Skip to main content
SpringerLink
Log in

Reliability of time-constrained multi-state network susceptible to correlated component faults

  • S.I.: Reliability Modeling with Applications Based on Big Data
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

Correlation can seriously degrade reliability and capacity due to the simultaneous failure of multiple components, which lowers the probability that a system can execute its required functions with acceptable levels of confidence. The high cost of fault in time-critical systems necessitates methods to explicitly consider the influence of correlation on reliability. This paper constructs a network-structured model, namely time-constrained multi-state network (TCMSN), to investigate the capacity of a computer network. In the TCMSN, the physical lines comprising the edges of the computer network experience correlated faults. Our approach quantifies the probability that d units of data can be sent from source to sink in no more than T units of time. This probability that the computer network delivers a specified level of data before the deadline is referred to as the system reliability. Experimental results indicate that the negative influence of correlation on reliability could be significant, especially when the data amount is close to network bandwidth and the time constraint is tight. The modeling approach will subsequently promote design and optimization studies to mitigate the vulnerability of networks to correlated faults.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Abbreviations

MSN:

Multi-state network

MP:

Minimal path

TCMSN:

Time-constrained multi-state network

s :

Source node

t :

Sink node

n :

Number of edges

m :

Number of nodes excluding the source s and the sink t

e i :

ith edge with i = 1, 2, …, n

N:

Set of nodes

E:

{ei|i = 1, 2, …, n}: set of edges

w i :

Number of physical lines in ei which determines the maximal bandwidth of ei

W:

{wi|i = 1, 2, …, n}: maximal bandwidth pattern

l i :

Lead time of ei

L:

{li|i = 1, 2, …, n}: set of lead times

G :

(N, E, W, L): a TCMSN

r i :

Reliability of physical lines in ei

ρ i :

Correlation among physical lines in ei

x i :

Current bandwidth of ei

X :

Current bandwidth pattern

K :

Number of minimal paths

P j :

jth minimal path with j = 1, 2, …, k

d :

Data amount

T :

Time constraint

y i :

Minimal bandwidth of ei for satisfying d

Y v :

vth minimal bandwidth pattern satisfying d with v = 1, 2, …, h

References

  • Aggarwal, K. K., Gupta, J. S., & Misra, K. B. (1975). A simple method for reliability evaluation of a communication system. IEEE Transactions on Communications, 23, 563–566.

    Google Scholar 

  • Alexopoulos, C. (1985). A note on state-space decomposition methods for analyzing stochastic flow networks. IEEE Transactions on Reliability, 44, 354–357.

    Google Scholar 

  • Aven, T. (1985). Reliability evaluation of multistate systems with multistate components. IEEE Transactions on Reliability, 34, 473–479.

    Google Scholar 

  • Bai, G., Tian, Z., & Zuo, M. J. (2016). An improved algorithm for finding all minimal paths in a network. Reliability Engineering & System Safety, 150, 1–10.

    Google Scholar 

  • Chang, P. C. (2019). Reliability estimation for a stochastic production system with finite buffer storage by a simulation approach. Annals of Operations Research, 277, 119–133.

    Google Scholar 

  • Chen, Y. L., & Chin, Y. H. (1990). The quickest path problem. Computers & Operations Research, 17, 153–161.

    Google Scholar 

  • Chen, G. H., & Hung, Y. C. (1993). On the quickest path problem. Information Processing Letters, 46, 125–128.

    Google Scholar 

  • Chen, G. H., & Hung, Y. C. (1994). Algorithms for the constrained quickest path problem and the enumeration of quickest paths. Computers & Operations Research, 21, 113–118.

    Google Scholar 

  • Chen, Y. L., & Tang, K. (1998). Minimum time paths in a network with mixed time constraints. Computers & Operations Research, 25, 793–805.

    Google Scholar 

  • Clímaco, J. C. N., Pascoal, M. M. B., Craveirinha, J. M. F., & Captivo, M. E. V. (2007). Internet packet routing: Application of a K-quickest path algorithm. European Journal of Operational Research, 181, 1045–1054.

