Jenn-Hwan Tarng, Bing-Wen Chuang
, Pei-Chen Liu
Department of Communication Engineering, National Chiao-Tung University, 1001 Ta-Shueh Road, HsinChu, Taiwan, ROC
a r t i c l e
i n f o
Article history:
Received 17 August 2007 Received in revised form 20 May 2008
Accepted 5 July 2008
Keywords:
Wireless sensor network Relay node deployment
a b s t r a c t
In this paper, a 2-D geometric and adaptive relay node deployment method with polynomial-time complexity is proposed to reduce relay nodes for bridging all disconnected node pairs of a wireless sensor network (WSN). In this method, proper locations for placing relay nodes are discovered on a plane, which gives a much larger degree of freedom to compare with the traditional 1-D search algorithm. In this way, the deployed relay node can bridge as many disconnected node pairs as possible around it. Besides, the method can also adapt to radio environments because that a sophisticated propagation model including large-scale path loss, shadowing, and multipath fading effects is used to estimate link connectivity. Simulation result validates its robustness and efficiency compared with the existing relay node deployment methods. The proposed method significantly reduces the total number of relay nodes compared with the related works in all of the investigated indoor environments.
&2008 Elsevier Ltd. All rights reserved.
1. Introduction
A wireless sensor network (WSN) is a network consisting of spatially distributed sensing devices that cooperatively observe physical/environmental conditions, such as temperature, sound, vibration, pressure, motion of objects, or pollutants (Romer and Mattern, 2004;Tubaishat and Madria, 2003). However, deploying a network with proper allocation of sensor nodes for a WSN is critical to prior operations. Two performance metrics when deploying a WSN are considered in literatures (Krishnamachari, 2006; Haenselmann, 2006; Wang et al., 2003): (1) network coverage, which measures the degree of covered sensing area of a given network (Huang and Tseng, 2003), and (2) network connectivity, which determines whether the network topology over which information routing can take place (Wan and Yi, 2004). Although it is very important to optimize the placement of sensors, it is often difficult to do that.
Connectivity of a WSN is critical to many of its fundamental operations such as data gathering, data dissemination, and peer-to-peer ad hoc routing. WSNs are by nature constructed automatically, and in particular, no connectivity is guaranteed: the nodes may be so sparsely located that they are unable to make up a connected network. Besides, given that the connectivity of a WSN is susceptible to node mobility, node failure, and unpredict-able environment influences, it is important to continuously
maintain connectivity under all these unfavorable conditions. For disconnected WSNs, additional relay nodes are deployed firstly to bridge disconnected node pairs and to reduce hop count number of shortest path, which can enhance network connectivity. Secondly, it also can increase the total number of available paths between two nodes to enhance network survivability. However, finding an optimal network that reaches prior goals is NP-complete and is also constrained by applied environments. This has motivated the research with primary interest in the connectivity improvement by deploying relay nodes for discon-nected WSNs. Most research effects have been concentrated on either analyzing the asymptotic connectivity of large-scale WSNs (Gupta and Kumar, 1998;Xue and Kumar, 2004;Penrose, 1997;Bettstetter, 2002) or devising topology control protocols to maintain connectivity in the presence of limited mobility (Li and Hou, 2004).
Several researchers have proposed relay node deployment methods; such as minimum spanning tree based (MST-based) (Pettie and Ramachandran, 2002) method and virtual wiring (VW) method (Vairamuthu et al., 2005) for solving related problem in practice, e.g., telemetry (Vairamuthu et al., 2005) and metropo-litan-scale mesh network (Audeh, 2004). In the MST-based method, sensor nodes of a given WSN are firstly grouped into network clusters, where a network cluster is formed by a set of initially connected nodes. In order to merge these clusters, the MST-based method constructs a tree with a minimum-cost link set, i.e., the minimum spanning tree. Thereafter, the method deploys relay nodes along the links of the tree to connect these clusters. The MST-based method is a straightforward solution for 1084-8045/$ - see front matter & 2008 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jnca.2008.07.003
Corresponding author.
