Optimized Operation for Infrastructure-Supported Wireless Sensor ...

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Secon 2010 proceedings.

Optimized Operation for Infrastructure-Supported Wireless Sensor Networks Eun-Sook Sung

Miodrag Potkonjak

Visual Display Division Samsung Electronics Suwon, Korea [email protected]

Computer Science Department University of California, Los Angeles Los Angeles, USA [email protected]

Abstract—Due to the energy-constrained nature of wireless sensor networks (WSNs), a variety of communication protocols which rely on cluster-based topologies to enhance network capacity or to prolong network operational lifetime have been well studied heretofore. In this paper, we instead study a comprehensive perspective that searches for an optimal operation that considers backbone node placement and communication scheduling methods, as well as network connectivity properties. Specifically, we aim to answer the following three questions: how many backbone nodes are necessary, where to position these nodes, and which backbone nodes can communicate simultaneously to maximally serve the networks. We study the scalability of our approach and its dependency on parameters such as network size and density and present simulation results.

I. I NTRODUCTION WSNs, where the constituent nodes are connected in an ad-hoc manner, have been widely used to monitoring various environments and obtaining fine-grained measurements from the physical world. These nodes take measurements and forward them regularly to the gateway, but need not communicate frequently with the Internet. Although WSNs are a special type of wireless ad-hoc networks that can operate without requiring any infrastructure, they can be differentiated from traditional ad-hoc networks in that the constituent nodes are extremely energy-constrained and the number of deployed nodes can be in the hundreds or even thousands. Furthermore, the networks are expected to operate for long periods of time without any human intervention. From the design perspective, the architecture of such resource-constrained networks must be different from that of general-purpose ad-hoc networks. Recent studies advocate that the various roles played by each node ought to be implemented differently to achieve the performance objectives effectively [18], [19]. The use of infrastructure nodes for WSNs has been proposed for several applications when it has been seen to be beneficial to achieve the goals of special tasks; for example, for location discovery a small number of beacons is provided so that each node need not be equipped with a GPS unit [24]. The use of a backbone has been shown to be a better way to save energy compared with a flat ad-hoc structure, and the related communication protocols have been intensively studied [6], [23]. However, the comprehensive network operational problem,

where the goal is to build an optimal number of backbone nodes in such a way that every node connects with high link quality to its backbone node and the backbone nodes maximally serve the network, has received little attention. This network operational problem consists of NP-complete sub-problems. There have been many studies for the subproblems, and the researchers examined the optimal placement methods that are based on the assumptions of backbone nodes that are regularly distributed or pre-defined [9], [10], [12], [13]. Those assumptions clearly limit the types of possible solutions. In this paper, we address the network operational problem and aim to prolong network operational lifetime by allowing the low-power nodes to turn their radios off for long periods of time. We separate the role of forwarding messages from the low-power nodes and designate specific infrastructure nodes for that purpose. These infrastructure nodes are dedicated to providing a communications backbone to relieve the forwarding overhead of the low-power nodes. Reducing the duty-cycle of the low-power nodes contributes significantly to extending the network lifetime. From an implementation perspective, the role of the backbone nodes can be served by special nodes that have superior capabilities including faster communication, increased processing power, and no battery limitations. Due to the high cost of deploying and managing such backbone nodes, it is important to construct a minimal infrastructure, by minimizing the number of actually deployed backbone nodes. We present an approach for building a minimal infrastructure and maximizing the number of nodes to be served simultaneously as well as satisfying communication quality between the infrastructure and constituent nodes. The starting point for our approach is to build a realistic model for wireless links using real packet traces. The reception rate over a link is modeled in terms of the distance between the sender and receiver. This model is used to create the objective functions for the backbone node placement problem. The backbone nodes are placed in such a way that for each low-power node there is always an associated backbone node. We formulate this placement problem using an integer linear programming (ILP) and non-linear programming (NLP) instance. We first present an ILP formulation to group nodes

