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Recent development in sensor technologies makes wireless sensor networks (WSN) very popular in the last few years. A limitation of most popular sensors is that sensor nodes have a limited battery capacity that leads to lower the lifetime of WSN. For that, it raises the need to develop energy efficient solutions to keep WSN functioning for the longest period of time. Due to the fact that most of the nodes energy is spent on data transmission, many routing techniques in the literature have been proposed to expand the network lifetime such as the Online Maximum Lifetime heuristics (OML) and capacity maximization (CMAX). In this paper, we introduce an efficient priority based routing power management heuristic in order to increase both coverage and extend lifetime by managing the power at the sensor level. We accomplished that by setting priority metric in addition to dividing the node energy into two ratios; one for the sensor node originated data and the other part is for data relays from other sensors. This heuristic, which is called pERPMT (priority Efficient Routing Power Management Technique), has been applied to two well know routing techniques. Results from running extensive simulation runs revealed the superiority of the new methodology pERPMT over existing heuristics. The pEPRMT increases the lifetime up to 77% and 54% when compared to OML and CMAX respectively.

Recent advances in Nano-electromechanical systems (NEMS) paved the way to new applications for Wireless sensor networks [1-3]. Sensor networks comprise a large number of small-size nodes with sensing, computation, and wireless communication capabilities. These nodes collaborate together by performing desired measurements, process measured data, and transmitting it to some special nodes, commonly referred to as sink node [

Energy depletion is mainly due to data reception and transmission, where the later is large when compared to data reception [

In our work, we are concerned with the first two methods and we try to balance between them when necessary to gain higher lifetimes and coverage as we will see later in the discussion. We accomplished this by developing energy-aware routing heuristics (pERPMT) that tries to optimize network lifetime by managing routes in a way that will save power as much as possible so that the lifetime of the network is maximized.

Prolonging the lifetime is the same as increasing the coverage of WSN. By prolonging the lifetime of sensor node, the vicinity of sensor node area is kept covered [2,3]. One of our purposes was to keep all or most of the network nodes active (alive) most of the network lifetime.

The reminder of the paper is organized as follows: Section 2 introduces the wireless sensor networks mathematical model. In Section 3, we provide simulation and modeling of pERPMT. Simulation data and discussion of pERPMT is introduced in Section 4. Section 5 is concluding the paper.

The main problem in most of energy-aware routing heuristics is that they find the lowest energy route and use it for every communication [2,7,8]. Using low energy path more frequently will leads to energy depletion of the nodes along that path especially the nodes closer to the sink. Once the sensor node dies it leads to network partition that cause blind areas (areas that can not be sensed by any node). Some heuristics have been proposed to solve this problem by taking into account the residual energy at nodes and delay the depletion of nodes that are already low in energy [9,10]. In [

In this work, we proposed a heuristic that delays the depletion of one-hop nodes by adding a priority metric. The priority number that we have is based on two factors. One is the number of hopes and the second is based on the energy level of the node. In order to have fair comparison, we perform a battery power management at the node level with and without priority based scheme, such that the total power of the sensor battery is divided into two parts; the first is dedicated for sending data generated by the sensor itself, while the other is for data relays from other sensors [9,10]. Our approach can be used along with any existing routing heuristics. For that, we compared pERPMT against two well known routing heuristics: OML, CMAX, and ERPMT.

A wireless sensor network is represented by a directed graph, where V is the set of nodes, and E is the set of edges between these nodes, there will be a directed edge from node v to node u (i.e.) if u and v in the range of each others. Such modeling can be used to represent Wireless Sensor Networks (WSN). for each, in case of single hop transmission from sensor u to sensor v, the current energy in sensor u, c_{e}(u) is represented by Equation (1) [

where c_{e}(u) is the current energy in sensor u, such as and is the energy required to make a single hop transmission from sensor u to sensor v, such that. We also assume that the receiver of a message consumes no energy during message reception. Thus, the current energy in sensor (v) is not affected by the transmission from u to v. In our work the energy is divided into two ratios, one for data originated from the node (α), the other is for relays from other sensors (β); if the data is originated from the node itself, it will use the energy from the first ratio otherwise it will use energy from the other ratio.

An adjacency matrix can be used to represent directed graphs of WSN [12-16]. The adjacency matrix of a finite directed graph G on n vertices (where), is the n × n matrix such that, the non-diagonal entry, represents the existence of an edge from sensor i to sensor j. While the diagonal entry is assigned by zeros here because we assume that there is no internal loops in the WSN.

There exists a unique adjacency matrix for each graph. For example,

In most of the studies to represent a sensor location as well as connectivity a random number from Uniform distribution was used [

shows sensor nodes distribution based on Poisson distribution, it is clear that the sensors location concentrated around the mean. This kind of deployment imitates a deployment of sensors via airplane in a terrain that is close to valleys. For fair comparisons with the heuristics in the literature we used Uniform distribution.

An example of sensor deployment application is avalanching predictions, mountainous terrains portrait all the challenges that may face sensor deployment in order to make full coverage. For that, deployment strategy has a major effect on evaluating a routing heuristic. This is due to the fact of terrain changes of real life environment.

To determine connectivity between the nodes, we used a threshold which was equal to the mean of the dimensions of network nodes. All nodes were recursively checked by comparing their X-, Yand Z-dimension in case of 3D deployment with the mean of the Euclidian dimensions for these 3 dimensions (X, Y, and Z) for all network nodes. For the case of 1D, we only work with just the X dimension. Each node with a dimension value greater than or equal to the mean of the same dimension will be considered connected, otherwise it will be disconnected [

We have used two well known heuristics to apply pERPMT on, these two different heuristics were proposed to extend the lifetime of the network and they obtained the best lifetime in the literature, CMAX and OML.