deploying relay nodes. Its shortcoming is, however, that each relay node can only be used to connect at most two clusters. As shown inFig. 1(a), the MST-based method would have placed two relay nodes to connect all three clusters, while in fact one node (placed at the position of u1inFig. 1(b)) is sufficient. Here the MST-based
method is regarded as a baseline method for performance comparisons in this research. In the VW method, every discon-nected node pair in a WSN is condiscon-nected by placing required number of relay nodes along the corresponding virtual wire, which is a straight line between the disconnected node pair. Although the VW method considers not only the network connectivity but also survivability, it may not provide an efficient solution in minimizing the total number of relay nodes.
In this paper, we propose a relay node deployment method, which aims to reduce the total number of relay nodes effectively. Under the assumption of meshed network topologies and shortest path (minimum-hop) routing protocols are utilized, proper locations for deploying relay nodes are discovered on a 2-D plane. This method should be better than the MST-based and VW methods (that are based on 1-D search algorithm) by nature as these relay nodes are allocated on a horizontal plane, which gives a large degree of freedom. With the proposed method, a deployed relay node can enlarge in bridging number of disconnected node pairs around it. In addition, a sophisticated propagation model including shadowing and multipath fading is employed in estimating link connectivity, which can reflect radio channel effects more properly to compare with the traditional model, the unit disk graph model (Khadar and Simplot-Ryl, 2007) utilized by most of the existing works. To the best of our knowledge, paper (Li and Hou, 2005) presents a 2-D relay node deployment method, named as the connectivity improvement Delaunay triangulation (CIDT). This method constructs a Delaunay triangulation in the disconnected network, and place relay nodes in selected triangles. We also made comparison with this method based on simulation results.
2. The proposed relay node deployment method 2.1. Problem statement
Given a set of initial sensor nodes to form a disconnected WSN, solving the problem of deploying as few as relay nodes to yield a connected WSN is our major goal. Let V ¼ {v1, v2,y, vn} is the set
of sensor nodes and there exists a link formed by a 1-hop path between any node pairs in V and is denoted by (va, vb), va, vbAV. Therefore, the topology of a WSN is represented by an undirected simple geometric graph G ¼ (V, E) in a Euclidean plane R2, where
E is the set of connected links and is defined by E ¼ {(vb, vb): l
(vb, vb)4
l
, vb, vbAV}. Here l(vb, vb) denotes the probability that the message transmitted by node vbis received by node vb, andl
is a threshold value. For every source and destination pair (SD pair) (i, j) in V, if there exists a connected route, which is a path formed by a set of connected links in E, the graph G is connected. Otherwise, the graph G is disconnected and the network is regarded as a disconnected WSN.
Here, a relay node deployment method is designed to insert a set of additional relay nodes U ¼ {u1, u2,y, uk} in a
disconnec-ted WSN in order to yield a connecdisconnec-ted topology G* ¼ (V*, E*) ¼ (V[U, E*), where E* is the set of connected links in the augmented graph G* and is defined by E* ¼ {(vc, vd): l(vc, vd)4
l
, vc, vdAV*}.2.2. The proposed method
The flowchart of the proposed relay node deployment method, named as 2-D geometric and adaptive (2DGA) method, is given in Fig. 2. Firstly, with a given WSN, the link connectivity of every link is estimated by the proposed estimation method and the topology of the network is determined. Then, the SD pairs without any connected route are regarded as disconnected SD pairs. If there exists disconnected SD pairs in the network, a 2-D geometric deploying algorithm is employed to discover candidate locations for deploying relay nodes and places a relay node at the best location among candidates. The processing flow repeats until none of disconnected SD pairs exists in the augmented network. In the following paragraphs, we elaborate on the procedures in the proposed method.