    Google Scholar 

  • Dai, Y., Levitin, G., & Trivedi, K. (2007). Performance and reliability of tree-structured grid services considering data dependence and failure correlation. IEEE Transactions on Computers, 56, 925–936.

    Google Scholar 

  • Dhillon, B., & Anude, O. (1994). Common-cause failures in engineering systems: A review. International Journal of Reliability, Quality and Safety Engineering, 1, 103–129.

    Google Scholar 

  • Fathabadi, H. S., Khezri, S., & Khodayifar, S. (2015). A simple algorithm for reliability evaluation in dynamic networks with stochastic transit times. Journal of Industrial and Production Engineering, 32, 115–120.

    Google Scholar 

  • Fiondella, L. (2010). Reliability and sensitivity analysis of coherent systems with negatively correlated component failures. International Journal of Reliability, Quality and Safety Engineering, 17, 505–529.

    Google Scholar 

  • Fiondella, L., & Xing, L. (2015). Discrete and continuous reliability models for systems with identically distributed correlated components. Reliability Engineering & System Safety, 133, 1–10.

    Google Scholar 

  • Ford, L. R., & Fulkerson, D. R. (1962). Flows in networks. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Forghani-Elahabad, M., & Mahdavi-Amiri, N. (2015). An efficient algorithm for the multi-state two separate minimal paths reliability problem with budget constraint. Reliability Engineering & System Safety, 142, 472–481.

    Google Scholar 

  • Huang, C. F. (2019). Evaluation of system reliability for a stochastic delivery-flow distribution network with inventory. Annals of Operations Research, 277, 33–45.

    Google Scholar 

  • Huang, F. M., Lan, C. W., & Yang, J. H. (2009). An optimal QoS-based Web service selection scheme. Information Sciences, 179, 3309–3322.

    Google Scholar 

  • Hudson, J. C., & Kapur, K. C. (1985). Reliability bounds for multistate systems with multistate components. Operations Research, 33, 153–160.

    Google Scholar 

  • Hung, Y. C., & Chen, G. H. (1992). Distributed algorithms for the quickest path problem. Parallel Computing, 18, 823–834.

    Google Scholar 

  • Ito, K., Zhao, X., & Nakagawa, T. (2017). Random number of units for k-out-of-n systems. Applied Mathematical Modelling, 45, 563–572.

    Google Scholar 

  • Jafary, B., & Fiondella, L. (2016). A universal generating function-based multi-state system performance model subject to correlated failures. Reliability Engineering & System Safety, 152, 16–27.

    Google Scholar 

  • Jain, N., Yadav, O. P., Rathore, A. P. S., & Jain, R. (2017). Reliability assessment framework for a multi-state multi-component system. Journal of Industrial and Production Engineering, 34, 580–589.

    Google Scholar 

  • Jian, S., & Shaoping, W. (2007). Integrated availability model based on performance of computer networks. Reliability Engineering & System Safety, 92, 341–350.

    Google Scholar 

  • Lee, D. T., & Papadopoulou, E. (1993). The all-pairs quickest path problem. Information Processing Letters, 45, 261–267.

    Google Scholar 

  • Levitin, G., & Xie, M. (2006). Performance distribution of a fault-tolerant system in the presence of failure correlation. IEEE Transactions on Reliability, 2006(38), 499–509.

    Google Scholar 

  • Lin, Y. K. (2003). Extend the quickest path problem to the system reliability evaluation for a stochastic-flow network. Computers & Operations Research, 30, 567–575.

    Google Scholar 

  • Lin, Y. K., Chang, P. C., & Fiondella, L. (2012). Quantifying the impact of correlated failures on stochastic flow network reliability. IEEE Transactions on Reliability, 61, 692–701.

    Google Scholar 

  • Lin, Y. K., & Chen, S. G. (2016). Double resource optimization for a robust computer network subject to a transmission budget. Annals of Operations Research, 244, 133–162.

