Dynamic Dependability Analysis of Shuffle-exchange Networks using HOL Theorem Proving

Dynamic dependability models, such as dynamic fault trees (DFTs) and dynamic reliability block diagrams (DRBDs), are introduced to overcome the modeling limitations of traditional models. Recently, higher-order logic (HOL) formalizations of both models have been conducted, which allow the analysis of these models formally, within a theorem prover. In this report, we provide the formal dynamic dependability analysis of shuffle-exchange networks, which are multistage interconnection networks that are commonly used in multiprocessor systems. We use DFTs and DRBDs to model the terminal, broadcast and network reliability with dynamic spare gates and constructs in several generic versions. We verify generic expressions of probability of failure and reliability of these systems, which can be instantiated with any number of system components and failure rates to reason about the failure behavior of these networks.

[1]  Indra Gunawan,et al.  Redundant paths and reliability bounds in gamma networks , 2008 .

[2]  Sheroz Khan,et al.  On Reliability Analysis of Fault-tolerant Multistage Interconnection Networks , 2008 .

[3]  Osman Hasan,et al.  Integrating DFT and DRBD Formalizations in HOL4 , 2019, ArXiv.

[4]  Osman Hasan,et al.  A Formally Verified Algebraic Approach for Dynamic Reliability Block Diagrams , 2019, ICFEM.

[5]  Indra Gunawan,et al.  Reliability prediction of distributed systems using Monte Carlo method , 2013 .

[6]  Mohsen Jahanshahi,et al.  Analyzing the reliability of shuffle-exchange networks using reliability block diagrams , 2014, Reliab. Eng. Syst. Saf..

[7]  Mohamed Othman,et al.  Reliability Review of Interconnection Networks , 2016 .

[8]  S. Distefano,et al.  A new approach to modeling the system reliability: dynamic reliability block diagrams , 2006, RAMS '06. Annual Reliability and Maintainability Symposium, 2006..

[9]  Sofiène Tahar,et al.  Probabilistic Analysis of Dynamic Fault Trees using HOL Theorem Proving , 2019, FLAP.

[10]  Sofiène Tahar,et al.  A Methodology for the Formal Verification of Dynamic Fault Trees Using HOL Theorem Proving , 2019, IEEE Access.

[11]  Mohamed Othman,et al.  Evaluation of Replication Method in Shuffle-Exchange Network Reliability Performance , 2018, Advances in Data and Information Sciences.

[12]  V. P. Kumar,et al.  Fault-Tolerant Multistage Interconnection Networks for Multiprocessor Systems , 1988 .

[13]  Howard Jay Siegel,et al.  A Fault-Tolerant Multistage Interconnection Network for Multiprocessor Systems Using Dynamic Redundancy , 1986, ICDCS.

[14]  S. Rajkumar,et al.  Review of Multistage Interconnection Networks Reliability and Fault-Tolerance , 2016 .

[15]  Mohamed Othman,et al.  Reliability Evaluation for Shuffle Exchange Interconnection Network , 2015 .

[16]  Carl E. Landwehr,et al.  Basic concepts and taxonomy of dependable and secure computing , 2004, IEEE Transactions on Dependable and Secure Computing.

[17]  Mariëlle Stoelinga,et al.  Fault tree analysis: A survey of the state-of-the-art in modeling, analysis and tools , 2014, Comput. Sci. Rev..

[18]  Mohsen Jahanshahi,et al.  Determining the reliability importance of switching elements in the shuffle-exchange networks , 2018, Int. J. Parallel Emergent Distributed Syst..

[19]  David A. Patterson,et al.  Computer Architecture: A Quantitative Approach , 1969 .