2.2.1. Estimate link connectivity
In order to devise a relay node deployment method to be able to adapt radio environments, a sophisticated propagation model including large-scale path loss, shadowing, and multipath fading effects is employed to estimate link connectivity. The connectivity of a link from node a to node b, l(a, b) ¼ sab, is defined as the
probability of the received signal power R(a, b) exceeding a threshold value
d
, i.e., sab¼Prob.{R(a, b)4d
}, where R(a, b) isrepresented by a continuous random variable which takes into account radio propagation effects. It is noted that the probabilistic distribution function for the R(a, b) random variable should be selected adaptive to the propagation environment where sensor nodes and relay nodes are located. Proper distributions for either outdoor or indoor environments are available in literature (Rappaport, 2001; Bettstetter and Hartmann, 2003). However, the indoor applications are our major concern and the applied R(a, b) is presented in Section 3 for further investigation. Fig. 1. An example of relay node deployment: (a) two nodes are deployed by using the MST-based method, and (b) an optimal deployment that requires only one relay node.
2.2.2. Determine disconnected SD pairs
With the estimated link connectivity, the network topology would be represented by a probabilistic graph (Khadar and Simplot-Ryl, 2007;Stojmenovic et al., 2005). In the graph, there would exist multiple routes between a given SD pair, where a route is a path formed by a set of links. Here the shortest path (minimum-hop) routing algorithm is utilized as a baseline routing method. However, in order to determine the disconnected SD pairs in a probabilistic graph, the best route of every SD pair that with the maximum route connectivity is discovered by using a search algorithm modified from the well-known all-pairs shortest path search algorithm (Cormen et al., 1990). Here the route connectivity of a SD pair (i, j) is given by
wpij¼
Y
9ða;bÞ2pij
sab; 8pij2Pij (1)
where Pijis the set formed by all routes with source node i and
destination node j; pij the denotes a route in Pij; and sab the
connectivity of a link (a, b) belonging to route pij.
With Eq. (4), the best route qij for SD pair (i, j) is found.
However, we need to justify whether the best route is connected or not. Here an SD pair (i, j) is connected when the following conditions are met: (1) wqij is larger than a threshold
k
¼l
h,where h denotes the maximum possible hop count number for constructing a route in the network. Here, h ¼ 7, and (2) every link in qijwith its link connectivity is larger than
l
. The SD pairs thatdo not fulfill the above conditions forms a set of disconnected SD pairs, denoted by D. The flow of the proposed method stops when D is empty. Otherwise, the method starts to deploy proper relay nodes in order to bridge the SD pairs in D.
2.2.3. Discover relay node candidates
With disconnected SD pairs, relay node candidates for bridging these SD pairs are discovered by the proposed 2-D geometric deploying algorithm. The pseudo code of proposed algorithm is depicted inFig. 3. Firstly, one SD pair in D need to be selected for further relay node discovering. From our preliminary study, three criteria for selecting SD pair, including (1) select the SD pair with
max route connectivity, (2) select the SD pair with min route connectivity, and (3) select SD pair randomly, have been investigated. The SD pair with maximum route connectivity usually leads to better solution than other criteria and is utilized in step 3. A relay node candidate is discovered from steps 4 to 13. It fulfills the requirements that the node is close to the disconnected SD pair found in step 3 and bridges as many as possible other disconnected SD pairs around it. The disconnected SD pairs that are bridged by the relay node candidate are removed from D in step 14, and the procedure repeats until D is empty. 2.2.4. Deploy relay nodes
The best relay node is selected from the candidates discovered by the previous process by using the following metrics:
|Bc|, the number of disconnected SD pairs that could be bridgedby deploying a relay node candidate c, where Bc¼ fða; bÞ : 9ða; bÞ 2 D; sca4
l
and scb4l
g |Nc|, the number of neighboring nodes of a relay nodecandidate c, where Nc¼ fm : 9m 2 V; scm4
l
g savgc , the averaged link connectivity of the links connectingrelay node candidate c and its neighboring nodes, where savg c ¼ 1 jNcj X m2Nc scm
Here the maximum |Bc| is the first criteria to screen candidate
locations of relay nodes. If more than one candidate is left, the maximum |Nc| is the second criteria for screening. If again more
than one candidate is left, maximum savgc criteria are applied.Fig. 4
depicts network topologies of an initial network and the augmented networks after deploying relay nodes by using the proposed method, the MST-based method, and the VW method, respectively. It is obvious that most of relay nodes are placed at proper locations by using the proposed method. These relay nodes can bridge more initial nodes compared with that of the MST-based or the VW method, which effectively reduce the Fig. 2. The flow chart of the 2-D geometric and minimum relay nodes (2DGMRN)
number of required relay nodes for constructing a connected network.
