A New Path-Constrained Rendezvous Planning Approach for Large-Scale Event-Driven Wireless Sensor Networks
Abstract
:1. Introduction
- Modeling the problem by a Mixed Integer Linear Programming (MILP).
- Analyzing the theoretical aspects of the problem and proving its NP-hardness.
- Proposing distributed and comprehensive heuristics for constructing a comprehensive framework in our approach.
- The first heuristic determines a suitable set of RPs. To cope with the uncertainties in the environment, we designed a Fuzzy Decision System (FDS) model for identifying the potentiality of a sensor-node for becoming a RP.
- After selecting the RPs, our second heuristic attempts to find appropriate locations for the mobile-sink to stop and collect the data from the sensor-nodes which are called “sojourn locations”.
- And the third heuristic constructs routing trees for the sensor-nodes which cannot contact with the mobile-sink directly. These sensor-nodes transfer their data to the related RP.
- Our experimental results prove the effectiveness of our approach.
2. Related Work
3. Preliminaries
3.1. Network Model
- A target field without limitation based on geographical differences.
- One mobile-sink in the network.
- The sensor-nodes have enough computational capabilities and are able to run our proposed solution.
- Each sensor-node has a unique ID which is known for the mobile-sink and the base-station.
- The sensor-nodes and the base-station are stationary after installation in the target field.
- The network is homogenous that means all of the sensor-nodes are in the same type. And in the beginning of network’s operation, they have the same amount of initial energy.
- We assume that the conditions of MAC layer are ideal and communication links between sensor-nodes can establish or cannot. In case of establishment, the sensor-nodes can contact with each other with high quality (based on the standards for wireless communication) (This is an ideal assumption which might not be practical in real wireless communication fashion. The reason for this assumption is to facilitate our simulation. Generally, if two sensor-nodes or a sensor-node with the mobile-sink cannot contact with each other based on the expected quality, they will not be considered in the communication range of each other).
- The sensor-nodes and the mobile-sink are able to control their transmission power to the desired destination (This assumption is arguable in practical implementations. However, the correctness of our assumption just implies that the sensor-nodes can conserve their energy by adjusting their transmission power and operate longer in the network. Our proposed approach does not rely on this assumption).
- The sensor-nodes and the mobile-sink are able to calculate the distance from the received signal strength (Some scholars might doubt on the possibility of this assumption. Indeed, our approach does not need the accurate distance between the sensor-nodes. It is just important to recognize the neighbor sensor-nodes, correctly).
- The radio link is symmetric which means energy consumption for data transmission from node A to node B is same as from node B to node A (This assumption is ideal. We relied on this assumption because of facilitating our simulation).
- We neglect communication time between the sensor-nodes.
3.2. Energy Model
4. Problem Statement and Formulation
4.1. Problem Definition
4.2. MILP Formulation
4.2.1. Objective
4.2.2. Constraints
- The maximum number of RPs on the trajectory should not exceed .(Note) The method for calculating the maximum number of RPs:Since the trajectory of the mobile-sink is pre-defined to obtain the maximum number of RPs, we assume in an ideal case that all of the RPs are located beside the trajectory with dense distribution as illustrated in Figure 3a in which, as an example, the sensor-nodes A, B and C are in the communication range of each other and all of them can contact with the mobile-sink directly. However, among these three sensor-nodes one of them should contact with the mobile-sink as RP and other two sensor-nodes should transfer their data to the selected RP. Otherwise, the mobile-sink should collect the data from all of RPs in the periphery of the trajectory that consumes a considerable amount of time in every tour. Thus, the maximum number of RPs can be obtained as follows.In Equation (10), D represents the total distance of the trajectory. By assuming dense distribution of the sensor-nodes in the periphery of the trajectory, the maximum number of RPs can be obtained by dividing the total distance D to the summation of communication diameter of the two consecutive sensor-nodes with subtracting from the intersected line that is represented by . The obtained value should be multiplied by 2 because in this part of the trajectory two RPs should be selected. And by considering the symmetry condition in another side of the trajectory, the obtained value should be multiplied by 2. The value of is user-defined. Obviously, due to assuming dense distribution of the sensor-nodes in the whole trajectory, we need to consider two arbitrary consecutive sensor-nodes and the obtained value will be same for rest of the sensor-nodes.
- To optimize energy-consumption in communication between sensor-nodes, the solution should not contain energy-triangles. For example, if sensor-node A can contact with sensor-node C directly, then sensor- node B cannot play hop-role between them because . The following expressions illustrate the constraint formally., and :
- The selected RP should be in communication range of the sojourn location.and :
- Each sensor-node should send its data to only one RP for preventing data redundancy and extra energy-consumption in the network.and :
- Balanced assignment of the sensor-nodes to RPs as much as possible to prevent hot-spot phenomenon.and :
4.3. Limitation of MILP-Based Approach
- Identifying a finite set of sojourn locations from a continuous trajectory. Thus, there should be a function or methodology to do this procedure.
