^{1}

^{2}

^{3}

^{1}

^{2}

^{3}

When the connection in Wireless Sensor Networks (WSNs) is broken, a subset of nodes which serve as the data collection points (CPs) can buffer the data from sensors and transfer these data to mobile data collectors (MDCs) to restore the connectivity of WSNs. One of the existing problems is how to decide the numbers and positions of CPs for obtaining an optimal path of MDC. In order to deal with this problem, a selection method of CPs is proposed to reduce the traveling distance of MDCs. Meanwhile, with this selection method, the changing rules and the stability of the path of MDC are theoretically proved. A 100-node WSN is implemented to test the proposed method. The evaluation results verify that the proposed method is efficient and valuable.

WSNs have attracted much attention from research and engineering communities in recent years due to their numerous applications [

Within the WSNs, all the sensors are expected to form a connected network to coordinate their actions in the execution of a task and transmit the collected data to a base station (BS). However, most of the sensor nodes are battery-driven with limited processing capacity; they will face the risk of depleting their energy and becoming nonfunctional and even getting damaged in the harsh surrounding. In these cases, the network communication is disconnected; correspondingly the data transmission could be restricted. In order to retain the connectivity under the failure of some nodes, node redundancy method is proposed by deploying more nodes than necessary [

Integrating mobile data collectors into WSN can effectively solve the above communication problem and also improve the performance of networks, such as increasing efficiency and reducing energy consumption [

According to above analysis, a novel CPs’ selection method is proposed to find the area of the optimal CPs. On the basis of the selection method, the changing rules and the stability of the path of MDC are theoretically proved in this paper. Firstly, the use of MDC for restoring the connectivity of disjoint WSN is investigated, and then different numbers of CPs are selected from each cluster for path optimization to find the shortest tour of MDC. Secondly, the number of CPs in each cluster and the region they may stay in are decided when the optimal path is formed. Finally, the region partition method of optimum CPs is proposed, and the impact of CPs’ selection on optimal path is analyzed.

This paper is organized as follows. The next section presents the related work. Section

As mentioned in [

By considering the connectivity of the selected RPs and the cluster centers, the collection points are obtained [

Recently, some approaches have been proposed to exploit the mobility for data collection in WSNs [

In this paper, the available nodes are roughly divided into multiple clusters. Based on the way of cluster-based routing protocol, the internal nodes which belong to the same cluster keep well connectivity by multihops [

The Fuzzy

Let

RPs are the static sensor nodes with the shortest Euclidean distance to

Let

A WSNs example with four given clusters is illustrated in Figure

The selection mode of CPs when the cluster’s location presents the convex side.

From the geometric distribution point, the example in Figure

The selection mode of CPs when the cluster’s location presents concave side.

Considering real situation, the connection diagram for the clusters is not only the convex or concave polygons, but also there appears more complex mesh structure. However, based on the geometric theory, the complex mesh structure can be decomposed into several convex and concave edges. Therefore, this research only focuses on the case of convex side and the concave edge with one concave point. And only one CP is selected in the cluster which has a concave point.

The aim of deploying MDC is to transmit data, and the moving path of MDC needs to be planned. Assuming that the MDC’s moving path

The simulation diagram of global optimal path.

Therefore, the choice of optimal path is divided into the following two steps:

Determine the shortest path

Compare

Among (1) and (2),

With the process in Figure

The formation process of optimal path when the cluster’s location presents convex side.

Similarly, once the cluster’s location presents concave side, the MDC’s moving path (drawn by the dashed line) and the indicated minimum cost path (drawn by the solid line) are selected and shown in Figure

The formation process of optimal path when the cluster’s location presents concave side.

In order to find the optimal area of the CPs, two additional definitions are given.

Let

Let

The selection method of CPs varies according to the position of clusters, so the area of optimal CPs should change as well.

For the convenience of regional division, the shape of each cluster is assumed to be circular, and the transmission range of sensor node is considered to be a point; that is, RPs are equivalent to CPs. With the example of four clusters, the problem can be divided into the two following cases.

As shown in Figure

The regional division of optimum CP may stay in when the cluster’s location presents convex side.

This method can technically ensure that the local optimal path that includes the path from

Let

Then

In this case, firstly, the cluster with concave point should be determined. Then, for this cluster, one CP is selected. And for each of the other clusters, two CPs are selected. With the similar method of dividing and the principle of the situation with convex side, the area that optimal CPs may stay in is noted as the shadow parts in Figure

The regional division of optimum CP may stay in when the cluster’s location presents concave side.

It is noteworthy that although

The selection method of CPs changes and the MDC’s moving path will change accordingly. On account of the fact that more than one CP may participate in path optimization, we need to pick out the CPs that are the best location for optimization so as to minimize the moving path.

As shown in Figure

Impact on the optimal path of more than one CP when the cluster’s location presents convex side.

From Figure

Then there are three cases, that is,

Figure

Impact on the optimal path of more than one CP when the cluster’s location presents concave side.

Also the number of clusters is extended to

For the arbitrarily placed

The specific proof of Theorem

(1) When

(2) When

When a single CP is chosen for each cluster, the length of section

(1) When

Three kinds of relationships may exist between

(2) When

Three kinds of relationships may exist between

So the result of

(3) In the same way, when

Inequality

So the result has three conditions:

Proof is completed.

