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The optimum sensor redeployment scheme using the most frangible clusters set

Chu-Fu Wang

a,*

, Jen-Wen Ding

b

a

Department of Computer Science, National Pingtung University of Education, No. 4-18 Ming-Shen Road, Pingtung 900, Taiwan

b

Department of Information Management, National Kaohsiung University of Applied Sciences, No. 415, Jiangong Road, Kaohsiung city 80778, Taiwan

a r t i c l e

i n f o

Article history:

Received 28 December 2007 Received in revised form 10 June 2008 Accepted 16 June 2008

Available online 21 June 2008 Keywords:

Wireless Sensor Networks Topology control Sensor redeployment Network lifetime

a b s t r a c t

Sensors redeployment is a straightforward way to increase the lifetime of a Wireless Sensor Network (WSN) by deploying additional sensor devices in the sensing region. This paper considers the problem of finding positions to deploy sensors so that the network lifetime will be the most prolonged when a fixed total quantity of energy of sensor devices is given. We formulated the redeployment problem in WSNs as a network optimization problem called the OCSRP (Optimum Clusters Set Redeployment Problem). Two heuristic algorithms, the MFCSPA-static (Most Frangible Clusters Set Prediction Algorithm for static routing), and the MFCSPA-dynamic are proposed to solve the OCSRP in WSNs under static and dynamic routing schemes, respectively. By integrating the above sensor redeployment algorithms with monitoring facilities, a topology control scheme for maintaining the energy usage of a WSN is also proposed. The sim-ulation results show that both proposed algorithms can find better solutions than other heuristic algo-rithms. Moreover, both proposed algorithms greatly outperform the other algorithms in the percentage of successfully predicting the earliest energy drain out node.

Crown copyright Ó 2008 Published by Elsevier B.V. All rights reserved.

1. Introduction

Due to recent technological advances and the fact that many comprehensive wireless device usages are proposed in diverse scopes, there is an impetus to increase the speed of the devel-opment of wireless communication technology. One of the new growing fields of wireless computer networks in recent years is Wireless Sensor Networks (WSNs)[1,2]. A WSN consists of hun-dreds or thousands of sensor nodes that are usually scattered over a certain area to perform monitoring tasks. The sensor nodes are low-cost, are equipped with limited battery power, and are small sized devices. Besides, they can monitor specific measurement data (e.g. temperature, humidity, and pressure) to detect abnormal events (e.g. a forest fire). Initially the sensor nodes are deployed manually or randomly in the sensing field to form a WSN. The end user may connect to a data concentra-tion center called the sink node (or base staconcentra-tion) via Internet or Satellite to send a request for querying a specific event or phe-nomenon on this sensing field. Once a sensor node detects an unusual situation as designated by the sink node, it has to quickly propagate such an event occurred message to notify the end user. The WSN may also have fault-tolerance capability; that is, if the sensing data is lost, sensor nodes may recover the lost data from their inner caches. The end user will then

even-tually receive the reported information correctly from the sink node.

The WSNs not only apply in conventional work, but can also overcome difficult missions such as battlefield surveillance, weather monitoring, ecology tracking, and even universe discov-ery. Since WSNs are in widespread use, many researchers have paid much attention to this field [3–9]. For more information, we encourage the readers to refer to two survey papers

[10,11]. Since the WSNs are usually deployed for use in harsh environments, the sensor nodes are not easily to be replaced or recharged when they run out of battery power. Thus, the most important research issue in the area of WSNs is how to conserve the limited battery energy to maximize the network lifetime. Several research topics have been broadly discussed to fulfill the above objective; for example, designing energy aware routings [12–16], designing scheduling power-saving modes of sensor nodes [17–19], and developing comprehensive power management and topology control methods[20–25], etc. After performing several rounds of monitoring and data relay-ing, the energy level of the sensor devices in a WSN will be-come lower and lower, and then the WSN will eventually cease functioning. Proper power management and topology con-trol methods can monitor the energy level of the WSN. If the energy level drops below a given threshold, a warning message will be sent out to notify the supervisors. One of the straight-forward methods for supervisors to deal with such a circum-stance is the deployment of additional sensor nodes in the sensing field to prolong the residual network lifetime of the 0140-3664/$ - see front matter Crown copyright Ó 2008 Published by Elsevier B.V. All rights reserved.

doi:10.1016/j.comcom.2008.06.004

* Corresponding author. Tel.: +886 8 7226141; fax: +886 8 7215034.

E-mail addresses: cfwang@mail.npue.edu.tw (C.-F. Wang), jwding@cc.kuas. edu.tw(J.-W. Ding).

