Research on energy efficient fusion-driven routing in wireless multimedia sensor networks

A. System model

Network model: In this article, we adopt a WMSN formed by n randomly deployed sensor nodes, denoted by S= {s₁, s₂, ..., s _n } and only one static sink node acts as the destination of the whole network. All the sensor nodes are used for data collection in the monitoring area and keep stable after the deployment. In addition, for improving the performance of WMSNs, we also introduce m mobile agent nodes, denoted as G = {g₁, g₂, ..., g _m }, where m is far less than n due to their higher cost. These agent nodes can control their moving traces and are responsible for collecting the sensory data generated by the surrounded sensor nodes, then relay to the sink node. The main distinguished features of the system are as the followings:

We focus only on the communications among the sensor nodes, the mobile agents, and the sink node, whereas the communications between the sink node and devices outside the network are out of the scope of this article.

where D(s _i , p) and D(s _j , p) represent the data amount of attribute p generated by node s _i and s _j , respectively. σ represents the data correlation coefficient between node s _i and s _j . From this equation, it can be seen that the higher σ can generate less data amount.

Energy model: We assume that all the nodes have the same initial energy while only the sink node and mobile agent node are not limited by energy supply. Similar to [19], the energy spent by transmitting 1 bit data over distance d is e _t (d) = ε_elec + ε_amp · d ^k , where ε_elec is the energy spent by transmitter electronics, ε_amp is the transmitting amplifier, and k(k ≥ 2) is the propagation loss exponent. ε_elec and ε_amp are both system parameters. The corresponding energy dissipation in data reception is e _r = ε_elec. In addition, although data fusion can reduce the energy consumption, it still introduces the extra energy consumption, where each fusion for 1 bit data is denoted by e _f .

B. Problem statement

Now we begin to formulate the problem. As shown in Figure 1, the multimedia sensor network consists of three parts: a large amount of sensor nodes, some mobile agent nodes, and one sink node. These mobile agent nodes are uniform distributed in the network, then the whole network is divided into some clusters. Each cluster has one agent node act as cluster head which needs to manage the data collection in its cluster. According to different task requirements, sensor nodes complete data collection and send the sensory data to agent node in their cluster, then the agent node relays these data to the sink node. To meet the requirements of different tasks, the network is carried with a series of various sensors. Each kind of sensor can generate data with different attributes. We assume that there are t kinds of sensors, then there are t kinds of sensory data with different attributes. Each sensor node is equipped with q (1 ≤ q ≤ t) kinds of the sensors.

Data collection is divided into two phases, one is intra-cluster collection and the other one is inter-cluster collection. For the intra-cluster collection, the sensor nodes are the source and the agent node is the destination. For the inter-cluster collection, the agent node is the source and the sink node is the destinations. As the communication capacity of sensor node is limited, most of them cannot directly transmit the data to the mobile agent node; hence multi-hop transmissions are necessary to solve this problem. For avoiding the data loss, each sensor node needs to establish at least one path to the mobile agent in its cluster.

Definition 3.1 Data collection space: Let D _p be the data set that complete the p kind of task for data collection. Each kind of task corresponds to one kind of data set, and we assume there are k kinds of tasks. Then, the generated k kinds of data sets compose the data collection space, denoted as $\hat{D}=D_1\times D_2\times \cdots \times D_k$.

Definition 3.2 Efficient data fusion: Only those fusion processes that can reduce the energy consumption of network are regarded as efficient data fusion.

Definition 3.3 Energy efficiency: Energy efficiency refers to complete the task with the least energy while the energy consumption is more balanced.

where x(s _i , s _j ) represents whether a connection exists between node s _i and s _j . If node s _j is the forwarding node of node s _i , then x(s _i , s _j ) = 1, otherwise x(s _i , s _j ) = 0. e(s _i , s _j ) represents the energy consumption on the edge from node s _i to s _j consists of three components: node s _i transmitting data, node s _i receiving data and fusing data. In Equation 2, the constraint specifies that the node s _i has only one forwarding node.

A. Network topology

As shown in Figure 2, we divide the network into cluster and each cluster is composed by a series of grids. Both cluster and grid are square structure. There are many sensor nodes randomly deployed in each cluster, and the blue dots are the mobile node, which acted as cluster head. With increasing the communication distance, the energy consumption increases quickly, so it should avoid a long distance of single hop. Therefore, we adopt three kinds of communication distance for such topology. The longest one is used for mobile agent node to receive and transmit data from a long distance between different cluster, marked as R. The rest two short transmission distances are, respectively, used for data transmission between different sensor nodes in same and neighbor grid, marked as r and r'. The communication range should also cover all the possible nodes to guarantee that there is no data loss during the transmission. Suppose the length of each grid is a, this condition for any two sensor nodes in the same grid that can communicate is $r\ge \sqrt{2}a$ while any two sensor nodes in the neighbor grid is $r^{\prime }=\sqrt{5}a$.

