Dependability models of RAID using stochastic activity networks
The development of CTMCs to model RAIDs with a general failure-repair process seems a complex task. The introduction of a technique with higher modeling level, that facilitates the description of the failure-repair processes is essential to deepen in the dependability analysis of these systems.
In this paper, different dependability models of RAID level 5 are presented. The chosen technique is an extension of timed Petri nets known as Stochastic Activity Networks (SAN). As will be shown, it is relatively simple to describe a SAN equivalent to the developed CTMC. This model will be called the basic model. Furthermore, the flexibility introduced by these nets, through the cases associated with its timed activities and the input and output gates, allows an extension of the basic SAN model in order to obtain more accurate results or to adapt it to a new specification of the system operation. Thus, the basic model will be modified to represent the repair process with detail, differentiating its two phases: replacement and reconstruction. Also, the influence of a limited number of on-line spares on the reliability of the system will be considered. Thereinafter, using the structure of the basic model, a SAN of a RAID with a higher protection level (RAID level 6) is presented.
KeywordsRepair Time Continuous Time Markov Chain Maintenance Policy Input Gate Disk Array
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- 1.G. A. Gibson, Redundant Disk Arrays: Reliable, Parallel Secondary Storage. MIT Press, 1992.Google Scholar
- 2.M. Malhotra, Specification and Solution of Dependability Models of Fault-Tolerant Systems. PhD thesis, Duke University, May 1993.Google Scholar
- 3.R. Geist and K. S. Trivedi, “An analytic treatment of the reliability and performance of mirrored disk subsystems,” in FTCS-23, pp. 442–450, June 1993.Google Scholar
- 4.Centre for Reliable and High-Performance Computing. Coordinated Science Laboratory. University of Illinois at Urbana-Champaign, UltraSAN. Users's Manual. Version 3.0. 1995.Google Scholar
- 5.W. Sanders, W. Obal II, M. Qureshi, and F. Widjanarko, “UltraSAN version 3: architecture, features and implementation,” Tech. Rep. 95S02, Center for Reliable and High-Performance Computing. Coordinated Science Laboratory. University of Illinois at Urbana-Champaign, 1995.Google Scholar
- 6.R. H. Katz, G. A. Gibson, and D. A. Patterson, “Disk system architectures for high performance computing,” Proc. IEEE, vol. 77, pp. 1842–1858, Dec. 1989.Google Scholar
- 7.D. A. Patterson, G. Gibson, and R. H. Katz, “A case for redundant arrays of inexpensive disks (RAID),” in In International Conference on Management of Data (SIGMOD). ACM., (N. Y. ACM, ed.), pp. 109–116, June 1988.Google Scholar
- 8.M. Schulze, G. Gibson, R. H. Katz, and D. A. Patterson, “How reliable is a RAID?,” in Procedures of the IEEE Computer Society International Conference (COMPCON), pp. 118–123, Spring 1989.Google Scholar
- 9.P. M. Chen, E. K. Lee, G. A. Gibson, R. H. Katz, and D. A. Patterson, “RAID: high-performance, reliable secondary storage,” ACM Computing Surveys, vol. 26, pp. 145–185, June 1994.Google Scholar
- 10.S. W. Ng, “Crosshatch disk array for improved reliability and performance,” in In Proceedings the 1994 International Symposium on Computer Architecture, (IEEE, ed.), IEEE (New York), 1994.Google Scholar
- 11.R. K. Iyer, D. J. Rosetti, and M. C. Hsueh, “Measurement and modeling of computer reliability as affected by system activity,” ACM Transactions on Computer Systems, vol. 4, pp. 214–237, 1986.Google Scholar
- 12.H. M. Sierra, An Introduction to Direct Access Storage Devices. Academic Press, 1990.Google Scholar
- 13.M. Holland, G. A. Gibson, and D. P. Siewiorek, “Fast, on-line failure recovery in redundant disk arrays,” in Proceedings of the 23rd International Symposium on Fault Tolerant Computing, (Washington, D.C.), pp. 422–431, IEEE Computer Society, 1993.Google Scholar
- 14.G. A. Gibson and D. A. Patterson, “Designing disk arrays for high data reliability,” Journal of Parallel and Distributed Computing, vol. 17, pp. 4–27, Jan. 1993.Google Scholar
- 15.J. Meyer, A. Movaghar, and W. Sanders, “Stochastic activity networks: structure, behavior and application,” in Proceedings of the International Conference on Timed Petri Nets, (Torino, Italy), pp. 106–115, July 1985.Google Scholar
- 16.J. Meyer and W. Sanders, “Specification and construction of performability models,” in Proceedings of the Second International Workshop on Performability Modeling of Computer and Communication Systems, (Mont Saint-Michel, France), pp. 28–30, June 1993.Google Scholar
- 17.W. Sanders and J. Meyer, “Reduced base model construction methods for stochastic activity networks,” IEEE Journal on Selected Areas in Communications, vol. 9, pp. 25–36, Jan. 1991.Google Scholar
- 18.V. Santonja, Evaluaci'on y modelado de prestaciones y garantía de funcionamiento en matrices redundantes de discos (RAID). PhD thesis, Universitat Politècnica de Valencia, Jul 1996.Google Scholar