In the Internet of Things (IoT) system, relay communication is widely used to solve the problem of energy loss in long-distance transmission and improve transmission efficiency. In Body Sensor Network (BSN) systems, biosensors communicate with receiving devices through relay nodes to improve their limited energy efficiency. When the relay node fails, the biosensor can communicate directly with the receiving device by releasing more transmitting power. However, if the remaining battery power of the biosensor is insufficient to enable it to communicate directly with the receiving device, the biosensor will be isolated by the system. Therefore, a new combinatorial analysis method is proposed to analyze the influence of random isolation time (RIT) on system reliability, and the competition relationship between biosensor isolation and propagation failure is considered. This approach inherits the advantages of common combinatorial algorithms and provides a new approach to effectively address the impact of RIT on system reliability in IoT systems, which are affected by competing failures. Finally, the method is applied to the BSN system, and the effect of RIT on the system reliability is analyzed in detail.

With the advancement of communication technology, the development of the IoT has reached a new stage [

A BSN system consists of the following three parts: biomedical sensors [

When the relay node fails, the remaining time during which a sensor node can communicate directly with the receiving device is determined by its remaining battery energy. In other words, the timing of the isolation effect is random. When the isolation effect occurs, it may have a dual effect: on the one hand, the performance of the system will be degraded, because when the biosensor is isolated, the receiving device will not receive the information it perceives on time; on the other hand, because the biosensor is isolated at this point, the PFs from this biosensor can be prevented from damaging other components in the system (such as jamming attacks [

The rest of this paper is structured as follows:

Solving competition failure problems has become a deep research field. There are different approaches to reliability analysis for different types of functional-dependent systems. The simulation method is highly applicable to all kinds of systems in the modeling of system behavior, but the results calculated by the simulation method are usually not accurate enough and can only provide rough results. If the calculation accuracy needs to be improved, the time cost will increase, so it is not suitable for accurate calculation of the reliability of large-scale systems [

This combination method has the advantages of high precision and high efficiency and is widely used in the reliability analysis of systems with competing faults. The combinatorial algorithm is used to solve the reliability analysis problem of single-stage [

In the case of relay failure, the study of random isolation time (RIT) and competition effect becomes very important in reliability analysis. However, as far as we know, few existing works consider or assume zero RIT when conducting reliability analyses. Although the literature [

In this paper, the failure of the competition combination method was improved compared with existing methods. This article considers the effects of competitive failure and random isolation time on system reliability and allow different biological sensors to use the same relay when transmitting data, solving the problem of data transmission among different biological sensors in the system that need to use the same relay. At the same time, the system element in this method can follow any failure time distribution. Please note that although this article is based on a discussion of BSN systems, the competitive failure behavior and the proposed method can be applied to other application systems, such as computer networks, smart homes, smart grids, etc.

According to the total probability theorem and divide-and-conquer principle, the reliability of the BSN system with competitive effect can be decomposed into several independent simplified problems without competitive effect.

The FT model is used to express the system’s fault behavior by ignoring the components’ propagating failure behavior. In the BSN system, the BSN system failing is the top event, and the relay component failure and the dependent component failure is the basic event. The sensor communicates with the receiver through the relay; thus, there is a functional dependency between the sensor and the relay. The functional dependency (FDEP) behavior in the dynamic FT model can be modeled in

Note that the failure probability of component

The next step is to construct an event space to consider all possible combinations of failure states for the relay component and dependent components. In the system under consideration, there exists one relay node T and n dependent nodes

Event | Space |
---|---|

In BSN system, SR is used to indicate system reliability. According to the event space

Because the system will occur propagation effects at

By calculating

When T experiences LF,

The modeling of the BSN system is shown in

According to

Events | Space |
---|---|

Similarly,

By calculating

The combined method employed herein is suitable for any failure time distributions of biosensors. The numerical analysis of system reliability in this paper is based on Weibull distribution in Weibull distribution. The probability density function for a random variable c conforming to a Weibull distribution is given below; where,

The expectation or average of c is as follows:

Let

Biosensors | ||
---|---|---|

(2.5e-4, 2.3) | (5.0e-5, 2.0) | |

(2.5e-3, 2.0) | (5.0e-5, 2.5) | |

(8.0e-3, 1.5) | (5.0e-3, 1.7) | |

(1.0e-3, 1.0) | (1.0e-5, 1.2) | |

(8.0e-3, 2.5) | (1.0e-4, 3.0) |

This section studies the effect of RIT of dependent components

For ease of calculation,

ATI | ||||
---|---|---|---|---|

t = 48 | t = 96 | t = 144 | ||

3600 | 0 | 0.904794 | 0.715011 | 0.520917 |

1 | 1 | 0.904794 | 0.715011 | 0.520916 |

8.33e-2 | 12 | 0.904893 | 0.715004 | 0.520856 |

4.17e-2 | 24 | 0.905068 | 0.714978 | 0.520384 |

8.33e-3 | 120 | 0.905628 | 0.714929 | 0.515390 |

2.5e-3 | 400 | 0.905927 | 0.715018 | 0.510697 |

1e-9 | 1e9 | 0.906223 | 0.715257 | 0.504964 |

According to the data given in

In all cases, the system will exhibit different levels of reliability with different values of

In more detail, with the increase of

Domination effect | ||
---|---|---|

48 | Negative effect | |

96 | Improvement effect | |

144 | Negative effect | |

Improvement effect |

As summarized in

ATP | ||||
---|---|---|---|---|

t = 48 | t = 96 | t = 144 | ||

1.7e-3 | 588 | 0.969440 | 0.884298 | 0.763712 |

2e-3 | 500 | 0.962640 | 0.862953 | 0.726789 |

2.2e-3 | 455 | 0.957646 | 0.847486 | 0.700598 |

As can be seen from the results in

ATL | ||||
---|---|---|---|---|

t = 48 | t = 96 | t = 144 | ||

8.8e-3 | 114 | 0.906152 | 0.715234 | 0.507270 |

1.5e-2 | 67 | 0.906016 | 0.716732 | 0.513059 |

2.7e-2 | 37 | 0.905988 | 0.720070 | 0.517253 |

5e-2 | 20 | 0.906678 | 0.721730 | 0.518988 |

The results in

As far as we know, there are few algorithms for random isolation time.

Methods | |||
---|---|---|---|

t = 48 | t = 96 | t = 144 | |

0.906037 | 0.728921 | 0.593224 | |

0.981971 | 0.852535 | 0.604406 | |

0.905873 | 0.725300 | 0.577328 | |

Proposed method | 0.904819 | 0.715011 | 0.520916 |

Note that when the number of dependent nodes is reduced to one, the method presented in this article is the same as for C3. Assume that only

In IoT systems, the energy of the biosensor comes from the batteries. Because of the existence of FDEPs, there are propagation effects and isolation effects compete with each other in time and have to consider the RIT problem However, to the best of our knowledge, existing working assumptions assume that isolation time is zero or that the relay node supports only one dependent node. In this paper, a combination method is proposed for computational reliability analysis to analyze RIT behavior. Although the Weibull distribution is used in this case, the method can be used for any type of failure time distribution. This method can decompose complex problems and then calculate them by traditional methods. Note that although the BSN system is used in this case study, the method can be used for any wireless communication system. Notably, this method assumes that the biosensor can only use one relay for data transmission. In our future work, we intend to allow multiples of the same sensor to use different relay nodes for data transmission, solving the problem of correlation between multiple groups of related FDEP.

The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.

This work was supported by the National Natural Science Foundation of China (NSFC) (Grant No. 62172058) and the Hunan Provincial Natural Science Foundation of China (Grant Nos. 2022JJ10052, 2022JJ30624).

The authors confirm contribution to the paper as follows: study conception and design: Shuo Cai and Tingyu Luo; data collection: Tingyu Luo and Fei Yu; analysis and interpretation of results: Shuo Cai and Pradip Kumar Sharma; draft manuscript preparation: Weizheng Wang. All authors reviewed the results and approved the final version of the manuscript.

The data used for the findings of this study are available within this article.

The authors declare that they have no conflicts of interest to report regarding the present study.