The square grid that we adopted has strong regularity and is easy to be analyzed. When the sensor nodes are deployed in uniform, the number of sensor node in each grid is same. Without loss of generality, we suppose that all nodes are random deployed, which make the number of sensor nodes in each cluster and grid are different. Then, we will analyze the energy efficiency of intra-grid and inter-grid.

B. Energy efficient data fusion of intra-grid

where D _ut (x,y), D _ur (x,y), D _uf (x,y) represent the total data amount of sensor nodes of grid g _u (x,y) in time T for transmitting, receiving, and fusing.

From Equation 4, it can be seen that the energy consumption is determined by the data amount of the above three operations. Aiming for energy efficiency, we need to judge whether sensor nodes should complete data fusion process during intra-grid data collection. D(s _i ) and D(s _j ) represent the data amount generated by node s _i and s _j in grid g _u (x,y). The decision of whether proceeding data fusion of intra-grid is based on the following theorem.

Theorem 1: ∀s _i , s _j ∈ g _u (x,y), the condition of intra-grid data fusion that can save energy is: $\sigma >\frac{D\left(s_i\right)\left[e_t\left(a\right)+e_r+e_f\right]+D\left(s_j\right)e_f}{min\left(D\left(s_i\right),D\left(s_j\right)\right)e_t\left(\sqrt{2}a\right)}$.

Hence, Theorem 1 is proved.

It can be seen from Theorem 1 that the energy-saving degree of fusion process is determined by the relativity of the processed data when the data amount is known.

C. Energy efficient data fusion of inter-grid

In Section 4.2, we have proved the condition of intra-grid data fusion that can save energy. Now, we will analyze the performance of data fusion of inter-grid. Based on the above analysis, this problem can be transformed to judge whether fusing the data from two different grids can save energy. As shown in Figure 3, g _u (x,y) and g _u (x',y') are two grids which have sensory data need to transmit to the mobile agent node g _u . To complete data collection, the nodes in two grids need to establish the path that can arrive at g _u . If the data in two grids need to be fused, their data transmission routes ought to meet at one grid before reaching the destination g _u . For example, the route of s _i in g _u (x,y) and s _j in g _u (x',y') meet at grid g _u (x₀,y₀).

Theorem 2: ∀s _i ∈ g _u (x,y), s _j ∈ g _u (x', y'), the condition of inter-grid data fusion that can save energy is $\sigma >\frac{\left[D\left(s_i\right)+D\left(s_j\right)\right]e_f}{min\left(D\left(s_i\right),D\left(s_j\right)\right)\left(e_t\left(\sqrt{2}a\right)+e_r\right)\left(\mid x_0\mid +\mid y_0\mid \right)}$

In the other situation, the routes of s _i and s _j to mobile agent node g _u meet at grid g _u (x₀, y₀), then their data are fused.

Hence, Theorem 2 is proved.

We can use Theorem 2 to direct the routing establishment and find the optimization strategy for saving energy. According to this point, the nodes in the same grid may establish different routes to the mobile agent node.

A. Cluster and grid division

The topology division of network includes the following two steps. The first is to divide the network into a series of larger equal square area and each square represents one cluster. There is only one mobile agent node in each cluster which can move freely. The second one is to further divide the cluster into many smaller equal square, and each square represents one grid. For the sake of avoiding data loss during transmission, the size of grid is not too large but should guarantee the communication of two random nodes in the neighbor grids. When the sensor node knows which grid it belongs to, it needs to broadcast the information with identification and receive the information from other nodes in the neighbor grid.

For completing more complicated tasks, sensor nodes are equipped with many different sensors so that the traditional data collection model is not valid. The network needs to complete more than one task, that one task is respond to one data set as described in Definition 3.1, then all the data sets compose of the data space. The mobile agent node needs to arrange the suitable nodes to complete data collection according to different tasks.

As shown in Figure 4, the operation procedure of EEFR is divided into a number of rounds and each round includes two phases, namely set-up phase and steady-state phase. The working process of set-up phase needs to complete the movement of mobile agent node, the establishment of routes, and the distribution of time-slot allocation. In steady-state phase, the sensor nodes complete the data collection under the management of mobile agent node.