- And finally assigning the rest of sensor-nodes to the related RPs as illustrated in Expression (6).
5. Proposed Heuristic
5.1. Stage I and II: Determining Sojourn Locations and RPs
- The mobile-sink moves in the trajectory at the first tour for introducing itself to the periphery sensor-nodes and when a sensor-node receives introduction message, it will consider itself as the candidate RP. The mobile-sink moves in the trajectory and broadcasts the introduction message. Therefore, in this stage the mobile-sink does not wait for reply message and by moving in the trajectory without stopping can accomplish this task.
- The candidate RP starts to do the process of identifying its potentiality for becoming RP based on our designed Fuzzy Decision System (FDS) which is being described with details in Section 5.1.1.
- The voting procedure will be started after the previous step to choose the most suitable sensor-nodes as RPs.
- The mobile-sink determines its sojourn locations based on the selected RPs.
- The rest of sensor-nodes will be assigned to the appropriate RPs based on our designed methodology for constructing balanced routing trees as explained in Section 5.2.
- After identifying the sojourn locations, the mobile-sink stops in each sojourn location to harvest data from the RPs which are being assigned to that specific sojourn location. Since the sensor-nodes are event-driven and their data includes information about an (some) event(s), the mobile-sink should harvest all of the buffered data from the RPs. To determine the waiting-time, the mobile-sink broadcasts a message by arriving to a sojourn location to inform the RPs about its arrival. Then RPs reply a message which includes the amount of their buffered data. And finally based on the channel capacity, the mobile-sink can calculate the required waiting-time. It should be mentioned that if during the waiting-time a RP receives new data, it informs the mobile-sink to extend the waiting-time.
5.1.1. Fuzzy Decision System
- Residual energy is the main factor for a sensor-node to be selected as RP. We designed the following linguistic variables to describe the amount of remaining energy for a sensor-node; very high, high, medium, low, and very low. Figure 5a illustrates the membership functions to map the crisp values of residual energy to the related linguistic values. The membership functions for the linguistic variables high, and very low are trapezoidal and triangular for the rest of linguistic variables.
- Number of neighbor-nodes is another factor that determines the popularity of a sensor-node in case of being selected as RP. In this factor, we just consider the sensor-nodes that can contact with the candidate-node directly. Therefore, a sensor-node with highest number of neighbor-nodes is more desirable. We defined three linguistic variables to describe the number of neighbor-nodes which are high, medium, and low. In Figure 5a, the membership functions for high and low are trapezoidal and for medium triangular.
- Distance from Mobile-Sink is the third factor in our designated Fuzzy inference system that is for obtaining the required energy for the sensor-node to contact with the mobile-sink in case of being selected as RP. Clearly, when a sensor-node is closer to the sojourn location, it can conserve its residual energy and extend the lifetime of the network. In the Fuzzy inference system, as shown in Figure 5b there are three linguistic variables to describe the distance from mobile-sink; high, medium, and low. The membership functions for high and low are trapezoidal and for medium the membership function is triangular.
5.1.2. RP-Selection
5.1.3. Sojourn Locations Selection
Algorithm 1: RP-Node Selection |
Input: i) Candidate RPs, , ; ii) Neighbor-Nodes, , and ; Output: i) RP-Nodes, , ; ii) The first group of sensor-nodes which follow the RPs, ; |
- If there is only one RP in the periphery of the trajectory and this RP cannot contact with other RPs, then the mobile-sink considers the closest distance to the RP as sojourn location.
- If there are two RPs which are in the communication range of each other, as shown in Figure 6, we should balance energy consumption among the RPs for data communication. To illustrate our solution, we follow the example in Figure 6 in which there are two RPs A and B. The line specifies the intersected trajectory that the sojourn location should be selected for covering the two RPs. To obtain the position that can balance energy consumption, we select the middle of which is identified as M. By comparing with the point M moves to the direction that has larger amount of energy consumption in the line . If then we can obtain the optimal solution. And if in we cannot obtain the optimal solution but obviously we can achieve to the most possible near optimal solution.
- For the condition that there are more than two RPs in the periphery of the trajectory, we proposed Algorithm 2 that is described with details in the following.