2.2.5. Complexity of proposed method
From the problem statement andFig. 1, the proposed method is divided into multiple parts. Let V ¼ |V| that denotes the nodes number of a WSN G and D ¼ |D| denotes the number of disconnected SD pairs in G. The running time of link connectivity estimation would be O(V2) and the determination of discon-nected SD pairs is based on the all-pairs shortest path search algorithm which has its complexity as O(V3log V) (Cormen
et al., 1990). As to the 2DGD algorithm, for each (i, j) pair in D, it takes |Kij| times for discovering the candidate relay node,
which leads to a overall time complexity as O(DV). Due to only one relay node is deployed within one iteration, the total time complexity of the whole method would be O(D*(V2+V3log
V+DV)) ¼ O(DV3log V).
3. Simulation results and comparisons
In order to evaluate the performance of the proposed relay node deployment method, some performance metrics are com-puted in solving a disconnected WSN. For comparison, related works, including the MST-based and VW node deployment methods are also evaluated. These methods are implemented and simulated by using the MATLAB toolboxes (MATLAB Version 7.2.0.232 (R2006a)). The following performance metrics are considered:
(1) Averaged number of relay nodes (ANRN): It is defined as the average number of deployed relay nodes over the samples.
The less the relay nodes are required, the more efficient the method is. For comparison, we further examine the reduction ratio of ANRN, which is defined as
r
ðA; BÞ ¼ ANRN difference between methods A and B ANRN using method Bwhere method B denotes a benchmark method. Here the MST-based method is chosen as a benchmark.
(2) Averaged node degree (AND): It is defined as the average number of node degree over the samples, where the node degree is defined as the average number of neighbors of all nodes in a WSN.
(3) Averaged number of network clusters (ANNC): It is the average number of network clusters of the augmented network over the samples. A cluster is formed by a group of connected nodes that belong to the network. It is noted that the number of network cluster is equal to 1 when the network is connected.
From Section 2.1, since indoor applications are our major concern, the received power in decibels (dB) is described by a model including large-scale path loss, shadowing, and multipath fading effects and is given by (Rappaport, 2001)
PRða; bÞ ¼ PTða; bÞ ½PLðdabÞ þ
X
t2T
NtPAFtþ ðr ¯rÞ ðdBÞ (2)
where PT(a, b) denotes the transmitted power of node a in dB and
PL(dab) represents the large-scale path loss in dB with propagation
distance daband is equal to
PLðdabÞ ¼PLðd0Þ þ10n log
dab
d0
(3) Fig. 4. Network topologies of an initial network and the augmented networks after deploying relay nodes: (a) the initial network, (b) augmented network by using the proposed method, (c) augmented network by using the MST-based method, and (d) augmented network by using the VW method.
two types of propagation scenarios are considered: (1) all direct PAFC Partition loss of a concrete wall (dB) 13–17
paths are not blocked, and (2) part of the direct paths are blocked by one, two, or three walls. In the second type, the percentage of zero, one, two, or three blockage is given as the followings: (1) light blockage: 50%, 50%, 0%, and 0%, respectively; and (2) heavy blockage: 25%, 25%, 25%, and 25%, respectively. Here, sufficient field measurements have been carried out at 9th floor of Engineering Building Four in the National Chiao-Tung University, to abstract value of indoor channel parameters such as PL(d0), n, and PAFt. Their ranges are shown inTable 1(d0is
equal to 1 m).
