Review:

# Improved Approach for Maximizing Reliability in Fault Tolerant Networks

## Baijnath Kaushik^{*}, Navdeep Kaur^{**}, and Amit Kumar Kohli^{***}

^{*}Punjab Technical University, PTU-Kapurthala Highway, Near Pushpa Gujral Science City, Kapurthala-144601, India

^{**}Computer Science Department, Chandigarh Engineering College, Landran, Mohall, Punjab, India

^{***}Electronics & Communication Engineering (ECED), Thapar University, P.O. Box 32, Patiala, Pin-147004, India

The objective of this paper is to present a novelmethod for achievingmaximumreliability in fault-tolerant optimal network design when networks have variable size. Reliability calculation is a most important and critical component when fault-tolerant optimal network design is required. A network must be supplied with certain parameters that guarantee proper functionality and maintainability in worse-case situations. Many alternative methods for measuring reliability have been stated in the literature for optimal network design. Most of these methods, mentioned in the literature for evaluating reliability, may be analytical and simulation-based. These methods provide significant ways for computing reliability when a network has a limited size. Significant computational effort is also required for growing variable-sized networks. A novel neural network method is therefore presented to achieve significant high reliability in fault-tolerant optimal network design in highly growing variable networks. This paper compares simulation-based analytical methods with improved learning rate gradient descent-based neural network methods. Results show that improved optimal network design with maximum reliability is achievable by a novel neural network at a manageable computational cost.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.17, No.1, pp. 27-41, 2013.

