Measures of Repairable Series-Parallel Computer Network with Fault Tolerant Device via Copula

Subject Areas : Reliability Engineering

Muhammad Salihu Isa ¹ (School of Mathematics and Statistics, Central South University, Changsha, China)
Jinbiao Wu ² (School of Mathematics and Statistics, Central South University, Changsha China)
Ibrahim Yusuf ³ (Department of Mathematical Sciences, Bayero University, Kano)

Received: 2023-01-04 Accepted : 2024-08-31 Published : 2024-09-07

Keywords: Reliability, Computer network, Cloud server, MTTF, Sensitivity,

Abstract :

This study presents stochastic model for analysing the behaviour of complex computer network comprises of cloud server, two load balancers, fog node and clients. Moreover, coverage factor and two other repair rate are incorporated between failed, partial and perfect state.The main objective of this research is to determine the reliability measures of series-parallel computer network with fault tolerant device. For this reason,four different techniques are explored, namely general repair, coverage, copula, copula-coverage. All the rates of failure are constant and subsequently assumed to follow exponential distribution while the rates of repair follow General and Gumbel-Hougaard family copula distributions. The computer network is modelled as a finite Markov Process. To assess reliability of the computer network a system of first order partial differential equations are derived from the transition diagram and solved using Laplace transforms and supplementary variables technique. Time-dependent measures of reliability such as mean time to failure (MTTF), availability, cost analysis, sensitivity analysis and reliability were obtained by Laplace transforms and supplementary variables technique. This research work provides comparative analysis for measures of reliability using technique stated above, while detail result referring to which techniques make the computer network more reliable was developed. However, numerical simulations are explored to validate the analytical results.

References:

[1] Yusuf I., Ismail A.L, Singh V.V, Ali U.A and Sufi N.A (2020). Performance analysis of multi-computer system consisting of three subsystems in series configuration using copula repair policy, SN Computer Science, https://doi.org/10.1007/s42979-020-00258-0 1:241.
[2] Yusuf I., Ismail A.L, and Ali U.A (2020). Reliability analysis of communication network system with redundant relay station under partial and complete failure, Journal of Mathematical and Computational Science, 10(4) 863:880, DOI: 10.28919/jmcs/4408
[3] Singh V.V, Ismail A.L, Chand U. and Maiti S.S (2022). Performance assessment of complex system under the k-out-of-n: g type configuration with k consecutive degraded states through the copula repair approach, International Journal of Reliability, Quality and Safety Engineering, DOI: 10.1142/S0218539321500479.
[4]. Liu, L. (2016), Optimization Design of Computer Network Reliability Based on Genetic Algorithms, Chemical Engineering Transactions, 51:775-780, https://doi.org/10.3303/CET1651130
[5] Singh V.V, Ismail A.L, Yusuf I. and Abdullahi A.H (2021). Probabilistic Assessment of Computer-Based Test (CBT) Network System Consists of Four Subsystems in Series Configuration Using Copula Linguistic Approach, Journal of Reliability and Statistical Studies, 13(2): 401-428, DOI: 10.13052/jrss0974-8024.132410
[6] Isa M.S, Yusuf I., Ali U.A., Suleiman K., Yusuf B., and Ismail A.L,(2022). Reliability Analysis of Multi-Workstation Computer Network Configured as Series-Parallel System via Gumbel - Hougaard Family Copula, International Journal of Operations Research, 19(1): 13-26, DOI: 10.6886/IJOR.202203_19(1).0002
[7] Isa M.S, Abubakar M.I., Ibrahim K.H., Yusuf I. and Tukur I. (2021). Performance Analysis of Complex Series Parallel Computer Network with Transparent Bridge Using Copula Distribution, International Journal of Reliability, Risk Safety: Theory and Application, 4(1): 47-59, DOI: 10.30699/IJRRS.4.1.7
[8] Garg, H. (2018). Multi objective non-linear programming problem for reliability optimization in intuitionistic fuzzy environment, Frontiers in Information Systems, 2:197-229. DOI: 10.2174/9781681087139118020013
[9] Garg S., Sejwal, S. and Solanki J. (2019). An approach to resolve heterogeneity using rpc in client server systems. International Journal of Engineering Applied Sciences and Technology, 4(04):301–305. DOI: 10.33564/IJEAST.2019.v04i04.049
[10] Yusuf I. and Auta A.A (2021). Availability analysis of a distributed system with homogeneity in client and server under four different maintenance options. Life Cycle Reliability and Safety Engineering, https://doi.org/10.1007/s41872-021-00177-w
[11] Handoko H., Isa S.M, Si S. and Kom M. (2018). High Availability Analysis with Database Cluster, Load Balancer and Virtual Router Redudancy Protocol, 2018 3rd International Conference on Computer and Communication Systems (ICCCS), 2018:482-486. DOI: 10.1109/CCOMS.2018.8463263
[12] Ivanovic M., Vidakovic M., Budimac Z and Dejan M. (2017). A scalable distributed architecture for client and server-side software agents. Vietnam Journal of Computer Science, 4: 127–137. https://doi.org/10.1007/s40595-016-0083-z
[13] Kamal J., Murshed M and Buyya R. (2016). Workload-aware incremental repartitioning of shared-nothing distributed databases for scalable OLTP applications, Future Generation Computer Systems, 56: 421-435. https://doi.org/10.1016/j.future.2015.09.024
[14] Khan Z., Alam M. and Haidri R.A (2017). Effective load balance scheduling schemes for heterogeneous distributed system. International Journal of Electrical and Computer Engineering, 7(5): 2757–2765. DOI: http://doi.org/10.11591/ijece.v7i5.pp2757-2765
[15] Ke J.C and Liu T.H (2014). Repairable system with imperfect coverage and reboot. Applied Mathematics and Computation, 246(2014) 148-158. https://doi.org/10.1016/j.amc.2014.07.090
[16]. Kumar P., Jain M and Meena R.K (2021). Optimal control of fault tolerant machining system with reboot and recovery in fuzzy environment using harmony search algorithm. ISA Transactions, 119(2022)52-64. DOI: 10.1016/j.isatra.2021.02.027
[17] Tyagi V., Arora R., Mangey R and Ioannis S.T (2021). Copula based measures of repairable parallel system with fault coverage. International Journal of Mathematical, Engineering and Management Sciences, 6(1) 322-344. DOI: 10.33889/IJMEMS.2021.6.1.021
[18] Rausand M. Barros A. and Hoyland A. "System Reliability Theory: Models, Statistical Methods and Applications" Wiley (2021). DOI:10.1002/9781119373940
[19] Yusuf I., Ismail A.L, Sufi N.A., Ambursa F.U., Sanusi A. and Isa M.S (2021) Reliability analysis of distributed system for enhancing data replication using gumbel hougaard family copula approach joint probability distribution. Journal of Industrial Engineering International, 17(3) 59-78..DOI: 10.30495/jiei.2021.1944531.1177
[20] Maihulla, A. S., Yusuf, I., and Bala, S. I. (2023). Reliability and performance analysis of a series-parallel photovoltaic system with human operators using Gumbel-Hougaard family copula. International Journal of Mathematics in Operational Research, 24(1), 29-52. DOI: 10.1504/IJMOR.2023.128637
[21] Singla, S., Mangla, D., Malik, A. K., and Modibbo, U. M. (2024). Reliability Optimization Methods: A Systematic Literature Review. Yugoslav Journal of Operations Research. http://dx.doi.org/10.2298/YJOR230715031S.
[22] Panwar, N., and Kumar, S. (2021). Stochastic modelling and performance analysis of feeding unit in paper plant. International Journal of Mathematics in Operational Research, 19(3), 302-316. https://doi.org/10.1504/IJMOR.2021.116965
[23] Wu, J., & Isa, M. S. (2024). Reliability estimation of a fault coverage distributed system with replacement options under four different scenarios. Sigma Journal of Engineering and Natural Sciences, 42(4), 1214-1238. DOI: 10.14744/sigma.2024.00097
[24] Tohidi, H., & Jabbari, M. M. (2012) “CRM in organizational structure design,” Procedia Technology, 1, 579-582. https://doi.org/10.1016/j.protcy.2012.02.126
[25] Tohidi, H., & Jabbari, M. M. (2012) “The necessity of using CRM,” Procedia Technology, 1, 514-516. https://doi.org/10.1016/j.protcy.2012.02.110
[26] Farahani, A., Tohidi, H., Shoja, A. (2019). An integrated optimization of quality control chart parameters and preventive maintenance using Markov chain. Advances in Production Engineering & Management. 14(1), pp 5–14. https://doi.org/10.14743/apem2019.1.307
[27] Isa, M. S., Wu, J., & Yusuf, İ. (2024). Performance estimation of honeynet system for network security enhancement via copula linguistic. Sigma Journal of Engineering and Natural Sciences, 42(4), 1169-1182. DOI: 10.14744/sigma.2024.00095
[28] Isa, M. S., Wu, J., Yusuf, İ., Ali, U.A., Waziri, T.A., and Abdulkadir, A.S (2023). Performance assessment of multi-unit web and database servers distributed system. International Journal of Computational Science and Engineering, DOI: 10.1504/IJCSE.2023.10060450
[29] Kumar, M., and Singh, S. B. (2024). Analysis of system reliability based on weakest t-norm arithmetic operations using Pythagorean fuzzy numbers. International Journal of System Assurance Engineering and Management, 15(4), 1467-1482. https://doi.org/10.1007/s13198-023-01906-3