Contents lists available atScienceDirect

Computer Communications

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WSN. The sensor deployment issues can be classified into three categories: the pre-deployment, the movement-assisted deploy-ment and the redeploydeploy-ment schemes. A brief introduction of each is given below.

Sensors pre-deployment scheme: The pre-deployment issues are considered in the construction phase of a WSN. Two important factors, network coverage and network connectivity, are usually considered as constraints [21–23]. In order to re-duce the construction costs, the coverage issue aims at how to deploy as few sensor nodes as possible in a sensing field while ensuring that the constructed WSN has no coverage holes (or communication holes). Besides, since some of the sensor nodes may be drained of battery power after executing several rounds of tasks, the WSN will become disconnected. Accordingly, the network connectivity constraint will ensure that the constructed WSN has a certain level of connectivity. The higher the connectivity of a WSN, the more robust it will be, and then the network will possibly continue to be con-nected when some sensor nodes have exhausted their battery power.

Movement-assisted sensor deployment scheme: Assuming that some sorts of sensor nodes are capable of moving then we can accommodate the energy level of a WSN by moving sensor nodes into lower energy areas. Many lectures[24–27] have fo-cused on this issue. For example, Wang et al. [24] modeled a WSN on the Voronoi diagram, which can detect the coverage hole of a network. They proposed three algorithms (VEC, VOR, and Minimax) to determine how to move the sensor nodes so that the problem of coverage holes will be relieved. Wu et al.

[25] considered a balancing problem of a WSN with a Mesh

structure. An algorithm called SMART was proposed to determine the moving strategy so that the number of sensor nodes in each square area of the WSN was equal, and the number of moves was minimized.

Sensor redeployment scheme: Deploying additional sensor nodes in a low energy level of a WSN is a straightforward meth-od to increase its network lifetime[28]. The problem of where to deploy these additional nodes in the sensing fields is the key point of this issue. Intuitively, the sensor nodes that are close to the sink will consume much more battery energy than others. Therefore, deploying more sensor nodes into these areas will prolong the residual network lifetime of the WSN. However, the hop count to the sink node is just one of the key factors that affects the performance of the redeployment. The other key fac-tors include the residual battery energy of sensor nodes, the occurrence probability of an event happening in each sensing area, and their routing scheme, etc. These factors will all influ-ence the length of the residual network lifetime. To our best knowledge, little research has investigated the sensor redeploy-ment problem for WSN.

In this paper, we consider the redeployment problem in WSNs, and formulate it as a network optimization problem called the OCSRP (Optimum Clusters Set Redeployment Problem) to find the best locations for placing the additional sensor nodes. We propose two heuristic algorithms, the MFCSPA-sta-tic (Most Frangible Clusters Set Prediction Algorithm for staMFCSPA-sta-tic routing) and the MFCSPA-dynamic, to solve the OCSRP on a static and a dynamic routing scheme, respectively. We also propose a sensor topology control scheme, which synthesizes the above methods to keep track of the WSN’s energy level. The remainder of this paper is organized as follows. Section

2 describes the network model and the formulation of the

OCSRP. Section 3 proposes the solution methods for solving the OCSRP. In Section 4, we will give the simulation results for these algorithms. Finally, the concluding remarks are given in Section 5.

2. The network model and problem formulation

In this section, we firstly describe the network model of a two-tiered hierarchical WSN under consideration in this paper, and then formulate a sensor node redeployment problem based on this network architecture.

2.1. Network model

As a hierarchical structure, the cluster-based WSN is known to be an efficient architecture for organizing a large amount of sensor nodes. Therefore, several hierarchical routing protocols

[3,29,30] have been proposed for this structure. These studies have revealed that the cluster-based WSN performs better, not only in terms of energy conservation for message routing, but also because it is easier for topology controlling than a flat WSN. A cluster-based WSN partitions the sensor nodes into a set of clusters. Each cluster contains sensor nodes which are close to each other, and one of the sensor nodes in each cluster is elected as a cluster head to be responsible for information relaying. Assuming an event randomly happens in a cluster’s sensing region, this event will be notified to the sink node by the following steps. First, the detected sensor node will trans-mit the event reporting message directly to its cluster head. Then the cluster head will relay the received message, hop by hop, toward the sink node along a predetermined routing path. The time interval from the start of the event to the message being correctly received by the sink node is called a successful event transmission round. We assume that a new event trans-mission round can not be started before the event reporting data has been received by the sink node in the previous round. A cluster-based WSN can be modeled as an undirected graph, called the cluster graph G ¼ ðV; EÞ, where V denotes the collection of clusters, and E represents the possibility of directly communi-cating between clusters. That is, if both clusters u and v can com-municate directly with each other, then ðu; vÞ 2 E. A residual energy function r : V ! Rþmaps each cluster node v to a positive