According to the above table, for simplification, PAFtis chosen
as 7 dB and PL(d0) ¼ 15 dB for simulation. In LOS (line-of-sight)
situations, n is equal to 2.5. In non-line-of-sight (NLOS) situations, n is ranged from 2 to 3 due to diversified indoor environments compared with LOS situations.
Fig. 5 depicts the ANRN versus node density and shows
that the proposed method always yields less number of relay nodes than other methods. It is noted that the proposed method provides significant reductions of ANRN compared with MST-based and VW methods in most of samples but trivial
reductions compared with CIDT in LOS situation. Besides, the reductions decrease when the node density is extremely small or is increasing. It is because that when the initial nodes are distributed sparsely (the node density is small), most of optimal locations for deploying relay nodes are on the line between disconnected SD pair, which can be effectively discovered by either 1-D or 2-D methods. It is also easy to understand that when the node density is large and there is a small need to add relay nodes. Therefore, ANRN is approaching to zero when the node density is large and increasing as well. It is found that the averaged reduction ratios of ANRN,
r
, by using the 2DGA method are 14.41%, 45.8%, and 35.8% in LOS situation, in NLOS situation with light blockage, and in NLOS situation with heavy blockage, respectively. By examining results in NLOS situations, it is found that the less the blockages, the better the reduction is obtained by using the proposed method. It is also noted that the proposed method performs better reduction than another 2-D method, i.e., CIDT, in NLOS situation. With better reduction in both NLOS and LOS situations indicates that our method is robust and is adaptive to complicated indoor radio environments.AND versus node density is depicted inFig. 6. The node degree of each method increases linearly with the increasing of node density in nature. It is shown that the proposed method provides near equivalent node degree comparing to other methods by deploying less number or relay nodes. As to the ANNC in NLOS situations, which is depicted inFig. 7, the 2DGA method always provides a connected WSN after deploying relay nodes. On the other hand, the 2-D method (i.e. CIDT) without precisely estimating link connectivity would lead to near equivalent ANNC as 1-D methods. With Figs. 6 and 7, the proposed method can guarantee to provide a connected network without increasing node degree. On the other hand, all of other methods are not robust in the NLOS situation, especially when the blockage is heavy.
Fig. 8 shows ANRN versus total number of initial node with constant node density as 1
250nodes/m
2. It is found that reduced
ANRN is achieved in all of the investigated topology sizes compared with other methods. It is noted that ANRN increases linearly with number of initial nodes. The averaged reduction ratios of ANRN are equal to 22.5%, 52.7%, and 41.6% in LOS situation, in NLOS situation with light blockage, and in NLOS situation with heavy blockage, respectively. The proposed method always provides a connected WSN whether the number of initial nodes is small or large.
4. Conclusion
In this research, we propose a heuristic method to reduce number of relay nodes for bridging all disconnected node pairs of a randomly dispersed WSN. This method has two major advantages over the traditional methods: (1) it improves the methodology for discovering relay node locations by utilizing a 2-D search algorithm, which yields every relay node to bridge maximum number of disconnected node pairs around it; (2) it enhances the robustness of the 2-D search algorithm by employ-ing a sophisticated radio propagation model for estimatemploy-ing link connectivity adaptively over applied radio environments. Simula-tion result validates its efficiency and robustness compared with Fig. 7. The ANNCs versus node density: (a) in NLOS situation with light blockage,
and (b) in NLOS situation with heavy blockage.
Fig. 8. The ANRNs versus number of initial nodes: (a) in LOS situation, (b) in NLOS situation with light blockage, and (c) in NLOS situation with heavy blockage.
existing methods. Above all, the proposed method is not only cost effective but also adaptive to complicated radio environments for deploying relay nodes.
Acknowledgment
This work is supported by the National Science Council of Republic of China under Contract numbers: NSC-95-2218-E-009-013 and NSC-95-2752-E-009-014-PAE.
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