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that rely on a backbone node and select only one node to represent the group, minimizing the number of selected nodes. The selected nodes are called representative nodes. We also study a heuristic algorithm for the representative node problem and compare the solution from the heuristic algorithm to that from the ILP. Once the representative nodes are chosen, the backbone node placement is determined by the NLP formulation with the locations of the representative nodes. We note that the proposed approach is based on a realistic wireless link model, while many previous studies assume a unit disk model. In the unit disk model, two nodes are in communication range if they are within a certain predefined range, and are not able to communicate otherwise. However, we advocate a more realistic and accurate model (which is therefore, useful) than the unit disk model. Our link model takes into account losses due to wireless channel propagation. We elaborate further on the specifics of the link model in Section III. With this model, we place a minimal number of backbone nodes. We then address the problem of scheduling when each backbone node will serve its associated low-power nodes, so that as many nodes as possible can be served. In this paper, network capacity is defined by the number of nodes served simultaneously without any communication interference. As a result, the capacity becomes a function of the number of low-power nodes under the control of the backbone nodes. As the number of nodes that want to communicate with a single backbone node increases, the number of packet collisions also increases. We aim to schedule to optimize the network capacity. It should be noted that our two sub-problems, placement and scheduling, have both been shown to be NP-complete [16]. One of our goals is to provide a general guideline for the number of infrastructure backbone nodes needed to serve a given number of low-power nodes, rather than to study approximation or distributed algorithms for a specific sub-problem. Our contributions are three-fold: We decompose the overall network operational problem into methodical sub-problems and obtain optimal and/or heuristic solutions for each sub-problem. We first present an ILP formulation to obtain the solution of the representative node selection problem. We then compare the solution from an optimal ILP to that from a heuristic algorithm. For solutions to the backbone node positioning problem, we use a NLP formulation. Next, we present an optimal scheduling method using a new graph coloring heuristic algorithm. Finally, we show that the proposed component solutions can be used in solving similar problems arising in other communication tasks. II. R ELATED W ORK There has been lots of research using hierarchical architectures. We group them into three areas: WSNs, Wireless Mesh Networks(WMSs), and Mobile Backbone Nodes(MBNs). In hierarchical WSNs, all nodes are divided into several clusters according to a certain clustering algorithm. LEACH [23] and

VCA [22] are two such algorithms. In each cluster, one node is selected as the head and the rest of the nodes communicate with the head. The focus is not so much to achieve an optimal distribution of cluster heads, but to balance the load among clusters, while our goal is to optimally operate the networks by employing high capacity nodes. Over the past few years, dominating set based approaches from WMNs have formed a generalized category, in which the capabilities of access points are examined. Many studies focus on energy-efficient communication protocols [6], fault tolerance solutions using the k-connected multiple dominating set method [12], and localized approximation algorithms of connected dominating sets [7], [11]. Scheideler et al. [11] theoretically analyze a good approximation algorithm of the distributed minimum dominating set problem for wireless communication, based on a physical interference model that incorporates physical carrier sensing and shadowing. Chandra et al. [17] present relaying algorithms to place Internet gateways in a multi-hop WMN. They formulate the gateway placement problems as a network flow problem, given the knowledge of traffic flow and a set of finite possible gateway locations. In WMNs, where wireless bandwidth is much more limited, the research focus is on how to maximize transport capacity, under certain assumptions. For example, Mao et al. [8] examined the upper and lower bound of network capacity under the assumption of regularly distributed base stations. Liu et al. [10] proposed a novel grid-based gateway deployment method and studied the different capacity scaling behaviors for different network dimensionality. Kozat et al. [9] also examined how much the per source node transport capacity can be achieved under the number of nodes per base station. However, we believe that a pre-defined topology or a given number of backbone nodes can limit the types of solutions that are possible. This restricts the optimal placements and operations of the infrastructure. There also has been active research on MBNs such as air support of ground vehicles [1], [2], [13]. The problem is to place a given number of mobile backbone nodes and assign the regular nodes to them in order to, for example, maximize the number of regular nodes that achieve a given throughput level. Srinivas et al. [2] focus on the minimum number of mobile backbone nodes needed for connectivity based on the unit disk model. Later they [13] present two techniques for placement and assignment that search over all possible mobile backbone node placements. They cast the problem as a maximum flow instance, in which the goal is to place a fixed number of backbone nodes to maximize fairness and throughput under node mobility. The authors also assume that different clusters operate on different frequencies to avoid communication interference, while we formulate this problem as an instance of graph coloring. Using graphcoloring algorithms for collision-free transmissions is not new. Among many, in Balasubramanian et al. [20], a method to improve the success rate of messages meeting their deadline in a small-scaled two-level hierarchical wireless network is proposed. They use a well-known graph-coloring heuristic