real number rðvÞ to represent cluster v’s total residual battery power. Note that, since the sink node ðs 2 VÞ is capable of using a charged power line, we thus assume that it has infinite battery power, i.e. rðsÞ ¼ 1. Besides, in order to represent the possibility of an event happening in each cluster, an event occurrence probability mass function p : V ! ½0; 1 associates each cluster node v in V with a probability value pðvÞ to represent the possibility. Note that pðsÞ ¼ 0 andPv2VpðvÞ ¼ 1. If there is no hot-zone for an event occurring in the

sensing region, then the function p will become a uniform

distribu-tion, which excludes the sink node s; that is

pðvÞ ¼ 1

jVj1;8v 2 V  fsg. In contrast, the function p is a non-uniform

distribution. Given an event occurring sequence for cluster node ðvi1;vi2; . . . ;vik; . . .Þ with respect to a function p, where vik2 V  fsg

indicates that an event will occur in cluster node vikat the k’th event

transmission round. Notice that the above event occurring sequence is designed to ease the discussion of the network model, and it will not be known in advance. The event transmission will be performed in rounds according to an event occurring sequence until a cluster node runs out of its battery power, and then the WSN will die. The number of event transmission rounds that the WSN can function well is defined as the residual network lifetime.

Fig. 1shows an example of a two-tiered cluster-based WSN. The lower layer of this figure shows the physical topology of the WSN. The sensor nodes in each circle form a cluster, and each cluster cor-responds to a node in the upper layer, which is an abstraction of the physical architecture. Assuming that a sensor node in cluster F detects an event occurring, then it will immediately emit a mes-sage to notify its cluster head. After the cluster head of F receives

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the reported data, it will relay the data along a predetermined path in the cluster graph, say path F  E  C  S. Now, considering the battery energy consumption in this transmission round, the cluster nodes F; E and C will spend their battery energy for data transmit-ting. Moreover, cluster nodes E; C and S will also consume their en-ergy for receiving data from their predecessor cluster nodes in this path. In our work, the energy depletion of wireless communication follows the first order radio model[3]. This radio model assumes that driving the transmitter or receiver circuitry takes Eelec¼

50 nJ=bit and the transmit amplifier costs



amp¼ 100 pJ=bit=m2.

The energy consumption of transmitting a k-bits message for a dis-tance d is given by:

ETxðk; dÞ ¼ ETxelecðkÞ þ ETxampðk; dÞ ¼ Eelec k þ



amp k  d2 ð1Þ and receiving this k-bits message is given by:

ERxðkÞ ¼ ERxelecðkÞ ¼ Eelec k ð2Þ For ease of discussion, we use EconsumptionuðvÞ to denote the total energy

consumed for message relaying on cluster node v, in case the event occurred on cluster node u. As shown inFig. 1, the routing path from F to S is F  E  C  S. Then, EconsumptionFðFÞ ¼ ETxðk; dðF; EÞÞ, where

dðF; EÞ denotes the distance between cluster nodes F and E. Since cluster nodes E and C have to carry out both the tasks of receiving a message from their predecessors and transmitting this message to their successors, EconsumptionFðEÞ ¼ ERxðkÞ þ ETxðk; dðE; CÞÞ

and EconsumptionFðCÞ ¼ ERxðkÞ þ ETxðk; dðC; SÞÞ. For the other cluster

nodes not in the routing path, due to the fact that they need not spend any battery energy during this event transmission round, EconsumptionFðAÞ ¼ EconsumptionFðBÞ ¼ EconsumptionFðDÞ ¼ 0.

The message transmission routing protocols for WSNs can be classified into a static routing and dynamic routing, depending on whether the route in each transmission round is fixed or not.

Fig. 2gives an example to illustrate the difference between these two routing schemes. In this figure, the routing path labeled k rep-resents the message transmission route for the kth event

transmis-sion round. Assuming the event occurring sequence is

ðF; C; F; A; B . . .Þ, notice that both of the event occurrence positions for the first and the third round are in the same cluster node F. For the static routing scheme (seeFig. 2(a)), path 1 and path 3 stay the same, since the routing is static. However, for the dynamic routing case (seeFig. 2(b)), the routing algorithm may determine their route according to some variable parameters (e.g., the current traffic volume or nodes’ residual energy), then the determined route may be altered during each event transmission round. Conse-quently the routes with respect to the same event occurrence clus-ter nodes in different rounds may not be the same.