Algorithm 2: Determining Sojourn Locations |
Input: i) RP-Nodes, , ; ii) The trajectory of the mobile-sink, , ; Output: i) Sojourn locations, , ; |
5.2. Stage III: Constructing the Routing Tree
Algorithm 3: Constructing Balanced Routing Tree |
Input: i) The set of all the sensor-nodes that can contact with RPs, directly, ; Output: i) Routing Tree for each RP; |
6. Numerical Results
6.1. Parameter Settings
6.2. Network Life-Cycle
6.3. Energy Consumption
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Residual Energy | Number of Neighbor-Nodes | Distance from Mobile-Sink | Potentiality |
---|---|---|---|
Very High | High | High | Low |
Very High | High | Medium | Low |
Very High | High | Low | Low |
Very High | Medium | High | Medium |
Very High | Medium | Medium | Medium |
Very High | Medium | Low | High |
Very High | Low | High | High |
Very High | Low | Medium | High |
Very High | Low | Low | High |
High | High | High | Low |
High | High | Medium | Low |
High | High | Low | Low |
High | Medium | High | Medium |
High | Medium | Medium | Medium |
High | Medium | Low | High |
High | Low | High | High |
High | Low | Medium | High |
High | Low | Low | High |
Medium | High | High | Medium |
Medium | High | Medium | Medium |
Medium | High | Low | Medium |
Medium | Medium | High | Low |
Medium | Medium | Medium | Medium |
Medium | Medium | Low | High |
Medium | Low | High | Medium |
Medium | Low | Medium | Medium |
Medium | Low | Low | Medium |
Low | High | High | Very Low |
Low | High | Medium | Very Low |
Low | High | Low | Low |
Low | Medium | High | Very Low |
Low | Medium | Medium | Very Low |
Low | Medium | Low | Low |
Low | Low | High | Very Low |
Low | Low | Medium | Very Low |
Low | Low | Low | Low |
Very Low | High | High | Very Low |
Very Low | High | Medium | Very Low |
Very Low | High | Low | Very Low |
Very Low | Medium | High | Very Low |
Very Low | Medium | Medium | Very Low |
Very Low | Medium | Low | Very Low |
Very Low | Low | High | Very Low |
Very Low | Low | Medium | Very Low |
Very Low | Low | Low | Very Low |
Parameter | WSN#1 | WSN#2 | WSN#3 | WSN#4 |
---|---|---|---|---|
Area (L × L) | 100 × 100 | 100 × 100 | 200 × 200 | 200 × 200 |
Number of sensor-nodes | 100 | 100 | 200 | 200 |
Initial energy of the sensor-nodes | 0.5 J | 0.5 J | 0.5 J | 0.5 J |
Communication radius of sensor-nodes | 10 m | 10 m | 20 m | 20 m |
50 nJ/bit | 50 nJ/bit | 50 nJ/bit | 50 nJ/bit | |
10 pJ/bit/ | 10 pJ/bit/ | 10 pJ/bit/ | 10 pJ/bit/ | |
0.0013 pJ/bit/ | 0.0013 pJ/bit/ | 0.0013 pJ/bit/ | 0.0013 pJ/bit/ | |
Energy for data aggregation () | 5 nJ/bit | 5 nJ/bit | 5 nJ/bit | 5 nJ/bit |
Aggregation rate | 0.6 | 0.8 | 0.6 | 0.8 |
Control packet | 200 bits | 200 bits | 200 bits | 200 bits |
Message packet | 4000 bits | 4000 bits | 4000 bits | 4000 bits |
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Vajdi, A.; Zhang, G.; Zhou, J.; Wei, T.; Wang, Y.; Wang, T. A New Path-Constrained Rendezvous Planning Approach for Large-Scale Event-Driven Wireless Sensor Networks. Sensors 2018, 18, 1434. https://doi.org/10.3390/s18051434
Vajdi A, Zhang G, Zhou J, Wei T, Wang Y, Wang T. A New Path-Constrained Rendezvous Planning Approach for Large-Scale Event-Driven Wireless Sensor Networks. Sensors. 2018; 18(5):1434. https://doi.org/10.3390/s18051434
Chicago/Turabian StyleVajdi, Ahmadreza, Gongxuan Zhang, Junlong Zhou, Tongquan Wei, Yongli Wang, and Tianshu Wang. 2018. "A New Path-Constrained Rendezvous Planning Approach for Large-Scale Event-Driven Wireless Sensor Networks" Sensors 18, no. 5: 1434. https://doi.org/10.3390/s18051434
APA StyleVajdi, A., Zhang, G., Zhou, J., Wei, T., Wang, Y., & Wang, T. (2018). A New Path-Constrained Rendezvous Planning Approach for Large-Scale Event-Driven Wireless Sensor Networks. Sensors, 18(5), 1434. https://doi.org/10.3390/s18051434