Abstract
Starting from the expertise in reliability and in performance evaluation, we present the notion of performability introduced by John Meyer in his famous paper. We recall that in the past, few industry leaders believed in stochastic models, most of them placing greater confidence in the development of deterministic models and the use of coefficients of security to take into account the different uncertainties. But now, the notion of risk has been emphasized by the development of new technologies, the generalization of insurance policies, and the practice of service level agreements. Therefore, this is the time to consider stochastic models, where former deterministic parameters are replaced by random variables, with the encouragement of industrial leaders. We illustrate these latter models through two variants of a case study.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Which are two of Kishor Trivedi’s areas of expertise, as already illustrated in his first book.
References
Aggarwal Krishan K, Gupta Jagdish S, Misra Krishna B (1973) A new method for system reliability evaluation. Microelectron Reliab 12(5):435–440
Baskett F, Chandy KM, Muntz RR, Palacios FG (1975) Open, closed, and mixed networks of queues with different classes of customers. J ACM (JACM) 22(2):248–260
Beaudry MD (1978) Performance-related reliability measures for computing systems. IEEE Trans Comput 100(6):540–547
Benetto Enrico, Dujet Christiane, Rousseaux Patrick (2008) Integrating fuzzy multicriteria analysis and uncertainty evaluation in life cycle assessment. Environ Model Softw 23(12):1461–1467
Blake JT, Reibman AL, Trivedi KS (1988) Sensitivity analysis of reliability and performability measures for multiprocessor systems. In: ACM SIGMETRICS performance evaluation review, vol 16. ACM, pp 177–186
Buzen Jeffrey P (1973) Computational algorithms for closed queueing networks with exponential servers. Commun ACM 16(9):527–531
Chen J, Brissette FP, Chaumont D, Braun M (2013) Performance and uncertainty evaluation of empirical downscaling methods in quantifying the climate change impacts on hydrology over two north american river basins. J Hydrol 479:200–214
Ciardo Gianfranco, Marie Raymond A, Sericola Bruno, Trivedi Kishor S (1990) Performability analysis using semi-markov reward processes. IEEE Trans Comput 39(10):1251–1264
Ciciani Bruno, Grassi Vincenzo (1987) Performability evaluation of fault-tolerant satellite systems. IEEE Trans Commun 35(4):403–409
Cohen JW (1969) The single server queue. North-Holland, New York, Amsterdam
Colbourn CJ (1999) Reliability issues in telecommunications network planning. In: Telecommunications network planning, pp 135–146. Springer
de Souza e Silva E, Gail HR (1998) An algorithm to calculate transient distributions of cumulative rate and impulse based reward. Stoch Models 14(3):509–536
de Souza e Silva E, Gail HR (1989) Calculating availability and performability measures of repairable computer systems using randomization. J ACM (JACM) 36(1):171–193
de Souza e Silva E, Gail HR (1992) Performability analysis of computer systems: from model specification to solution. Perform Eval 14(3):157–196
de Souza e Silva E, Gail HR (2000) Transient solutions for markov chains. In: Computational probability, pp 43–79. Springer
de Souza e Silva E, Gail HR, Campos RV (1995) Calculating transient distributions of cumulative reward. In: ACM-SIGMETRICS, pp 231–240
de Souza e Silva E, Gail HR et al (1986) Calculating cumulative operational time distributions of repairable computer systems. IEEE Trans Comput 100(4):322–332
Do Van P, Barros A, Bérenguer C (2008) Reliability importance analysis of markovian systems at steady state using perturbation analysis. Reliab Eng Syst Safety 93(11):1605–1615
Do Van P, Barros A, Bérenguer C (2010) From differential to difference importance measures for markov reliability models. Eur J Oper Res 204(3):513–521
Donatiello Lorenzo, Grassi Vincenzo (1991) On evaluating the cumulative performance distribution of fault-tolerant computer systems. IEEE Trans Comput 40(11):1301–1307
Donatiello L, Iyer BR (1987) Analysis of a composite performance reliability measure for fault-tolerant systems. J ACM (JACM) 34(1):179–199
Fricks R, Telek M, Puliafito A, Trivedi K (1998) Markov renewal theory applied to performability evaluation. In: State-of-the-art in Performance modeling and simulation. modeling and simulation of advanced computer systems: applications and systems. Gordon & Breach, Newark, NJ, pp 193–236
Furchtgott DG, Meyer JF (1984) A performability solution method for degradable nonrepairable systems. IEEE Trans Comput 100(6):550–554
Furchtgott DG, Meyer JF (1978) Performability evaluation of fault-tolerant multiprocessors. In: Digest 1978 government micro-circuit applications conference, pp 362–365. NTIS Springfield, VA
Garelli Marco, Ferrero Andrea (2012) A unified theory for s-parameter uncertainty evaluation. IEEE Trans Microwave Theory Tech 60(12):3844–3855
German Reinhard (2000) Markov regenerative stochastic petri nets with general execution policies: supplementary variable analysis and a prototype tool. Perform Eval 39(1):165–188
German Reinhard (2001) Iterative analysis of markov regenerative models. Perform Eval 44(1):51–72
German R, Telek M (1999) Formal relation of markov renewal theory and supplementary variables in the analysis of stochastic Petri nets. In: Proceedings of the 8th international workshop on Petri nets and performance models, IEEE, pp 64–73
Goyal Ambuj, Tantawi Asser N (1987) Evaluation of performability for degradable computer systems. IEEE Trans Comput 100(6):738–744