Fig. 1. Reception rate as function of distance: scatter-plot and monotonic regression fit.

high R2 value. In addition, the presented model confirms the recent well-known findings on the characteristics of lossy wireless links such as good links, transitional links, and bad links [25]. There are two types of communication: high power nodes’ radio signals for the purpose of forming a backbone across the whole network, and low-power nodes’ radio signals. Backbone nodes can be assumed, not necessarily, to have two radios, one low power radio for communicating with lowpower nodes, and one high power radio for communicating with other backbone nodes. We assume that the high power and low power radio levels have been pre-determined and adjusted. In our study, one-hop communication capability of backbone nodes is assumed to be stronger than that of lowpower nodes so that the backbone nodes are connected. B. System description and assumptions

algorithm to maximize the number of messages that can be sent simultaneously in a collision-free manner. Although the optimal solution for the placement problem is claimed to be obtained in polynomial time in [13], their proposed heuristics are prohibitively complex to be applied in practice unless the network is very small. Our approach is different from the above in that we focus on investigating an optimal number and placement of backbone nodes in fairly large scaled networks, instead of giving a theoretic framework only applicable to a small number of nodes. We explore a placement and operation problem given a set of randomly distributed nodes under a realistic wireless link model and present practical solutions and numerical estimates about how many backbone nodes are necessary, where to place these nodes, and how to operate them so that a network capacity objective is optimized. III. P RELIMINARIES We begin this section by introducing our low-power wireless link model. A. Communication model The starting point for the communication model is system measurement data conducted on traces of deployed nodes. The data is from a testbed of Mica 1 and Mica 2 mote nodes using the RFM TR1000 and Chipcon CC1100 radio chips [3], respectively. Figure 1 shows a scatter plot of reception rate (RR) versus the distance between the transmitter and receiver nodes. In fact, the actual wireless link data is often characterized by a random component in the sense that although two nodes are at a fixed distance, their link qualities show variability, as seen in the scatter plot of Figure 1. To circumvent this variability, we build a non-increasing continuous link model. The isotonic regression model of reception rate (RR) is shown in Figure 1. The bold piecewise linear line is the least square monotonic fit obtained by using the public package [14]. From a modeling perspective, the presented model is simple but more convincing than the unit disk model. It is also accurate in the sense that it is based on real data and has a relatively

Nodes are deployed randomly over a two-dimensional field to monitor the physical phenomena and collect measurements. We limit our attention to networks of static nodes, since in most monitoring and surveillance systems the network nodes are fixed and do not move. We consider dense networks composed of a very large number on the order of several thousands to deal with the problems related with fault tolerance and network coverage. The lowpower nodes directly send/receive messages to/from the designated backbone nodes, instead of using multi-hop routing methods. The sensor data reaches the end user via the backbone nodes. These backbone nodes are assumed to use a time division multiple access scheme for direct communication to the low-power nodes. Time is divided into slots, and during each time slot a node is scheduled to communicate with its associated backbone node. The low-power nodes are assumed to deactivate the radio module or stay asleep during the rest of the communication service to minimize their energy consumptions. C. Problem formulation We seek a method where a minimal set of backbone nodes is optimally placed within a randomly distributed network of low-power nodes so that the communication quality between each low-power node and its associated backbone node is good. To this end, we decompose this network-planning problem into three sub-problems and propose the following three methods to solve each sub-problem. In the first phase, a set of representative nodes that cover the whole network is identified, so that every node must be mapped to at least one backbone node. In the next phase, we use the locations of the representative nodes to determine the best locations of backbone nodes for both optimizing overall communication quality of the network and satisfying a link quality requirement. Specifically, the link quality requirement dictates that each low-power node is required to be within a predefined communication range from at least one backbone node. In the last phase, the problem of scheduling backbone node communication is addressed so that as many backbone nodes as possible can transmit simultaneously. Backbone


