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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Recent research has indicated that using the mobility of the actuator in wireless sensor and actuator networks (WSANs) to achieve mobile data collection can greatly increase the sensor network lifetime. However, mobile data collection may result in unacceptable collection delays in the network if the path of the actuator is too long. Because real-time network applications require meeting data collection delay constraints, planning the path of the actuator is a very important issue to balance the prolongation of the network lifetime and the reduction of the data collection delay. In this paper, a multi-hop routing mobile data collection algorithm is proposed based on dynamic polling point selection with delay constraints to address this issue. The algorithm can actively update the selection of the actuator's polling points according to the sensor nodes' residual energies and their locations while also considering the collection delay constraint. It also dynamically constructs the multi-hop routing trees rooted by these polling points to balance the sensor node energy consumption and the extension of the network lifetime. The effectiveness of the algorithm is validated by simulation.

A wireless sensor network is composed of a number of collectors and many low-cost, resource-limited sensor nodes. Sensor nodes are distributed in the region of interest, collect sensor data from that region and, then, forward those data to a remote data sink for environmental monitoring, military surveillance, fire detection, animal tracking or other applications. Because it is difficult to replace or recharge sensor node batteries while the sensor node is in service, one of the main concerns of a wireless sensor network is to increase its energy efficiency.

In traditional wireless sensor networks, the locations of sensor nodes and data sinks are fixed once they have been distributed, and the data created by the sensors are forwarded to the sinks by a multi-hop relay. Network efficiency is increased by optimizing the scheduling policy, aggregate routing [

In wireless sensor actuator networks, mobile data gathering is achieved by the mobility of the actuator and unlimited hardware resources to reduce energy consumption. During each data gathering period, the actuator starts from the sink, travels through the entire network and collects the data from nearby sensor nodes while in motion, before returning to forward its collected data to the sink. In ideal circumstances, the actuator's moving distance is not limited. It is able to visit all of the sensor nodes in the network in order, communicating with the sensor nodes by single-hop relay, thus minimizing energy consumption during communication. However, in practical applications, strict restrictions are placed on the data collection delay. Thus, the key issue of using actuators in wireless sensor networks is planning reasonable paths for the actuator and optimizing the data exchange mechanisms with the sensor nodes.

Further research indicates that actuators increase the energy efficiency of wireless networks by reducing the number of relay hops within the network. However, the sensor nodes close to the polling points still require the transmission of more data packets whose energies expire quickly, leading to non-uniform energy consumption and restricting the network's lifetime. With meeting the network convergence delay requirements as a prerequisite, this paper aims to increase the network lifetime by proposing a multi-hop routing mobile data collecting algorithm based on dynamic polling point selection under delay constraints. The dynamic selection of polling points will improve the network's energy efficiency and extend the network lifetime as much as possible; multi-hop communications and an optimized actuator moving path will guarantee the network data collection delay.

The rest of this paper is organized as follows. In Section 2, related works are reviewed. In Section 3, assumptions concerning the integer linear programming (ILP) problem and its formulation are discussed. In Section 4, a uniform energy consumption algorithm is introduced. In Section 5, the comparative performance evaluation and simulation results are shown. Finally, the conclusions are drawn in Section 6.

The issue of energy efficiency has been extensively studied in static wireless sensor networks. Those works have mostly focused on energy conservation or the balancing of energy consumption. The methods suggested to reduce network energy consumption include one or more of the following: topology controls, transmission power control, sensor node scheduling, coverage control, clustering and energy efficient routing.

Recent works have exploited the availability of the controlled mobile actuators to balance the energy consumption of sensor nodes. Based on the mobile actuator's transmission hop numbers, the existing research works are classified into two categories: single hop and multiple hops. In the first category, the mobile actuators only collect data from sources within a single hop. In [

The second category allows the mobile actuators to collect data via multi-hop routings. The maximum amount shortest path (MASP) data collection strategy proposed by Gao

Utilizing multiple actuators can reduce the network energy consumption further and also improve the data delivery ratio [

Those approaches can effectively reduce the energy consumption and extend the network lifetime. However, they do not impose any constraint on the data latency caused by the actuator's mobility. In [

Further research shows that the sensor nodes adjacent to the actuator's current polled position still need to forward more data packages. Therefore, those sensor nodes exhaust their energy earlier than other sensor nodes, which results in non-uniform energy consumption and constraints on the network lifetime. To address this problem, this paper proposes a uniform energy consumption algorithm for wireless sensor and actuator network (WSAN) based on dynamic polling point selection.