2.2. Problem formulation

Given a cluster graph G ¼ ðV; EÞ, a residual energy function r and an event occurrence probability mass function p, the total number of event transmission rounds that could be successfully executed before the first node dies is defined as G’s residual network life-time, and we denote it by LðG; r; pÞ. Considering the redeployment problem, assume now that there is a certain number of sensor nodes with total amount of energy, say k  Esupply, to be deployed

on k positions to prolong the residual network lifetime with the deployment unit of Esupply. An energy redeployment set U is a

mul-tiset of cluster nodes with cardinality k that represents the number of energy units to be allocated; that is, for each cluster node v 2 U of G, we will deploy Esupplyunit of battery power of sensor nodes

into this cluster. The resulting residual energy function value for each cluster node v 2 V after deploying the additional sensor nodes according to the energy redeployment set U is as follows:

rUðvÞ ¼ rðvÞ þ c  Esupply; where c denotes the multiplicity of v in U

ð3Þ

We use cluster graph G ofFig. 1as an example. Assuming the rede-ployment budget is 3 units of energy Esupply(e.g., Esupply¼ 50 mJ) and

the energy redeployment set U ¼ fB; D; Dg, then the resulting resid-ual energy function rUwith respect to the energy redeployment set

U will become, rUðAÞ ¼ 100; rUðBÞ ¼ 200; rUðCÞ ¼ 200; rUðDÞ ¼ 190;

rUðEÞ ¼ 250, and rUðFÞ ¼ 300.

Then, our considered probabilistic based network optimization problem, called the Optimum Clusters Set Redeployment Problem (OCSRP), is to determine an optimum energy redeployment set U

for deploying these additional sensor nodes into the WSN, such that the residual network lifetime will be prolonged as much as possible; that is, LðG; rU;pÞ P LðG; rU;pÞ, for any feasible energy

redeployment set U. Note that since the residual network lifetime of a WSN is determined by the event occurring sequence for cluster nodes, finding the exact optimum solution for OCSRP will not be possible except when the event occurrence sequence is given in advance. We will propose heuristic algorithms for the OCSRP and demonstrates their performance through simulations. In our con-sidered problem, we only determine which clusters are for deploy-ing the additional sensor devices. The exactly positions for placdeploy-ing Fig. 1. An example for cluster-based WSN.

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them in each determined cluster are not considered in this research.

3. The Sensor redeployment scheme

In general, when finding the positions for the redeployment of the additional sensor nodes, one may intuitively choose the lower energy value cluster nodes or the weak cluster nodes in the net-work topology with respect to certain evaluation metrics such as the network reliability or the fault tolerance, etc. Till now, many solutions have been proposed to fulfil these objectives. For exam-ple, finding the most vital node (edge) in a network [31,32] is one of the attractive problems. The most vital node (edge) is de-fined as the node (edge) whose removal will minimize the network reliability when compared with other nodes (edges) in the net-work. However, using the solutions of these optimization problems as our redeployment positions might not be a good choice, because the traditional problems fail to consider the following two factors, which will certainly affect the objective value (the residual net-work lifetime) of the OCSRP. The first one is the event occurrence probability mass function p. Notice that in our consideration of the network model, the position of the occurrence of an detected event in each transmission round is not deterministic, but just hap-pens by chance. The cluster nodes where detected events fre-quently occur will thus consume much more battery energy than other cluster nodes in the WSN. Besides, the routing scheme for message delivery is also another major factor that traditional prob-lems fail to consider in the energy consumption of our network model. Both factors will be taken into consideration in our solution methods to gain better performance.

Since the residual network lifetime LðG; r; pÞ is stochastic, it is not easy to predict this value correctly. The job of predicting the best energy redeployment set will thus become harder. In order to cope with the variation in such a stochastic problem, we will use an expectation-based prediction approach to estimate the va-lue LðG; r; pÞ. Then, based on the estimation of the LðG; r; pÞ, a clus-ter node set called the most frangible clusclus-ter set in clusclus-ter graph G ¼ ðV; EÞ is proposed as the redeployment positions under both the static and dynamic routing scheme, respectively. Finally a sen-sors topology control scheme is then developed.