    Google Scholar 

  • Lin, Y. K., & Chen, S. G. (2019). An efficient searching method for minimal path vectors in multi-state networks. Annals of Operations Research. https://doi.org/10.1007/s10479-019-03158-6.

    Article  Google Scholar 

  • Lin, Y. K., Fiondella, L., & Chang, P. C. (2013). Quantifying the impact of correlated failures on system reliability by a simulation approach. Reliability Engineering & System Safety, 109, 32–41.

    Google Scholar 

  • Lin, Y. K., & Pan, C. L. (2014). Considering retransmission mechanism and latency for network reliability evaluation in a stochastic computer network. Journal of Industrial and Production Engineering, 31, 350–358.

    Google Scholar 

  • Lin, Y. K., & Yeh, C. T. (2011). Using minimal cuts to optimize network reliability for a stochastic computer network subject to assignment budget. Computers & Operations Research, 38, 1175–1187.

    Google Scholar 

  • Lu, L., Xu, Z., Wang, W., & Sun, Y. (2013). A new fault detection method for computer networks. Reliability Engineering & System Safety, 114, 45–51.

    Google Scholar 

  • Martins, E. D. Q. V., & Santos, J. L. E. D. (1997). An algorithm for the quickest path problem. Operations Research Letters, 20, 195–198.

    Google Scholar 

  • Mizutani, S., Zhao, X., & Nakagawa, T. (2019). Random age replacement policies with periodic planning times. International Journal of Reliability, Quality and Safety Engineering, 26, 1950023.

    Google Scholar 

  • Pascoal, M. M. B., Captivo, M. E. V., & Clímaco, J. C. N. (2005). An algorithm for ranking quickest simple paths. Computers & Operations Research, 32, 509–520.

    Google Scholar 

  • Vaurio, J. (1998). An implicit method for incorporating common-cause failures in system analysis. IEEE Transactions on Reliability, 1998(47), 173–180.

    Google Scholar 

  • Xue, J. (1985). On multistate system analysis. IEEE Transactions on Reliability, 34, 329–337.

    Google Scholar 

  • Yarlagadda, R., & Hershey, J. (1991). Fast algorithm for computing the reliability of communication network. International Journal of Electronics, 70, 549–564.

    Google Scholar 

  • Yeh, C. T., & Fiondella, L. (2017). Optimal redundancy allocation to maximize multi-state computer network reliability subject to correlated failures. Reliability Engineering & System Safety, 166, 138–150.

    Google Scholar 

  • Zhao, X., Qian, C., & Nakagawa, T. (2018). Age replacement models with constant and random replacement times. International Journal of Reliability, Quality and Safety Engineering, 25, 1850029.

    Google Scholar 

  • Zuo, M. J., Tian, Z., & Huang, H. Z. (2007). An efficient method for reliability evaluation of multistate networks given all minimal path vectors. IIE Transactions, 39, 811–817.

    Google Scholar 

Download references

Acknowledgements

Funding was provided by Ministry of Science and Technology, Taiwan (MOST 106-2221-E-507-004-MY3).

Author information

Authors and Affiliations

  1. Department of Industrial Engineering and Management, National Chiao Tung University, Hsinchu, 300, Taiwan, ROC

    Yi-Kuei Lin

  2. Department of Electrical & Computer Engineering, University of Massachusetts, Dartmouth, MA, USA

    Lance Fiondella

  3. Department of Industrial Engineering and Management, National Quemoy University, Kinmen County, 892, Taiwan, ROC

    Ping-Chen Chang

Authors
  1. Yi-Kuei Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lance Fiondella
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ping-Chen Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ping-Chen Chang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lin, YK., Fiondella, L. & Chang, PC. Reliability of time-constrained multi-state network susceptible to correlated component faults. Ann Oper Res 311, 239–254 (2022). https://doi.org/10.1007/s10479-019-03428-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-019-03428-3

Keywords

Search

Navigation