The algorithm must address two key problems: (1) how to generate the shortest path tree of the network; and (2) how to select the polling points and drive actuator movements to meet the constraints on data collection delay. In particular, to balance the energy consumption, the sensor node's residual energy should be incorporated into the algorithms, so that the path tree and actuator movement can be updated dynamically.

In this section, the definitions of the network lifetime, in-degree and energy consumption model are given. We then present the system network topology using graph-theoretical methods. We assume that the system network topology of WSAN (excluding the actuators and the sink) is a tree structure, which has been widely discussed by previous works. At the same time, several assumptions of the network are proposed as basic conditions. We then propose a energy consumption model for each component of the network and derive the cost between neighboring sensor nodes. Accordingly, an integer linear programming (ILP) problem, called the energy efficient relay, and a sink routing problem are formulated, and the definition of the problem is given.

From the literature [

The in-degree is one of the most essential concepts of the graph theory. There is a good deal of literature illustrating the concept of the in-degree. The definition of the in-degree is illustrated below:

Definition 1: For the case of undirected graph, _{1},_{2},…,_{n}_{i}_{j}_{j}_{i}_{i}_{j}_{i}_{i}_{ij}_{ij}_{i}_{j}_{i}_{i}_{i}^{+}(_{i}_{i}^{−}(_{i}_{i}_{i}^{+}(_{i}^{+}(_{i}_{i}^{−}(_{i}^{−} (_{i}_{i}^{+}(_{i}^{−}(_{i}_{i}

A sensor node is composed of the sensors, processing unit, memory, RFtransceiver and battery. The total energy consumption by the sensor node can be expressed as the sum of the energy consumption by each element [

First, the energy consumption by the sensor is expressed as follows:
_{stabilization}_{measure}_{sensor}_{soft}_{μc}_{μc}

After that, the data transmission depends on the goal of the application. In some cases, it is possible to aggregate several measurements before sending data. In other applications, the data are sent only when an event is detected. Moreover, in many cases, a receiver is needed to acknowledge the sender, to respond to the data sink request and to relay data from another sensor node. The energy consumption of the transmitter and receiver is defined as, respectively:
_{bits_trans}_{bits_recv}_{inst}_{trans}_{recv}

Finally, the consumption of the microcontroller is expressed as follows:

The network topology of the WSANs is modeled as a directed graph, _{1}, _{2}, …, _{n}_{i}_{j}_{i}_{j}_{ij}

There are several assumptions for the WSAN:

The sensor nodes are stationary and distributed in a two-dimensional region. All the sensor nodes have the same transmission power and initial energy. Additionally, these sensor nodes operate in the duty cycle mechanism [

The actuators have no energy limit and can move freely throughout the region to collect data and then upload to the sink; when the actuator collects data, the sensor node will send its active time window, attaching to the sensor data packets to polling points, which then relay these data to the actuator, so that the actuator can update the sensor node state and select an active sensor node set properly.

Certain sensor nodes are chosen as polling points, which aggregate the data from sensor nodes and deliver them to the actuator. The actuator will visit those polling points one by one and, finally, return to the sink.

The data traffic originates from each sensor node with a fixed generation rate and flows to one of the polling points within a single-hop or multi-hops. Polling points have sufficient storage capacity to buffer the total volume of data generated by the sensor nodes within delivery deadline

The actuator moves with a constant speed,

The sensor nodes and actuators are assumed to know their own physical locations through the GPS or a locations service in the network.

Sensing, information processing and data transmitting and receiving are three factors in the energy consumption of a sensor node.

Assumptions (i) and (ii) guarantee that the best possible energy saving and balancing under the time-constraint can be achieved; an actuator's tour is defined by assumption (iii); that is, the location of the polling points will be the sojourn points of the actuators. Nesamony

In addition, we ignore the influence of transmission interference between relevant sensor nodes and data error during transmission, so some additional assumptions are proposed as follows: (1) end-to-end data transmission is assumed to be reliable; and (2) radio interference can be avoided by a multiplex mechanism, such as frequency-division multiplexing (FDM), time-division multiplexing (TDM) or code-division multiplexing (CDM).

In this paper, the polling-based, multi-hop mobile data collection scheme can be formulated into an optimization problem, called the energy efficient relay and moving path-planning problem. The problem clearly consists of two sub-problems. The first is the energy minimization path-planning problem. The second is the energy balancing load assignment problem. The two problems can be formulated as the following integer linear programming (ILP) problem, which is formulated by

Its optimal objective is represented by

There are key constraints that must be considered for practical data collection applications. The constraints should be comprised of aspects, such as: the polling point selection, the data packet routing, avoiding repeated loop visits and the moving length and total energy constraints. The following

The objective of this paper is to solve the two sub-problems: the energy balancing load assignment problem and the energy minimization path-planning problem. Due to the constraints of the ILP problem, the two sub-problems can be translated into the following issues: (1) the generation of the shortest path tree of the network; and (2) the selection of the polling points and the strategy for actuator movement.