- [1] A. Lendasse, V. Wertz, and M. Verleysen, “Model selection with cross-validations and bootstraps application to time series prediction with RBFN models,” Lecture Notes in Computer Science, Springer Berlin/Heidelberg 2714, 2003.
- [2] Y. S. Dai, M. Xie, and K. L. Poh, “Modeling and analysis of correlated software failures of multiple types,” IEEE Trans. Reliability, Vol.54, No.1 pp. 100-106, 2005.
- [3] Y. S. Dai, M. Xie, Q. Long, and S. H. Ng, “Uncertainty analysis in software reliability modeling by Bayesian approach with maximum entropy principle,” IEEE Trans. Software Engineering, Vol.33, No.11, pp. 781-795, 2007.
- [4] Y. S. Dai and G. Levitin, “Reliability and performance of treestructured grid services,” IEEE Trans. Reliability, Vol.55, No.2, pp. 337-349, 2006.
- [5] Y. S. Dai, M. Xie, and X. Wang, “A heuristic algorithm for reliability modeling and analysis of grid systems,” IEEE Trans. Systems, Man, and Cybernetics, Part A: Systems and Humans, Vol.37, No.2 pp. 189-200, 2007.
- [6] Y. S. Dai, Y. Pan, and X. K. Zou, “A hierarchical modeling and analysis for grid service reliability,” IEEE Trans. Computers, Vol.56, No.5, pp. 681-691, 2007.
- [7] Y. S. Dai, G. Levitin, and K. S. Trivedi, “Performance and reliability of tree-structured grid services considering data dependence and failure correlation,” IEEE Trans. Computers, Vol.56, No.7, pp. 925-936, 2007.
- [8] B. Dengiz, F. Altiparmak, and O. Belgin, “A Hybrid ant colony approach for the design of reliable networks,” IEEE Congress on Evolutionary Computation pp. 1118-1125, 2007.
- [9] T. Aven, “Availability evaluation of oil gas-production and transportation systems,” Reliability Engineering & System Safety, Vol.18, pp. 35-44, 1987.
- [10] D. A. Savic and G. A. Walters, “An evolution program for pressure regulation in Water distribution networks, Engineering Optimization,” Vol.24, pp. 197-219, 1995.
- [11] K. Aggarwal, J. Gupta, and K. Misra, “A simple method for reliability evaluation of a communication system,” IEEE Trans. Communications, Vol.23, No.5, pp. 563-566, 1975.
- [12] K. K. Aggarwal and S. Rai, “Reliability evaluation in computercommunication networks,” IEEE Trans. on Reliability, Vol.30, pp. 32-35, 1981.
- [13] S. Rai, “A cutset approach to reliability evaluation in communication networks,” IEEE Trans. on Reliability, Vol.1, pp. 428-431, 1982.
- [14] J. S. Provan and M. O. Ball, “The complexity of counting cuts and of computing the probability that a graph is connected,” SIAM J. of Computing, Vol.12, pp. 777-788, 1983.
- [15] M. A. Samad, “An efficient algorithm for simultaneously deducing minimal paths as well as cuts of a communication-network,” Microelectronics and Reliability, Vol.27, pp. 437-441, 1987.
- [16] G. Chaudhuri, K. Hu, and N. Afshar, “A New Approach to System Reliability,” IEEE Trans. on Reliability, Vol.50, No.1, pp. 75-84, 2001.
- [17] T. Jin and D.W. Coit, “Approximating network reliability estimates using linear and quadratic unreliability of minimal cuts,” Reliability Engineering and System Safety, Vol.82, pp. 41-48, 2003.
- [18] W. J. Ke and S. D. Wang, “Reliability evaluation for distributed computing networks with imperfect nodes,” IEEE Trans. Reliability, Vol.46, No.3, pp. 342-349, 1997.
- [19] P. Doulliez and E. Jalnoulle, “Transportation network with random arc capacities,” Rech. Operations Research, Vol.3, pp. 45-60, 1972.
- [20] S. Lolas and O. A. Olatunbosun, “Prediction of vehicle reliability performance using artificial neural networks,” Expert Systems with Applications, Vol.34, pp. 2360-2369, 2008.
- [21] J. B. Cardoso, “Structural reliability analysis using Monte Carlo simulation and neural networks,” Advances in Engineering Software, Vol.39, pp. 505-513, 2008.
- [22] J. E. Hurtado and D. A. Alvarez, “An optimization method for learning statistical classifiers in structural reliability,” Probabilistic Engineering Mechanics, Vol.25, pp. 26-34, 2009.
- [23] W.-C. Yeh, Y.-C. Lin, and Y. Y. Chung, “Mingchang Chih, A Particle Swarm Optimization Approach based on Monte Carlo Simulation for Solving the Complex Network Reliability Problem,” IEEE Trans. on Reliability, Vol.59, No.1, pp. 212-221, 2010.
- [24] E. Inohira and H. Yokoi, “An optimal design method for artificial NN by the DOE method,” J. of Adv. Comp. Intelligence and Intelligent Informatics, Vol.11, No.6, pp. 593-594, 2007.
- [25] B. Kaushik, N. Kaur, and A. K. Kohli, “A New ANN method for measuring overall reliability and performance in growing computer networks with static and variable connections,” Int. J. of Computer Science and Commu., Vol.2, No.1, pp. 79-87, 2011.
- [26] B. Kaushik, N. Kaur, and A. K. Kohli, “An optimized ANN design for measuring overall reliability for growing computer networks with fixed and varying links,” Int. J. of Compu. Eng. & Man., Vol.11, pp. 12-21, 2011.
- [27] B. Kaushik, N. Kaur, and A. K. Kohli, “A Computational study on the design of overall reliability measures of optimized ANN for computer networks with fixed and varying link reliabilities,” IEEE explore, 2011.
- [28] B. Kaushik, N. Kaur, and A. K. Kohli, “A New method for measuring overall reliability and performance in growing computer networks with static and variable Connections,” Int. J. of Computer Tech. & App., Vol.2, No.1, pp. 1-14, 2011.
- [29] B. Kaushik, N. Kaur, and A. K. Kohli, “An Enhanced ANN approach for optimizing design of highly reliable variable sized computer networks,” J. of Artificial Intelligence, Vol.2, pp. 31-41, 2011.
- [30] M. R. Garey and D. S. Johnson, “Computers and Intractability: A Guide to the Theory of NP Completeness,” E. H. Freeman and Company, San Francisco, 1979.
- [31] C. J. Colbourn, “The Combinatorics of Network Reliability,” Oxford, New York, 1987.