Goyal Ambuj, Tantawi Asser N (1988) A measure of guaranteed availability and its numerical evaluation. IEEE Trans Comput 37(1):25–32
Goyal A, Tantawi AN, Trivedi KS (1985) A measure of guaranteed availability. In: IBM Thomas J, Watson Research Center
Grassi Vincenzo, Donatiello Lorenzo (1992) Sensitivity analysis of performability. Perform Eval 14(3):227–237
Haverkort BR, Meeuwissen AMH (1995) Sensitivity and uncertainty analysis of markov-reward models. IEEE Trans Reliab 44(1):147–154
Haverkort BR, Niemegeers IG (1996) Performability modelling tools and techniques. Performance Eval 25(1):17–40
Heidelberger P, Goyal A (1987) Sensitivity analysis of continuous time markov chains using uniformization. In: Proceedings of the second international workshop on applied mathematics and performance/reliability models of computer/communication systems
Hirel C, Sahner R, Zang X, Trivedi K (2000) Reliability and performability modeling using sharpe 2000. In: Computer performance evaluation. Modelling techniques and tools, pp 345–349. Springer
Iyer Balakrishna R, Donatiello Lorenzo, Heidelberger Philip (1986) Analysis of performability for stochastic models of fault-tolerant systems. IEEE Trans Comput 100(10):902–907
Jackson PS, Hockenbury RW, Yeater ML (1982) Uncertainty analysis of system reliability and availability assessment. Nuclear Eng Des 68(1):5–29
Kulkarni VG, Nicola VF, Smith RM, Trivedi KS (1986) Numerical evaluation of performability and job completion time in repairable fault-tolerant systems. In: 16th international symposium on fault-tolerant computing, IEEE
Lanus M, Yin L, Trivedi KS (2003) Hierarchical composition and aggregation of state-based availability and performability models. IEEE Trans Reliab 52(1):44–52
Lüthi Johannes, Haring Günter (1998) Mean value analysis for queueing network models with intervals as input parameters. Performance Eval 32(3):185–215
Lüthi Johannes, Majumdar Shikharesh, Kotsis Gabriele, Haring Günter (1997) Performance bounds for distributed systems with workload variabilities and uncertainties. Parallel Comput 22(13):1789–1806
Majumdar S, Ramadoss R (1995) Interval-based performance analysis of computing systems. In: Proceedings of the third international workshop on modeling, analysis, and simulation of computer and telecommunication systems, 1995. MASCOTS’95, pp 345–351. IEEE
Marie RA, Reibman AL, Trivedi KS (1987) Transient analysis of acyclic markov chains. Performance Eval 7(3):175–194
Meyer John F (1980) On evaluating the performability of degradable computing systems. IEEE Trans Comput 100(8):720–731
Meyer John F (1982) Closed-form solutions of performability. IEEE Trans Comput 100(7):648–657
Meyer John F (1992) Performability: a retrospective and some pointers to the future. Performance Eval 14(3):139–156
Meyer John F, Furchtgott David G, Liang TWu (1980) Performability evaluation of the sift computer. IEEE Trans Comput 100(6):501–509
Misra Krishna B (1970) An algorithm for the reliability evaluation of redundant networks. IEEE Trans Reliab 19(4):146–151
Moore EF, Shannon CE (1956) Reliable circuits using less reliable relays, part i. J Franklin Inst 262(3):191–208
Moskowitz Fred (1958) The analysis of redundancy networks. In: Transactions of the American institute of electrical engineers, part i: communication and electronics 77(5):627–632
Nabli Hédi, Sericola Bruno (1996) Performability analysis: a new algorithm. IEEE Trans Comput 45(4):491–494
Pattipati KR, Li Y, Blom HAP (1993) A unified framework for the performability evaluation of fault-tolerant computer systems. IEEE Trans Comput 42(3):312–326
Reibman Andrew, Smith Roger, Trivedi Kishor (1989) Markov and markov reward model transient analysis: an overview of numerical approaches. Eur J Oper Res 40(2):257–267
Reibman Andrew, Trivedi Kishor (1988) Numerical transient analysis of markov models. Comput Oper Res 15(1):19–36
Reibman Andrew, Trivedi Kishor (1989) Transient analysis of cumulative measures of markov model behavior. Stoch Models 5(4):683–710
Rubino Gerardo, Sericola Bruno (1995) Interval availability analysis using denumerable markov processes: application to multiprocessor subject to breakdowns and repair. IEEE Trans Comput 44(2):286–291
Smith RM, Trivedi KS, Ramesh AV (1988) Performability analysis: measures, an algorithm, and a case study. IEEE Trans Comput 37(4):406–417
Suné V, Carrasco JA, Nabli H, Sericola B (2010) Comment on performability analysis: a new algorithm. IEEE Trans Comput 59(1):137–138
Trivedi KS, Malhotra M (1993) Reliability and performability techniques and tools: a survey. In: Messung, modellierung und bewertung von rechen-und kommunikationssystemen, pp 27–48. Springer
Van Slyke R, Frank Howard (1971) Network reliability analysis: part i. Networks 1(3):279–290
Wübbeler Gerd, Krystek Michael, Elster Clemens (2008) Evaluation of measurement uncertainty and its numerical calculation by a monte carlo method. Meas Sci Technol 19(8):084009
Yin L, Smith MAJ, Trivedi KS (2001) Uncertainty analysis in reliability modeling. In: Proceedings of the reliability and maintainability symposium, 2001, Annual, pp 229–234. IEEE
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Marie, R.A. (2016). From Performability to Uncertainty. In: Fiondella, L., Puliafito, A. (eds) Principles of Performance and Reliability Modeling and Evaluation. Springer Series in Reliability Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-30599-8_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-30599-8_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-30597-4
Online ISBN: 978-3-319-30599-8
eBook Packages: EngineeringEngineering (R0)