3.1. The static routing case

Given a cluster graph G ¼ ðV; EÞ, a residual energy function r and an event occurrence probability mass function p, for each cluster node v 2 V, we let path Pvsbe the static route for message delivery

from cluster node v to the sink node s in each transmission round. Note that one of the frequently used paths for static route is the shortest path. If we regard the Euclidean distances between the pair of cluster nodes in each edge as the link cost, then the static route with respect to each cluster node can be easily obtained by using the Dijkstra’s algorithm. Since the message delivery path with respect to each cluster node v 2 V is determined and is static in each event transmission round, the energy consumption quanti-ties EconsumptionuðvÞ;8u; v 2 V can be easily obtained using Eqs.(1)

and (2)in Section2. Due to the fact that the event occurrence prob-ability of cluster node u is pðuÞ, pðuÞ  EconsumptionuðvÞ is equal to the

energy consumption rate of cluster node v in an event transmission round when the event occurs at cluster node u. Therefore, the Expectation of Energy Consumed of cluster node v 2 V, denoted by EEC(v) in one event transmission round can be defined as follows:

EECðvÞ ¼X

u2V

pðuÞ  EconsumptionuðvÞ ð4Þ

and the Expectation of Residual Lifetime of cluster node v, denoted by ERL(v), can be obtained by:

ERLðvÞ ¼ rðvÞ

EECðvÞ ð5Þ

In the example of Fig. 1, since the routing paths that pass through node C are PDS;PFS;PES, and PCS, the expectation of energy

consumed with respect to node C (EEC(C)) in one transmission round according to Eq.(4)is shown as follows:

EECðCÞ ¼1 6 EconsumptionDðCÞ þ 1 6 EconsumptionFðCÞ þ 1 6 EconsumptionEðCÞ þ1 6 EconsumptionCðCÞ ¼1 6 f½ETxðk; dðC; SÞÞ þ ERxðkÞ þ ½ETxðk; dðC; SÞÞ þ ERxðkÞ þ ½ETxðk; dðC; SÞÞ þ ERxðkÞ þ ETxðk; dðC; SÞÞg

Thus, using Eqs.(4) and (5), the expectation of energy consumed in one event transmission round, and the expectation of residual life-time for each cluster node can then be obtained. Note that the net-work lifetime is defined as the time at the first cluster node dies; thus we can use the minimum value of the residual expectation life-time among all cluster nodes as the residual network lifelife-time of G, denoted by ERLðGÞ. That is, ERLðGÞ ¼ minv2VERLðvÞ. We call the

clus-ter node with the minimum value of expectation residual lifetime the most frangible cluster node.

Assuming the budget for sensor redeployment is k units of en-ergy (Esupply), we now have to determine a best energy

redeploy-ment set U of cardinality k. Based on the above discussion, the

solution method MFCSPA-static for the OCSRP is stated as follows. Firstly, compute the EEC(v) and ERL(v) values for each cluster node v 2 V with respect to the given cluster graph G, the event occur-rence probability mass function p, and the residual energy function r, using Eqs.(4) and (5). Let vbe the most frangible cluster node in

G; that is, ERLðvÞ ¼ min

v2VERLðvÞ, then put v into set U

ðU¼ U[ fvgÞ. Meanwhile, the new residual energy function r U

with respect to Uhas also to be updated according to Eq.(3). By repeating the above two steps k times, a complete energy rede-ployment set U, which consists of the most frangible cluster nodes

can then be obtained. We call set Uthe most frangible cluster set.

The complete Most Frangible Cluster Set Prediction Algorithm for static routing scheme (MFCSPA-static) is shown inFig. 3.

3.2. The dynamic routing case

In general, using a dynamic routing scheme on WSNs for event reporting has the merit of balancing the energy consumption with-in networks so that their residual network lifetime will be pro-longed, compared to the static routing scheme. Most of the proposed energy-aware routing protocols[12–15] for WSNs be-long to the dynamic routing case. Among these studies, Huang and Jan [14] proposed an energy-aware, load balanced routing method, called the Maximum Capacity Path (MCP) routing, which can conserve battery energy usage better than many other pro-posed algorithms. In this paper, we will use the MCP routing as the underlying routing scheme to illustrate our proposed solution method in the dynamic routing case. Note that it is easy to modify our proposed redeployment method to integrate other existing dy-namic routing schemes into the algorithm. In the following subsec-tions, the MCP routing will be introduced first, followed by our proposed algorithm.

3.2.1. An example of a dynamic routing scheme – the Maximum Capacity Path (MCP)

Let G ¼ ðV; EÞ be a cluster graph, and r be the residual energy function that is associated with cluster node set V. Let level Lvwith

respect to cluster node v 2 V denote the minimum hop count from v to the sink node s. The MCP firstly constructs G into a layered

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routing scheme. In the future, we will consider the optimum pre-deployment problem under our consideration of the network envi-ronment and assumptions.

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Fig. 2 gives an example to illustrate the difference between these two routing schemes
Fig. 18. Number of successful hits vs. redeployment budget using non-uniform distribution (with n ¼ 70 and dynamic routing).

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