nodes then allocate MAC layer time-slots to the low-power nodes to send and receive messages. IV. P LACEMENT AND O PERATION A. Selection of representative nodes Our objective is to place a minimal number of backbone nodes so that every node has a high-quality link with its associated backbone node. For an efficient organization of such backbone nodes, clustering the low-power nodes into a number of groups could be the first step. However, it is well known that this clustering problem is NP-complete [16]. Rather, we observe that nodes that are physically close may effectively share a backbone node. Based on this observation, we decide to group the nodes that rely on a backbone node and select only one node to represent the group. In other words, if the selected representative node transmits or receives messages from its backbone node, the other nodes in the group should also have a high probability of being able to transmit or receive messages. During the actual backbone node placement phase, if there exists a node with less than the predefined link quality to its backbone node, an additional backbone node is placed. The problem of finding representative nodes can be solved as a dominating set problem. We first show an ILP formulation to this dominating set problem that produces an optimal solution. We randomly generate a set of nodes, S={Si }, i = 1, . . . , N . We introduce the binary indicator variables of the formulation di , i = 1, . . . , N , denoting whether node Si is selected as a representative node, shown in (2). Then, the objective function (OF) of this optimization problem is to minimize the number of representative nodes, shown in (1). OF : min di =

N

di

(1)

i=1

1, if Si is selected as a represented node 0, otherwise

(2)

To solve this problem, we introduce another term, Cij , indicating whether the link quality between Si and Sj is above a predefined link quality, a high RR value. 1, Si and Sj are within a communication-range Cij = 0, otherwise (3) Then, our constraint, shown in (4), restricts the condition that for each Si , either Si is selected as a representative node (i.e., di = 1), or Si has at least one neighbor, say Sj , (i.e., Cij = 1, i = j) that belongs to the representative nodes (i.e., dj = 1). di +

N

Cij dj ≥ 1, i = 1, . . . , N

(4)

j,j=i

Solving (1) under the constraint of (4) produces the solutions to our first phase sub-problem. While the ILP formulation provides the optimal solution in polynomial time, it is infeasible to obtain solutions for very large scaled networks. For this reason, we also study a

heuristic algorithm to the minimum dominating set problem, which is based on the scoring idea of [4]. We will compare the results about the numbers of selected nodes from both algorithms in Section V. The idea of the heuristic algorithm is that a node is added to the dominating set only if that node or its neighbor becomes isolated. To this end, a scoring method that determines the order of nodes to be examined is introduced. The scores and degrees of nodes are initialized by the number of nodes’ one-hop neighbors. The algorithm iteratively picks the node with the lowest score to check either its isolation or its neighbors’ isolation. Initially, all isolated nodes are their own representative node. The score of the added node is set to the largest value to signify that this node is no longer considered. Whenever a node has a neighbor with degree one, i.e., the node should cover the neighbor, the node is added to the representative set. Otherwise, if the degrees of its all neighbors are greater than one, the associated score and degree values are updated as follows. The scores of the node’s neighbors become incremented one, which accounts for the fact that the nodes are not considered yet, and thus increase their worth. On the other hand, the degrees of its neighbors are one step lower, which accounts for the fact that the node does not connect or dominate its neighbors anymore. Then, the score of the node is set to the maximum value, to mark the node that has been already examined. For the next step, the algorithm is continued to pick the node with the lowest score. Following the description, the algorithm is guaranteed to terminate after a number of iterations less than or equal to the number of nodes. In Figure 2 (a) and (b) compare examples of scatter plots of representative nodes selected from the ILP and heuristic algorithm in 200 node and 600 node networks, respectively. Small dots denote regular low-power nodes, and the bigger dots denote the representative nodes chosen by the algorithms. In Figure 2, there are two things to note. First, although the solutions from the ILP and heuristic approaches are not exactly the same, they have much in common, and the heuristic algorithm gives a solution that is close to the optimal ILP solution. More importantly, in comparing the solutions in 200 node and 600 node networks, we observe that the representative nodes become sparse and located far from each other. This is especially prominent in Figure 2 (b). From this, we conjecture that as the network size becomes larger the set of representative nodes might converge to a regular structure such as a square or triangle, shown in Figure 3. Looking at closely only the boxes in Figure 2, we observe that this convergence is faster in ILP solutions (upper left, lower left) than in heuristic solutions (upper right, lower right). To investigate this effect further, we experiment on larger scaled networks only using the heuristic algorithm because it is infeasible to obtain an ILP solution for such large network. In Figure 4, we notice that the representative sets in these very large networks are generally far from each other. Thus, we believe that the pattern of representative nodes might converge roughly to a pattern similar to that shown in Figure 3. For this reason, we believe that if there is no placement


