analysis of Scheduled Maintenance Systems (Springer, Berlin, 1999), pp. 7–23
A. Bondavalli, S. Chiaradonna, F. Di Giandomenico, I. Mura, Dependability modeling and evaluation of multiple-phased systems using DEEM. IEEE Trans. Reliab. 53(4), 509–522 (2004)
C.G. Cassandras, S. Lafortune, Introduction to Discrete Event Systems (Springer, New York, 2006)
S. Chew, S. Dunnett, J. Andrews, Phased mission modelling of systems with maintenance-free operating periods using simulated Petri nets. Reliab. Eng. Syst. Saf. 93(7), 980–994 (2008)
H. Choi, V. Mainkar, K.S. Trivedi, Sensitivity analysis of deterministic and stochastic petri nets, in International Workshop on Modeling, Analysis, and Simulation on Computer and Telecommunication Systems (MASCOTS), San Diego (1993), pp. 271–276
H. Choi, V.G. Kulkarni, K.S. Trivedi, Markov regenerative stochastic Petri nets. Perform. Eval. 20(1–3), 337–357 (1994)
R. German, Performance Analysis of Communication Systems with Non-Markovian Stochastic Petri Nets (Wiley, New York, 2000)
C. Hockley, Design for success. J. Aerosp. Eng. 212(6), 371–378 (1998)
I. Mura, A. Bondavalli, Markov regenerative stochastic petri nets to model and evaluate the dependability of Phased Mission Systems dependability. IEEE Trans. Comput. 50(12), 1337–1351 (2001)
I. Mura, A. Bondavalli, X. Zang, K.S. Trivedi, Dependability modeling and evaluation of Phased Mission Systems: a DSPN approach, in International Conference on Dependable Computing for Critical Applications (IEEE Press, New York, 1999), pp. 299–318
Z. Peng, Y. Lu, A. Miller, Uncertainty analysis of phased mission systems with probabilistic timed automata, in 7th IEEE International Conference on Prognostics and Health Management (PHM’16) (2016)
R. Pyke, Markov Renewal Processes with Finitely Many States (Columbia University, New York, 1959)
A.K. Somani, J.A. Ritcey, S.H. Au, Computationally-efficient phased-mission reliability analysis for systems with variable configurations. IEEE Trans. Reliab. 41(4), 504–511 (1992)
W.J. Stewart, Probability, Markov Chains, Queues, and Simulation : The Mathematical Basis of Performance Modeling (Princeton University Press, Princeton, 2009)
K.S. Trivedi, Probability and Statistics with Reliability, Queuing, and Computer Science Applications (Wiley, New York, 2002)
University of Torino, The GreatSPN tool homepage. http://www.di.unito.it/~greatspn/index.html
L. Xing, S. Amari, Reliability of phased-mission systems, in Handbook of Performability Engineering, ed. by K. Misra (Springer, London, 2008), pp. 349–368
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Amparore, E.G., Donatelli, S. (2019). Modelling and Efficient Solution of Multiple-Phased Systems. In: Puliafito, A., Trivedi, K. (eds) Systems Modeling: Methodologies and Tools. EAI/Springer Innovations in Communication and Computing. Springer, Cham. https://doi.org/10.1007/978-3-319-92378-9_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-92378-9_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-92377-2
Online ISBN: 978-3-319-92378-9
eBook Packages: EngineeringEngineering (R0)