Figure 1.
Generalized functional structure of the hierarchical underwater sensor network.
Figure 2.
Schematic hierarchical structure of the USN with X0 = 13 and imax = 3.
Figure 3.
A homogeneous Markov chain for calculating the probability of failure of the i-th level of the USN.
Figure 4.
A homogeneous Markov chain for calculating the probability of failure of the last (highest) level of the USN.
Figure 5.
A block diagram of the designing method of fault-tolerant structures for USNs.
Table 1.
Main parameters of the initial USN’s structure
| i | Type of hierarchy level | pMi | Xi | Xic |
|---|---|---|---|---|
| 0 | Initial sensors | 0.025 | 16 | 8 |
| 1 | UUVs | 0.0125 | 8 | 4 |
| 2 | Buoys | 0.01 | 4 | 2 |
| 3 | Terrestrial communication nodes | 0.001 | 2 | 1 |
| 4 | Main terrestrial communication node | 0.0005 | 1 | 1 |
Table 2.
Main parameters of the USN’s structure at the 1st iteration
| i | Type of hierarchy level | pmi | Xi | Xic | Ni max |
|---|---|---|---|---|---|
| 0 | Initial sensors | 0.025 | 16 | 8 | 781 |
| 1 | UUVs | 0.0125 | 8 | 4 | 1045 |
| 2 | Buoys | 0.01 | 4 | 2 | 924 |
| 3 | Terrestrial communication nodes | 0.001 | 2 | 1 | 6955 |
| 4 | Main terrestrial communication node | 0.0005 | 1 | 1 | 13914 |
Table 3.
Main parameters of the USN’s structure at the 2nd iteration
| i | Type of hierarchy level | pmi | Xi | Xic | Ni max |
|---|---|---|---|---|---|
| 0 | Initial sensors | 0.025 | 32 | 16 | 1245 |
| 1 | UUVs | 0.0125 | 8 | 4 | 1045 |
| 2 | Buoys | 0.01 | 4 | 2 | 924 |
| 3 | Terrestrial communication nodes | 0.001 | 2 | 1 | 6955 |
| 4 | Main terrestrial communication node | 0.0005 | 1 | 1 | 13914 |
Table 4.
Main parameters of the USN’s structure at the 3rd iteration
| i | Type of hierarchy level | pmi | Xi | Xic | Ni max |
|---|---|---|---|---|---|
| 0 | Initial sensors | 0.025 | 32 | 16 | 1245 |
| 1 | UUVs | 0.0125 | 8 | 4 | 1045 |
| 2 | Buoys | 0.01 | 8 | 4 | 1307 |
| 3 | Terrestrial communication nodes | 0.001 | 2 | 1 | 6955 |
| 4 | Main terrestrial communication node | 0.0005 | 1 | 1 | 13914 |
Table 5.
Main parameters of the USN’s structure at the 4th iteration
| i | Type of hierarchy level | pmi | Xi | Xic | Ni max |
|---|---|---|---|---|---|
| 0 | Initial sensors | 0.025 | 32 | 16 | 1245 |
| 1 | UUVs | 0.0125 | 16 | 8 | 1569 |
| 2 | Buoys | 0.01 | 8 | 4 | 1307 |
| 3 | Terrestrial communication nodes | 0.001 | 2 | 1 | 6955 |
| 4 | Main terrestrial communication node | 0.0005 | 1 | 1 | 13914 |
Figure 6.
Changing of the real value NΣ during the implementation of the method.