- [32] D. R. Shier, “Network Reliability and Algebraic Structure,” Oxford, New York, 1991.
- [33] W. C. Yeh and C. H. Lin, “A squeeze response surface methodology for finding symbolic network reliability functions,” IEEE Trans. Reliability, Vol.58, No.2, pp. 374-382, 2009.
- [34] S. R. V. Majety, M. Dawande, and J. Rajgopal, “Optimal reliability allocation with discrete cost-reliability data for components,” Operations Research, Vol.47, No.6, pp. 899-906, 1999.
- [35] A. N. Venetsanopoulos and I. Singh, “Topological optimization of communication networks subject to reliability constraints,” Prob. of Control and Info. Theory, Vol.15, pp. 63-78, 1986.
- [36] C. S. Ratana and A. E. Smith, “Estimation of all-terminal network reliability using an artificial neural network,” Computers & Operations Research, pp. 1-28, 1999.
- [37] C. Srivaree-ratana, A. Konak, and A. E. Smith, “Estimation of all-terminal network reliability using an artificial neural network,” Computers and Operations Research, Vol.29, No.7, pp. 849-868, 2002.
- [38] F. Altiparmak, B. Dengiz, and A. E. Smith, “A general neural network model for estimating telecommunication network reliability,” IEEE Trans. on Reliability, Vol.58, No.1, pp. 2-9, 2009.
- [39] D. W. Coit and A. E. Smith, “Solving the redundancy allocation problem using a combined neural network/genetic algorithm approach,” Computers and Operations Research, Vol.23, pp. 515-526, 1996.
- [40] D. W. Coit and A. E. Smith, “Reliability optimization of seriesparallel systems using a genetic algorithm,” IEEE Trans. Reliability, Vol.45, No.2, pp. 254-260, 1996.
- [41] B. Dengiz, F. Altiparmak, and A. E. Smith, “Local search genetic algorithm for optimal design of reliable networks,” IEEE Trans. Evolutionary Computation, Vol.1, No.3, pp. 179-188, 1997.
- [42] B. Dengiz, F. Altiparmak, and A. E. Smith, “Efficient optimization of all-terminal reliable networks using an evolutionary approach,” IEEE Trans. on Reliability, Vol.46, pp. 18-26, 1997.
- [43] Y. C. Liang and A. E. Smith, “An ant colony optimization algorithm for the redundancy allocation problem (RAP),” IEEE Trans. Reliability, Vol.53, No.3, pp. 417-423, 2004.
- [44] R. Meziane, Y. Massim, A. Zeblah, A. Ghoraf, and R. Rahli, “Reliability optimization using ant colony algorithm under performance and cost constraints,” Electric Power Systems Research, Vol.76, No.1-3, pp. 1-8, 2005.
- [45] S. K. Konak, A. E. Smith, and D. W. Coit, “Efficiently solving the redundancy allocation problem using Tabu search,” IIE Trans., Vol.35, No.6, pp. 515-526, 2003.
- [46] B. Dengiz, C. Alabas, and O. Dengiz, “A Tabu search algorithm for neural networks training,” J. of Operation Research, Vol.60, No.2, pp. 282-291, 2009.
- [47] M. Ouzineba, M. Nourelfatha, and M. Gendreau, “Tabu search for the redundancy allocation problem of homogenous series-parallel multistate systems,” Reliability Engineering and System Safety, Vol.93, No.8, pp. 1257-1272, 2008.
- [48] J. Kennedy and R. C. Eberhart, “Particle Swarm Optimization,” IEEE Int. Conf. on Neural Networks, pp. 1942-1948, 1995.
- [49] G. Levitin, X. H. Hu, and Y. S. Dai, “Particle swarm optimization in reliability engineering,” Int. Conf. on Computational Intelligence in Reliability Engineering, pp. 83-112, 2006.
- [50] M. K. Pandey, M. K. Tiwari, and M. J. Zuo, “Interactive enhanced particle swarm optimization: A multi-objective reliability application,” J. of Risk and Reliability, Vol.221, No.3, pp. 177-191, 2007.
- [51] W. C. Yeh, “A two-stage discrete particle swarm optimization for the problem of multiple multi-level redundancy allocation in series systems,” Expert Systems with Applications, Vol.36, No.5, pp. 9192-9200, 2009.
- [52] O. Dengiz, A. Konak, and A. E. Smith, “Connectivity management in mobile ad hoc networks using particle Swarm optimization,” Ad Hoc Networks, Vol.9, pp. 1312-1326, 2011.
- [53] S. Pierre, M. A. Hyppolite, J. M. Bourjolly, and O. Dioume, “Topological design of computer communication networks using simulated annealing,” Engineering Applications of Artificial Intelligence, Vol.8, pp. 61-69, 1995.
- [54] I. Gertsbakh, “Reliability Theory,” Springer-Verlag, 2000.
- [55] S. J. Kamat and M. W. Riley, “Determination of reliability using event based Monte Carlo simulation,” IEEE Trans. reliability, Vol.24, No.1, pp. 73-75, 1975.
- [56] S. J. Kamat and W. E. Franzmeier, “Determination of reliability using event-based Monte Carlo simulation, Part2,” IEEE Trans. Reliability, Vol.25, No.3, pp. 254-255, 1976.
- [57] G. S. Fishman, “A Monte Carlo sampling plan for estimating network reliability,” Operations Research, Vol.34, pp. 81-594, 1986
- [58] P. Kubat, “Estimation of reliability for communication/computer networks simulation/analytical approach,” IEEE Trans. Communications, Vol.37, No.9, pp. 927-933, 1989.
- [59] T. L. Landers, H. A. Taha, and C. L. King, “A reliability simulation approach for use in the design process,” IEEE Trans. Reliability, Vol.40, No.2, pp. 177-181, 1991.
- [60] J. Y. Lin and C. E. Donaghey, “Monte Carlo simulation to determine minimal cut sets and system reliability,” Proc. of Annual Rel. and Maintainability Symp, 1993.
- [61] H.Wang and H. Pham, “Survey of reliability and availability evaluation of complex networks using Monte Carlo techniques,” Microelectronics and Reliability, Vol.37, No.2, pp. 187-209, 1997.
- [62] W. C. Yeh, “A MCS-RSM approach for network reliability to minimize the total cost,” Int. J. of Adv. Manu. Tech., Vol.22, pp. 681-688, 2003.
- [63] Y. Shpungin, “Networks with unreliable nodes and edges: Monte Carlo Lifetime Estimation,” World Acad. of Sci., Eng. and Tech., Vol.27, pp. 349-354, 2007.
- [64] Neuralworks: Reference Guide and Software, NeuralWare, Pittsburgh, PA, Various Years.