In this section, we first discuss how to generate the shortest path tree with the cost between neighboring active sensor nodes in order to guarantee uniform energy consumption. Then, to solve the energy minimization path-planning problem, the algorithm for polling point selection and the strategies for actuator movement are presented. According to the above algorithms, a new algorithm, the in-degree priority algorithm (IPA), is introduced, which considers not only the distance between the neighboring sensor nodes, but also their residual energy. Finally, the case of multiple actuators is discussed by expanding IPA to the multiple actuator uniform energy consumption problem, called the in-degree priority algorithm for multiple mobile actuator (IPA-MMA).

In WSAN, the sensor nodes gather information and transmit data to the sink through single-hop or multi-hop communication. Thus, it is necessary to generate a tree with a root node that is the active sensor node nearest to the sink and with leaf nodes that are the other active sensor nodes transmitting data to the root node directly or via polling points. There are some works in the literature discussing how to create a shortest path tree (SPT). Xing

In this study, a definition of link cost _{ij}_{ij}_{ij}_{i}_{j}_{ij}_{ij}_{ij}

The energy consumption of a sensor node is related to two factors, the in-degree of the sensor node and the distance to its neighboring sensor nodes. Thus, the higher the in-degree and the longer the distance, the more easily the energy of the sensor node is exhausted. Based on these principles, a method of polling point selection and a strategy of actuator movement are proposed. The actuator movement strategy is actually to find the shortest round trip among the polling points and the sink, which is exactly the traveling salesman problem (TSP). We run the nearest neighbor algorithm [

However, the actuator does not have to go to the exact locations of the polling points to receive data, because the polling points have a communication range and can transmit the data to the actuator within the communication range. The communication range can be incorporated into the algorithm to further improve the efficient utilization of energy, so the location of polling points would be modified to a new nearby location according to the communication range of the polling points. In the paper, the modified location could be calculated by the “runtrack” algorithm to reduce the average hop number further [

First, a dynamic shortest path tree of the network is constructed as in Section 4.1, denoted by

The covered sub-tree, denoted by _{a}_{a}

An example is given in

In _{ij}_{i}_{j}

In this research, an in-degree priority algorithm (IPA) is introduced, which is comprised of two parts: (1) the generation of a shortest path tree with cost _{ij}_{a}_{u}

_{a}

_{u}

_{ij}

_{i}

_{j}

_{ij}

_{a}

_{a}

_{i}

_{i}

_{i}

_{a}

_{tsp}

_{a}

_{a}

_{tsp}

_{i}

There are two functions in the IPA algorithm. One is _{a}_{a}

The time complexity of IPA has three parts: the construction of a shortest path tree, the selection of polling points and the traveling salesman problem. We assume that there are a total of ^{2}) time to find the shortest path tree using the Dijkstra algorithm. The actuator's moving length is expanded by approximately half of the moving length in the last iteration, and one TSP tour is computed in the current iteration. The number of iterations is in the order of ^{2} +

By analyzing the spatial complexity of the IPA algorithm, its memory requirements can be estimated. In the IPA algorithm, the input parameters and temporal variables include the node coordinates, the in-degree, the residual energy and the address, so the space complexity is ^{2} + ^{2} + 6

Now, IPA is expanded to the multiple actuator uniform energy consumption problem, called IPA-MMA. IPA-MMA is based on the algorithm proposed by Zhao _{j}_{j}_{e}

When there are

In this section, several simulations have been conducted to compare and evaluate the behavior of our approach. The first group of simulations focuses on evaluating the network lifetime of three algorithms (IPA, SPT-DGA (data gathering algorithm) [

SPT-DGA is the shortest path tree based data gathering algorithm. The basic idea of SPT-DGA is to iteratively find a polling point among the sensor nodes on a shortest path tree, which is the nearest sensor to the root that can connect the remote sensors on the tree. Additionally, each polling point strives to link as many sensor nodes as it can reach within the relay hop bound to minimize the total number of polling points. RD-VT is the rendezvous design for variable tracks algorithm, for which the basic idea is to find a sub-tree, such that all the polling points on the sub-tree can be visited by a BStour no longer than

SPT-DGA and RD-VT do not consider the sensor nodes' residual energy, so the generated path tree is not dynamically updated; consequently, the selected polling points remain unchanged. However, in the proposed algorithm, IPA, the sensor nodes' residual energy is incorporated into the generated path tree; so, the path tree updates dynamically, and every round, new points would be selected as the polling points.

