Abstract
Self-stabilizing systems are often only evaluated in terms of worst-case time and space complexities for the recovery from arbitrary state disruptions. In this paper, we interpret and formalize well-known fault tolerance measures for masking fault-tolerant systems, namely reliabilty, instantaneous availability, and limiting availability in the context of self-stabilizing systems. This allows to additionally evaluate selfstabilizing systems by these well-accepted measures. The calculation is challenging due to a large (and possibly infinite) state space. We present an analysis procedure that comprises a suitable state abstraction thereby making the calculation tractable. Exemplarily, we apply the procedure to a system that constructs a depth-first search spanning tree showing that our approach is feasible and yields meaningful results.
This work was supported by the German Research Foundation (DFG) under grants GRK 1076/1 “TrustSoft” and SFB/TR 14 “AVACS.”
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References
Gärtner, F.C.: Fundamentals of fault-tolerant distributed computing in asynchronous environments. ACM Computing Surveys 31(1), 1–26 (1999)
Helal, A.A., Heddaya, A.A., Bhargava, B.B.: Replication Techniques in Distributed Systems. Kluwer Academic Publishers, Dordrecht (1996)
Pease, M., Shostak, R., Lamport, L.: Reaching Agreement in the Presence of Faults. Journal of the ACM 27(2), 228–234 (1980)
Dolev, S.: Self-Stabilization. MIT Press, Cambridge (2000)
Khalil, H.K., Teel, A.R., Georgiou, T.T., Praly, L., Sontag, E.: Stability. In: Levine, W.S. (ed.) The Control Handbook, pp. 889–908. CRC Press, Inc., Boca Raton (1995)
Trivedi, K.S.: Probability and Statistics with Reliability, Queuing and Computer Science Applications, 2nd edn. John Wiley and Sons Ltd., Chichester (2002)
Somani, A.K., Vaidya, N.H.: Understanding Fault Tolerance and Reliability. Computer 30(4), 45–50 (1997)
Suri, N., Hugue, M.M., Walter, C.J.: Reliability Modeling of Large Fault-tolerant Systems. In: 22nd Intern. Fault-Tolerant Comp. Symp., pp. 212–220. IEEE, Los Alamitos (1992)
Amir, Y., Wool, A.: Optimal Availability Quorum Systems: Theory and Practice. IPL 65(5), 223–228 (1998)
Babaog̃lu, Ö.: On the reliability of consensus-based fault-tolerant distributed computing systems. ACM Transactions on Computer Systems 5(4), 394–416 (1987)
Avižienis, A., Laprie, J.C., Randell, B., Landwehr, C.E.: Basic Concepts and Taxonomy of Dependable and Secure Computing. IEEE ToDSC 1(1), 11–33 (2004)
Hamming, R.W.: Error-detecting and Error-correcting Codes. Bell System Technical Journal 29(2), 147–160 (1950)
Collin, Z., Dolev, S.: Self-stabilizing Depth First Search. IPL 49(6), 297–301 (1994)
Graf, S., Saïdi, H.: Construction of Abstract State Graphs with PVS. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 72–83. Springer, Heidelberg (1997)
Das, S., Dill, D.L., Park, S.: Experience with Predicate Abstraction. In: 11th Intern. Conf. on CA Verification. Springer, Heidelberg (1999)
Cansell, D., Méry, D., Merz, S.: Predicate Diagrams for the Verification of Reactive Systems. In: Grieskamp, W., Santen, T., Stoddart, B. (eds.) IFM 2000. LNCS, vol. 1945, pp. 380–397. Springer, Heidelberg (2000)
Dijkstra, E.W.: Self-stabilizing Systems in Spite of Distributed Control. CACM 17(11), 643–644 (1974)
Cansell, D., Méry, D., Merz, S.: Formal Analysis of a Self-stabilizing Algorithm using Predicate Diagrams. In: Wirsing, M. (ed.) Workshop Integrating Diagrammatic and Formal Spec. Techniques (GI-/ÖCG-Jahrestagung), vol. 157/I, pp. 39–45 (2001)
Sorensen, E.V., Nordahl, J., Hansen, N.H.: From CSP mMdels to Markov Models. IEEE ToSE 19(6), 554–570 (1993)
Hoare, C.A.R.: Communicating Sequential Processes. Prentice Hall Int., Englewood Cliffs (1985)
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Dhama, A., Theel, O., Warns, T. (2006). Reliability and Availability Analysis of Self-stabilizing Systems. In: Datta, A.K., Gradinariu, M. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2006. Lecture Notes in Computer Science, vol 4280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-49823-0_17
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DOI: https://doi.org/10.1007/978-3-540-49823-0_17
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