http:/ /www.neuralware.com - [65] K. Hornik, M. Stinchcombe, and H. White, “Multilayer feed forward networks are Universal approximators,” Neural Networks, Vol.2, No.3, pp. 59-66, 1989.
- [66] H. White, “Connectionist nonparametric regression: multilayer feed forward networks can learn arbitrary mappings,” Neural Networks, Vol.3, No.5, pp. 35-49, 1990.
- [67] S. Geman, E. Bienenstock, and R. Doursat, “Neural networks and the bias/variance dilemma,” Neural Computation, Vol.4, pp. 1-58, 1992.
- [68] B. Cheng and D. M. Titterington, “Neural networks: a review from a statistical perspective,” Statistical Science, Vol.9, pp. 2-54, 1994.
- [69] K. Mehrotra and C. K. Mohan, “Sanjay Ranka, Elements of Artificial Neural Networks,” MIT Press, Chapter 3, pp. 65-106, 1996.
- [70] F. Karray and C. D. Silva, “Soft Computing and Intelligent Systems Design-Theory,” Tools and Applications, Addison Wesley, Chapter 5, pp. 249-293, 2004.
- [71] S. Rajasekran and V. Pai, “Neural Networks, Fuzzy Logic, and Genetic Algorithms-Synthesis and Applications,” PHI, Chapter 3, pp. 34-86, 2005.