algorithm available, the selection of representative nodes in the pattern of a square or triangle would not be a bad choice in a very large network. B. Placement of backbone nodes After a set of representative nodes is determined, the next step is to select the optimal locations of backbone nodes. This step fulfills the simple requirement of placing backbone nodes in such a way that every node in a network has a high-quality link to its associated backbone node. However, in our approach, we try to find the best locations to optimize link quality parameters of overall reception rates between backbone nodes and low-power nodes. We formulate this placement problem as an instance of NLP. The unknown variables for the NLP problem become the locations of backbone nodes.

(a) 200 nodes

(b) 600 nodes

Fig. 2. Scatter plots of representative nodes selected from ILP (Left) and heuristic algorithm (Right) in networks with (a) 200 nodes and (b) 600 nodes. Small black dots denote normal nodes and the bigger red dots denote the representative nodes.

a) Rectangle

Fig. 3.

b) Triangle

Example of regular structures

We refer to the coordinates of backbone nodes as (xBi , yBi ), i = 1, . . . , M , where M is the number of representative nodes. Since NLP solver normally requires good starting points or seeds for all the variables being optimized, we use the locations of the representative nodes, obtained from the first phase, as the initial values for the unknown variables in solving our NLP formulation. In our work the objective is to optimize overall communication qualities between the backbone nodes and low-power nodes, and the backbone nodes are placed such that the sum of link qualities to their associated low-power nodes is maximized, as shown in (5). We note that as opposed to ILP, an explicit constraint is irrelevant in NLP, and (5) is a sound NLP formulation. Let g denote the link quality model of reception rate shown in Figure 1, which is a function of the geometric distance between two nodes. Let dkj denote the geometric distance between backbone node Bj and its associated low-power node Sjk where k = 1, . . . , Nj and Nj is the number of nodesunder the control of Bj . The link quality between them is g( (xBj − xSjk )2 + (yBj − ySjk )2 ). The goal is to find the best location of B ={Bj }, {(xBi , yBi )}, such that every node under the control {Bj } is within a best communication range. Nj M g(dkj ) (5) OF : max j=1 k=1

(a) 1000 nodes

(b) 6000 nodes

Fig. 4. Representative nodes in a network with 1000 nodes and 6000 nodes

For this non-linear optimization we chose to use the conjugate direction-based unconstrained function optimization technique. The conjugate directional method has been known to be effective in solving general objective functions [15]. This method is similar to both the steepest decent method and Newton’s method, but tries to ameliorate the slow convergence associated with the steepest descent method while avoiding excessive information required by Newton’s method. We used the conjugate directional library provided in the public package WNLIB [5]. After obtaining the solution to the coordinates of backbone nodes from the NLP, it is necessary to evaluate whether every


low-power node satisfies the is because it is possible for of any backbone node, while representative nodes. If there backbone node is deployed.

link quality requirement. This nodes to be out of coverage they are within range of their is such a node, an additional

