Availability analysis for software system with intrusion tolerance

This paper is devoted to analyzing the instantaneous availability of a typical software system with intrusion tolerance. By formulating the system with a couple of ordinary differential and partial differential equations, this paper describes the system as a time-delay partial differential equation. Based on the time-delay model, both steady-state availability and instantaneous availability are investigated. The optimal policy for preventive patch management to maximize the steady-state availability of the software system is obtained, and its related availability criterions are also presented. Employing the finite difference scheme and Trotter-Kato theorem, we converted the time-delay partial equation into a time-delay ordinary equation. As a result, the instantaneous availability of the system is derived. Some numerical results are given to show the effectiveness of the method presented in the paper.

[1]  Tadashi Dohi,et al.  Analysis of software cost models with rejuvenation , 2000, Proceedings. Fifth IEEE International Symposium on High Assurance Systems Engineering (HASE 2000).

[2]  Wei Xie,et al.  Analysis of a two-level software rejuvenation policy , 2005, Reliab. Eng. Syst. Saf..

[3]  Rodolphe Ortalo,et al.  Experimenting with Quantitative Evaluation Tools for Monitoring Operational Security , 1999, IEEE Trans. Software Eng..

[4]  F. Huang,et al.  Well-posedness of linear partial differential equations with unbounded delay operators☆ , 2004 .

[5]  Bharat B. Madan,et al.  Modeling and quantification of security attributes of software systems , 2002, Proceedings International Conference on Dependable Systems and Networks.

[6]  Tadashi Dohi,et al.  Optimizing Security Measures in an Intrusion Tolerant Database System , 2008, ISAS.

[7]  Tadashi Dohi,et al.  Quantitative Evaluation of Intrusion Tolerant Systems Subject to DoS Attacks Via Semi-Markov Cost Models , 2007, EUC Workshops.

[8]  Kishor S. Trivedi,et al.  A workload-based analysis of software aging, and rejuvenation , 2005, IEEE Transactions on Reliability.

[9]  Tadashi Dohi,et al.  Availability Analysis of an Intrusion Tolerant Distributed Server System With Preventive Maintenance , 2010, IEEE Transactions on Reliability.

[10]  Bharat B. Madan,et al.  A method for modeling and quantifying the security attributes of intrusion tolerant systems , 2004, Perform. Evaluation.

[11]  H. Banks,et al.  Hereditary Control Problems: Numerical Methods Based on Averaging Approximations , 1978 .

[12]  Peng Liu,et al.  Modeling and Evaluating the Survivability of an Intrusion Tolerant Database System , 2006, ESORICS.

[13]  Weiwei Hu,et al.  Modelling and analysis of repairable systems with preventive maintenance , 2013, Appl. Math. Comput..

[14]  Amnon Pazy,et al.  Semigroups of Linear Operators and Applications to Partial Differential Equations , 1992, Applied Mathematical Sciences.

[15]  Weiwei Hu,et al.  Steady availability optimisation of repairable system with preventive maintenance policy , 2008, 2013 25th Chinese Control and Decision Conference (CCDC).

[16]  Kazufumi Ito,et al.  The Trotter-Kato theorem and approximation of PDEs , 1998, Math. Comput..

[17]  Susanna Piazzera,et al.  Semigroups and Linear Partial Differential Equations with Delay , 2001, 1211.7197.

[18]  Feiyi Wang,et al.  SITAR: a scalable intrusion-tolerant architecture for distributed services , 2003, Foundations of Intrusion Tolerant Systems, 2003 [Organically Assured and Survivable Information Systems].