In the worst case scenario, the time complexity of SPT-DGA is ^{2} +^{o}^{(}^{b}^{)}), for which ^{2} +

In this section, the simulation scene is constructed, and the parameters are set. There are

In the simulations, the network lifetime performance and energy consumption performance are compared among the above algorithms, IPA, SPT-DGA and RD-VT. By adjusting the simulation network scale, the flexibility of the proposed algorithm, IPA, is demonstrated. Using two groups of 3D figures, the energy uniformity features of these algorithms are analyzed, showing that the main characteristic of the proposed algorithm is to balance the network sensor node energy consumption. In addition, the simulation of multiple actuators is implemented to verify the effectiveness of IPA-MMA.

In this section, we investigate the expected network lifetime for the sensor network model with different network scales. As shown in

From the simulation results shown in

In this section, we compare the three algorithms' network energy consumption over time, where the number of sensor nodes

In this section, the performance of algorithms for uniform energy consumption is analyzed using two groups of 3D figures. In every 3D figure, the

As shown in

In this section, the energy consumption performance for the multi-actuator case where the number of sensor nodes,

IPA-MMA takes the sensor node's residual energy as one of the division parameters. Firstly, IPA-MMA constructs the shortest path tree using

IPA-MMA divides the sensing fields dynamically. The compared algorithms, SPT-DGA and RD-VT, with fixed divisions, will result in more energy consumption for center nodes, and energy holes are also created. IPA-MMA updates its division after certain rounds according to the new residual energy distribution and balances the weight of each division again. Thus, more uniform energy consumption can be achieved than the compared algorithms.

This paper has suggested a path-planning algorithm for the actuator in a wireless sensor-actuator network to collect data in delay-constrained real-time applications, especially for large-scale networks. In this algorithm, the shortest path tree topology is dynamically reconstructed using the residual energies in the sensor nodes as the weights based on an integrated energy model, which considers energy consumed during communications, node sensing and data processing, describing the energy consumption more closely to actual circumstances. Polling points are chosen for each round based on the in-degrees of sensor nodes in the shortest path tree. Additionally, the new polling point selection method takes into consideration the actuator communication range, so that the actuator can visit more polling points, while under the same time constraint, and increase network lifetime. The energy efficiency of large networks is thus raised at the cost of a slight increase in algorithm complexity. In order to address the application for multiple mobile actuators, an IPA-MMA algorithm is also proposed to adapt to large-scale networks. The simulation results show that the network lifetime is greatly extended at the cost of moderately increasing the total energy consumption of the network.

In the future, the variation of data transmission frequencies and the limitations of sensor node data buffers can also be incorporated into the algorithm design. Additionally, more delicate techniques based on convex optimization might be adopted to address the data collection problem when integrating these factors more flexibly.

This work is partially supported by the National Natural Science Foundation of China No. 61071096, 61073103, 61003233 and 61379111 and the Specialized Research Fund for Doctoral Program of Higher Education No. 20100162110012 and 20110162110042.

The authors declare no conflict of interest.

(

The polling point selection of in-degree priority algorithm (IPA). The black nodes represent the active sensor nodes; the triangle represents the sink, and the hollow nodes represent the polling points selected by the algorithm. IPA iterates four times and selects four polling points.

The dynamic moving path planning of IPA. The edges of the red polygons represent the moving path of the mobile actuator, and the blue circles represent the communication range of the polling points. IPA periodically reconstructs the shortest path tree and then re-selects the polling points before dynamically adjusting the path planning of the actuator.

Network lifetime comparison for three algorithms. The

Network energy consumption comparison for three algorithms. The

Distribution of network energy consumption with IPA. The

Distribution of network energy consumption with shortest path tree data gathering algorithm (SPT-DGA). The

Energy consumption

Notations used.

_{k} |
the sensor node set of the region assigned to actuator k; |

_{iu} |
if sensor node _{iu} |

_{u} |
if sensor node _{u} |

_{iju} |
if the data of sensor node _{iju} |

_{ij} |
if sensor node _{ij} |

_{uk} |
if sensor node _{uk} |

_{pqk} |
if link (_{pqk} |

_{pq}_{ij} |
the length of link ( |

_{init} |
the initial energy of the sensor node. |

Simulation parameters of different network scales.

18 | 30 × 30 | 20 |

32/50 | 40 × 40 | 30 |

72/98/128 | 70 × 70 | 100 |

162/200/242 | 100 × 100 | 200 |

288/338/392/450/512 | 150 × 150 | 450 |

578/648/722 | 200 × 200 | 700 |

841 | 500 × 500 | 850 |

1,156 | 1,000 × 1,000 | 1,000 |