Performance Analysis of Complex Series Parallel Computer Network with Transparent Bridge Using Copula Distribution

Document Type : Original Research Article


1 Department of Mathematics, Federal University Dutse

2 Department of Mathematics, Federal College of Education (Tech.), Bichi, Kano

3 Department of Mathematics, Aminu Kano College of Islamic and Legal Studies, Kano

4 Bayero University, Kano, Nigeria

5 Department of Mathematics, Kano State Polytechnic, Kano, Nigeria


A network bridge is a computer networking device that creates a single aggregate network from multiple communication network or network segments. One of the type of network bridge is transparent bridge saddle with responsibility of checking incoming network traffic to identify media access control addresses. In this present research work on series parallel computer network performance, availability and cost analysis of complex computer network was considered to focus on a network that has four subsystems A, B, C and D and all the subsystems are arranged in series-parallel, subsystem A and B are working on 1-out-of-2: G and 2-out-of-3: F policy respectively, C subsystem behaved as a bridge with one unit and D subsystem has five units and are working in 3-out-of-5: G scheme. The system has two types of failure, degraded (partial failure) or complete failed states. The system was analyzed using supplementary variables techniques and Laplace transform, general distribution and copula family were employed to restore the partial failure and complete failure states. Computed results have been highlighted by the means of tables and graphs to investigate the performance of computer network. The result has shown that computer network with transparent bridge will be more reliable to filter incoming frame and forward it to media access control (MAC).


Main Subjects

  • Chauhan, S.K and Mali, S.C. (2016) Reliability Evaluation of Series-Parallel and Parallel-Series Systems for Arbitrary Values of the Parameters. International Journal of Statistics and Reliability Engineering Vol. 3(1), pp. 10-19.
  • Fadi, N. and Sibai, F.N. (2014) Modeling and Output Power Evaluation of Series Parallel Photovoltaic Modules. International Journal of Advanced Computer Science and Applications, 5(1), 129-136.
  • Hu, L., Yue, D. and Li, (2012). Availability Analysis and Design Optimization for Repairable Series-Parallel System with Failure Dependencies. International Journal of Innovative Computing, Information and Control, 8(10A), 6693-6705
  • Khatab, A, Aghezzaf, E, Diallo, C. and Djelloul, I. (2017). Selective Maintenance Optimization for Series-Parallel Systems Alternating Missions and Scheduled Breaks with Stochastic Durations. International Journal of Production Research, 55:10, 3008-3024.
  • Mohammadi M., Mortazavi, S.M and Karbasian, M. (2018). Developing a Method for Reliability Allocation of Series-Parallel Systems by Considering Common Cause Failure. International Journal of Industrial Engineering & Production Research, 29(2), 213-230
  • Mustafa, A. (2017). Improving the Reliability of a Series-Parallel System Using Modiļ¬ed Weibull Distribution, International Mathematical Forum,12 (6),257–269.
  • Peng, R, Zhai, Q, Xing, L and Yang, J. (2016) Reliability Analysis and Optimal Structure of Series-Parallel Phased-Mission Systems Subject to Fault-level Coverage.IIE Transactions, 48:8, 736-746
  • Xie, L., Lundteigen, M.A and Liu, Y. (2020). Reliability and barrier assessment of series–parallel systems subject to cascading failures.
  • Muhammad S. Isa, U.I. Ali, Bashir Yusuf and Ibrahim Yusuf (2020) Cost-Benefit Analysis of Three Different Series-Parallel Dynamo Configurations. Life Cycle Reliability and Safety Engineering.


  • Zhang, F. (2019) Research on reliability Analysis of Computer Network Based on Intelligent Cloud Computing Method, International Journal of Computers and Applications, 41:4, 283-288.
  • Potapov, V. I., Shafeeva, O.P., Gritsay, A. S., Makarov, V. V., Kuznetsova, O.P., and Kondratukova, L.K. (2019). Reliability in the Model of an Information System with Client Server Architecture. Journal of Physics: Conf. Series 1260, 022007.
  • Kovalev, I.V., Zelenkov, P.V., Karaseva, M.V., Yu. M. Tsarev and Yu. Tsarev. (2015). Computer Model of the Reliability Analysis of the Distributed Computer Systems with Architecture “Client-Server” IOP Conf. Series: Materials Science and Engineering 70, 012009.
  • Nelsen, R. B., an Introduction to Copulas, 2nd Edition. Springer, New York, 2006.
  • Abubakar M.I. and Singh V. V. (2019) Performance Assessment of an Industrial System (African Textile Manufacturers, LTD). Through Copula Approach. Journal of Operations Research and Decisions.
  • Kabiru H. Ibrahim, Singh V.V. and Abulkareem Lado (2017). Reliability Assessment of Complex System Consisting Two Subsystems Connected in Series Configuration Using Gumbel-Hougaard Family Copula Distribution. Journal of Applied Mathematics and Bioinformatics, Vol.7, no.2, 1-27.
  • Ibrahim Yusuf, Abdulkareem Lado Ismail, Singh, V. V. Ali U. A. and Nasir Ahmad Sufi. (2020). Performance Analysis of Multicomputer System Consisting of Three Subsystems in Series Configuration Using Copula Repair Policy. SN Computer Science (2020) 1:241.
  • Singh, V.V. and Monika Gahlot (2020) Reliability Analysis of (n) Clients System under Star Topology and Copula Linguistic Approach.
  • Pratap Kumar, Kabiru H. Ibrahim, Abubakar, M.I. and Singh, V.V. (2020) Probabilistic Assessment of Complex System with Two Subsystems in Series Arrangement with Multi-Types Failure and Two Types of Repair Using Copula. Strategic System Assurance and Business Analytics.
  • Muhammad S. Isa, U.I. Ali, Bashir Yusuf, Ibrahim Yusuf and Yusuf J Umar (2020) Sensitivity Analysis of Three Different Series-Parallel Dynamo Configurations. Reliability: Theory and Application.