B. Movement of mobile agent node

When the mobile agent node moves to a new position, the coordinate of the grid will also change. Only the sensor nodes in the grids with the coordinate of (1, 1), (1, -1), (-1, -1), and (-1, 1) can directly send data to mobile agent node while all the other sensor nodes need to send their data to the mobile agent node by multi-hop method. In EEFR, multi-hop routes are formed between neighbor grids from source node to the mobile agent node, which can guarantee the sensory data generated by the farthest node not be lost. The data collection of inter-cluster starts from the outermost grid and ends when all data are transmitted to the mobile agent node. One-to-one or many-to-one mappings are formed among sensor nodes of neighbor grid. If a sensor node in grid g _u (x, y) has sensory data to be transmitted, it needs to select the corresponding relay node from its neighbor grids which is much closer to the mobile agent node. For example, when x, y > 0, the selected relay node should be in the grid g _u (x-1, y) or g _u (x, y-1). In this case, g _u (x, y) acts as a source grid, while g _u (x-1, y) or g _u (x, y-1) acts as the destination grid.

The data collection involves in many kinds of sensors to complete different tasks in EEFR. According to the Definition 1 in Section 3, the data collection space $\hat{D}$ consists of k data sets and denoted as $\hat{D}=D_1\times D_2\times \cdots \times D_k$. Each data set includes sensory data in different attributes.

where d and d _s represent the maximum correlation distance between nodes and the space distance between two sensor nodes, f represents the effect of the fusion algorithm on the data correlations, and p is the data attribute.

The mobile agent node is responsible to find the efficient data fusion which can reduce the energy consumption in its cluster and achieve the optimization target to direct the establishment of routing. Based on Theorems 1 and 2, we can judge whether the data fusion is effective and take use of the mobility of agent node to maximum the performance of saving energy by data fusion. s _i and s _j are any two nodes in different grid of the same cluster. The following Lemma 1 gives the calculation method of finding the mobile agent position which can realize the efficient data collection using the efficient data fusion in maximum.

Lemma 1: The energy efficiency can be realized if the location of a mobile agent node can meet the requirement of $max{\sum }_{s_j\in g_u\left(x^{\prime },y^{\prime }\right)s_i\in g_u\left(x,y\right)}\left[D\left(s_i\right)+D\left(s_j\right)\right]e_f-\left(e_t\left(\sqrt{2}a\right)+e_r\right)\left(\mid x_0\mid +\mid y_0\mid \right)\sigma \left(s_i,s_j\right)min\left(D\left(s_i\right),D\left(s_j\right)\right)$

Hence, Lemma 1 is proved.

According to different tasks, the mobile agent node can find the optimized position by Lemma 1, then complete the establishment of intra-cluster routing.

C. Routing establishment

Although the minimizing energy consumption is the prior target during the routing establishment, EEFR also try to balance the energy consumption among different sensor nodes. As the sensor nodes are deployed in high density, more than one node might meet the requirement of minimizing energy consumption during routing establishment. For the sake of balancing the energy consumption, the node with more remaining energy should be selected to undertake the routing task. The routing selection includes three steps.

The first step: the mobile agent node determines the sensor nodes to complete data collection in its cluster according to different tasks, then calculates the optimization position by Lemma 1. As shown in Figure 5a, the three optimization positions of mobile agent nodes data are separately found according to different data sets D₁, D₂, and D₃ generated by different tasks. Where, the black, purple, and green dots are the nodes generating data sets D₁, D₂, and D₃.

The second step: the mobile agent node determines the sensor nodes that participate the intra-grid data fusion by Theorem 1, and point the nodes with more remaining energy to complete the fusion by Theorem 1. As shown in Figure 5b, the nodes with short distance in the same grid participate intra-grid fusion process since they can meet the requirement of Theorem 1, while the nodes in long distance are forbidden in such operations.

For saving energy consumption, it is a general method to make the sensor nodes turn to sleep when they do not have any task. EEFR routing also adopts time-slot allocation to reduce the probability of communication collision and save energy. Let t_intra and t_inter represent the consumed time of intra-grid and inter-grid data fusion process. n_max-frepresents the maximum number of each grid to complete intra-grid fusion process. n _t (x, y) is the number of sending data from grid g _u (x, y) to other grids, n _r (x, y) is the number of receiving data of grid g _u (x, y) from other grids. T _u is the running time of a round. The following Lemma 2 gives the allocated operating time of a random grid g _u (x, y):

Lemma 2: For ∀g _u (x, y), the allocated operating time is $\frac{\left\{n_{max-f}{t}_{\mathsf{\text{intra}}}+\left[n_t\left(x,y\right)+n_r\left(x,y\right)\right]t_{\mathsf{\text{inter}}}\right\}{T}_u}{n_{max-f}{t}_{\mathsf{\text{intra}}}+{\sum }_{g_u\left(x,y\right)\in C_u}\left[n_t\left(x,y\right)+n_r\left(x,y\right)\right]t_{\mathsf{\text{inter}}}}$.

