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

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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.

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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

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Acknowledgements

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

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Correspondence to Ping-Chen Chang.

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Lin, YK., Fiondella, L. & Chang, PC. Reliability of time-constrained multi-state network susceptible to correlated component faults. Ann Oper Res (2019). https://doi.org/10.1007/s10479-019-03428-3

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Keywords

  • Correlated fault
  • Time-constrained multi-state network (TCMSN)
  • System reliability