With the above theory analysis and basic testing, the selection method of CPs can directly make the moving path of MDCs change as well. Based on Theorem

MATLAB_R2012a is used as simulation platform for performance evaluation. 100 nodes are randomly deployed in a 100 m × 100 m area. The number of clusters is chosen from 3 to 8 by using FCM clustering method. The communication of each node in the same cluster is normal. The transmission range of nodes and MDC is fixed as 10 m.

Under the condition of forming the specified number of clusters, two modes that choose two CPs (CTCP) in each cluster and the IDM-KMDC [

With the evaluation of CTCP, the performance of choosing multiple CPs in each cluster is tested. The TTL and MSL are also used to indicate the effect of number of CPs and number of clusters in the following sections.

With the testing circumstance, the values of TTL for two modes are obtained and shown in Table

The variance of TTL.

Number of clusters | TTL (m) | TTL decreasing rate (%) | |
---|---|---|---|

IDM-KMDC | CTCP | ||

3 | 45.0 | 43.2 | 4.0 |

4 | 61.3 | 59.9 | 2.3 |

5 | 76.9 | 75.8 | 1.4 |

6 | 121.6 | 119.6 | 1.6 |

7 | 205.9 | 181.7 | 11.8 |

8 | 210.8 | 207.0 | 1.8 |

The comparison of TTL for two modes with 3–8 clusters.

The comparison of MSL with different number of clusters.

As shown in Table

The results of CTCP and IDM-KMDC for the total tour length are shown in Figure

As mentioned previously, the indicator of maximum step length will directly show the data collection latency of MDC. That is to say, the smaller MSL is, the better related method is. From the results shown in Table

The variance of MSL.

Number of clusters | MSL (m) | MSL decreasing rate (%) | |
---|---|---|---|

IDM-KMDC | CTCP | ||

3 | 19.7 | 15.1 | 23.4 |

4 | 20.9 | 16.4 | 21.5 |

5 | 20.9 | 17.8 | 14.8 |

6 | 28.0 | 25.3 | 9.6 |

7 | 40.2 | 32.2 | 19.9 |

8 | 45.4 | 38.5 | 15.1 |

In Section

As shown in Table

The variance of TTL for multiple CPs.

Number of CPs in each cluster | Number of clusters | |||||
---|---|---|---|---|---|---|

3 | 4 | 5 | 6 | 7 | 8 | |

1 | 45.0 | 61.3 | 76.9 | 121.6 | 205.9 | 210.8 |

2 | 43.2 | 59.9 | 75.8 | 119.6 | 181.7 | 207.0 |

3 | 43.2 | 59.9 | 75.8 | 116.4 | 179.3 | 202.4 |

4 | 43.2 | 59.9 | 75.8 | 116.4 | 178.4 | 200.8 |

5 | 43.2 | 59.9 | 75.8 | 116.4 | 178.4 | 200.8 |

6 | 43.2 | 59.9 | 75.8 | 116.4 | 178.4 | 200.8 |

Figure

Total tour length as a function of clusters and CPs.

With the development of WSNs and the growing requirements of industry area, the number of nodes will be increased more and more fast. The performance of computing cost will be a key index for real applications.

For clearly testing the proposed determination method of CPs, the computing costs of different numbers of CPs and clusters are compared and listed in Table

The comparison of computing cost(s).

Number of CPs | Number of clusters | |||||
---|---|---|---|---|---|---|

3 | 4 | 5 | 6 | 7 | 8 | |

1 | 0.266 | 0.281 | 0.282 | 0.282 | 0.297 | 0.313 |

2 | 0.281 | 0.313 | 0.313 | 0.328 | 0.328 | 0.344 |

3 | 0.297 | 0.328 | 0.343 | 0.345 | 0.359 | 0.360 |

4 | 0.328 | 0.344 | 0.359 | 0.360 | 0.375 | 0.407 |

5 | 0.344 | 0.355 | 0.360 | 0.375 | 0.407 | 0.412 |

6 | 0.345 | 0.366 | 0.377 | 0.407 | 0.420 | 0.421 |

Through the above comparison of the different situations, CTCP is more suitable for the WSN that suffers from large-scale damage in the harsh environmental conditions. Also the comparison results verify that when two CPs are chosen in each cluster, the forming path is better than that of single CP.

In order to deal with the problem of the disjoint WSN operating in harsh environment, the MDC method is introduced to accomplish the data collection. By analyzing constraint of the existing researches, the method of regional division is proposed. The area in which the optimal CPs exist is determined and its unified description of the form is given. Meanwhile, the study results have verified that the TTL will monotonically decrease with the increase of the number of CPs in each cluster, and finally the TTL is tended to be stable. The simulation comparison and testing results clearly showed the correctness of the proposed method.

In the future, this work will focus on establishing the experiment system model and empowering the invulnerability of WSN and applying it to the industrial systems.

The authors declare that they have no conflicts of interest.

This work was supported by the Natural Science Foundation of Liaoning Province (Grant no. 201602557), the Program for Liaoning Excellent Talents in University (no. LR2015034), and Liaoning Province Science and Technology Public Welfare Research Fund Project (2016002006).