Hence, the allocated operation time of each grid is $T\left(x,y\right)=T_u\left[T_{\mathsf{\text{inter}}}\left(x,y\right)+T_{\mathsf{\text{intra}}}\left(x,y\right)\right]∕T_{\mathsf{\text{total}}}=\frac{\left\{n_{max\mathsf{\text{-}}f}{t}_{\mathsf{\text{intra}}}+\left[n_t\left(x,y\right)+n_r\left(x,y\right)\right]t_{\mathsf{\text{inter}}}\right\}{T}_u}{n_{max\mathsf{\text{-}}f}{t}_{\mathsf{\text{intra}}}+{\sum }_{g_u\left(x,y\right)\in C_u}\left[n_t\left(x,y\right)+n_r\left(x,y\right)\right]t_{\mathsf{\text{inter}}}}.$

Hence, Lemma 2 is proved.

Lemma 2 shows that the allocated time of grid is determined by the task amount undertaken by its nodes, where the longer time will be allocated because of more tasks.

A. Simulation environment

We use network lifetime and the number of alive nodes to evaluate the performance in our simulations. Generally, the network lifetime can be measured by three methods. One is the time when the first node exhausts its energy, the second is the time when the dead nodes reach a certain degree, and third is the time of all nodes dead. Here, we choose the third one as the network lifetime. The number of alive sensor node means the node still can normally work, which decreases with the network operation.

B. Network lifetime and node survival condition

In this simulation, we focus on evaluating the performance of EEFR by network lifetime and remaining energy. The network lifetime is recorded as the time when all the sensor nodes are energy exhausted. The longer network lifetime means the higher efficiency of saving energy. When the first dead node appears, the less remaining energy of other nodes means the better energy balancing performance.

The effect of network structure on EEFR performance is also considered by changing the number of the agent vary from 5 to 8. The coefficient relativity of data in neighbor grids is fixed at 0.3. Figure 6 gives the situation of energy consumption of whole network with time increasing. When the energy consumption of network reaches 40000 J, the whole energy of network are thoroughly consumed and will not change but keep constant. Then, the whole operating time is the network lifetime. We also notice that the network lifetime is longer with increasing the agent amount. This is because the cluster area is decreased by the increasing number of mobile agent nodes, which results in the decreasing of hop number. Therefore, the energy consumption of retransmission is saved.

Figure 7 shows the statistic result of the changing about the number of alive nodes along with network operating. We observe that the appearance time of the first and last dead node is similar, which means the energy consumption of network adopted by EEFR is quite balanced. It also can be seen that the increasing of mobile agent nodes delays the appearance time of dead node. The increasing number of mobile agent reduced the cluster area, then the hop number of the nodes in the far distance from the mobile agent node correspondingly reduced. As a result, the energy consumption difference between the node with largest and smallest hop number obviously decreased.

Figure 8 illustrates the network lifetime adopted by EEFR with different data correlation coefficient. We suppose the correlation coefficient of the sensory data in neighbor grids is changed from 0.1 to 0.8, and the correlation coefficient of sensory data reduces 0.1 when the interval of grid increases 1. It can be seen that the network lifetime increases with increasing data correlation coefficient.

C. Comparison with other routings

In this simulation, we evaluate the performance of EEFR by comparing it with a clustering hierarchy based on cellular topology (CHCT) and LEACH-MT. CHCT adopts the conception of virtual grid to form the cellular clusters in WMSNs and considers the remaining energy of sensor nodes during routing establishment. Five mobile agent nodes are used in the experiment operated by EEFR. LEACH-MT is modified from LEACH to make it be able to operate under a large-scale deployment. The multi-hop mechanism is introduced in LEACH-MT for data transmission among clusters. The rest of LEACH-MT is as same as LEACH. Fusion process is employed during data collection in these three protocols. Figure 9 illustrates the change of their energy consumption with correlation coefficient at 0.3. It can be seen that the energy consumption of network adopted by EEFR is always lower than that of CHCT and LEACH-MT with the same data correlation coefficient.