C. Scheduling After solving the problem of backbone node placement, we direct our attention to the operational issue of how to coordinate the deployed backbone nodes for efficient communication. Specifically, we determine which backbone nodes can transmit simultaneously without causing a collision at the receiving nodes. Given a set of deployed backbone nodes, {Bi } from the second phase of the proposed approach, the problem of safe transmissions can be solved by mapping it to the graph-coloring problem. We determine that a pair of backbone nodes Bi , Bj cannot transmit simultaneously if they cause any receiving node to experience a collision. The interference range, rI , is not necessarily same as the communication range rC . We pick a constant c > 1 such that dI ≤ c· dC , where dC and dI are distances for communication and interference, respectively. We transform the backbone node scheduling problem to an instance of graph coloring, by introducing a binary integer variable zij denoting the specified condition that restrains two backbone nodes from transmitting simultaneously: zij = 0 if Bi and Bj should not transmit simultaneously, and 1 otherwise. Two backbone nodes are not allowed to transmit their messages simultaneously if there exists a node which is within interference range of both backbone nodes, or two backbone nodes are within interference range of each other. This condition is represented as an edge between Bi amd Bj in the graph. The solution of the graph coloring problem includes: 1) the minimum number of colors needed to color the entire graph, (referred to as T) and 2) T sets of backbone nodes that are colored by the same color B={Bk }, k = 1, . . . , T . The minimum number of colors used represents the minimum total number of time slots that is needed in order for all the backbone nodes to transmit communication messages at least once. The backbone nodes that share a common color represent the groups of backbone nodes that can transmit simultaneously. The heuristic algorithm used is similar in spirit to DSATUR developed by Brelaz [21], in that it chooses the nodes with favorable characteristics earlier. For example, it is beneficial to choose nodes starting with the most constrained and ending with the least. In effect, it is better to choose nodes with the most constrained neighbors earlier than the most constrained nodes. In order to further enhance the quality of the solution, the notion of sensitivity is introduced. Essentially, the sensitivity of a node is the difference between the number of solutions given by choosing between the best and second best possible choice of color. In other words, a node is called to be sensitive if it makes the algorithm lose many possible options by taking the second best possible

choice of color, rather than the best possible choice of color. The way of setting a sensitivity is as follows. A sensitivity, which is initialized by zero, is computed by going through all of the uncolored neighbors and seeing to which colors they are adjacent. Each neighbor has a list of the colors adjacent to it. To compute the sensitivity, first, a node maintains a list of colors to which its neighbors are adjacent. For each color, a count of the neighbors with neighbors of that color is maintained, referred to q-value. Then, the q-value is subtracted from the number of uncolored neighbors in the current node, and the result stands for how many neighbors will be affected by choosing that color. Each color has a count associated with the number of affected nodes, referred to R. Although the idea of sensitivity of a node comes from the number of solutions given by the best and the second best possible choices of color, we improve this idea using the three best possible choices of color. We find the R values for those colors that would affect the most, the second-most, and the third-most numbers, referred to R1 , R2 , and R3 , respectively. To determine a sensitive measurement, two numbers are used. One is the difference between the counts associated with the colors with the highest number of affected nodes and the second highest numbers, which is R1 − R2 . The other number is the half of the difference between the second and 3 . The idea behind using third highest counts, which is R2 −R 2 this half of the difference between the second and the third highest counts is that more impact is given to the difference between the highest and the second highest R values, while the difference between the second and the third highest R values is still considered. Finally, the two numbers are added 3 , is stored as the sensitivity and the sum, (R1 − R2 ) + R2 −R 2 value for the node. In the phase of choosing the order of coloring, the sensitivity of each node is calculated by adding up the sensitivity of each of its neighbor nodes. The ordering where nodes are to be considered is based on their sensitivity: (i) the node with the most sensitive neighbor is chosen first. However, if there are multiple such nodes, a tie is broken by the following priority. (ii) The node that is the most sensitive is chosen. (iii) The node with the most constrained neighbors, i.e., the node with the most uncolored neighbors, is chosen. (iv) The most constrained node is chosen. (v) The first such node is picked if there is still a tie after applying the first four tie-breaking rules. A node maintains its sensitivity and the best color with which to color that node, which is determined in calculating the highest affected nodes. Once a node is colored, the list of neighbor colors for each of the node’s neighbors also is set. V. EXPERIMENTAL RESULTS We study the scalability of our method by varying the network size and density. The results of the experimentation are based on the wireless communication link model using data collected from deployed low-power wireless sensor networks [3]. The network density is defined by the number


Graph Coloring Algorithm for Scheduling Input: A graph with {Bi }, {Si }, and interference adjacency list Output: Interference-free scheduling: 1. Minimum number of time slots 2. Sets of backbone nodes that transmit simultaneously While ∃ uncolored node Do 1. pick a node according to the ordering method 2. color the node & add the color to its neighbors’ color list 3. update nodes’ sensitivity (a) density 0.1 networks

of nodes per square meter. Every result reported herein is obtained from more than 50 simulation runs, and all the results are shown as box-plots. The top and bottom lines of the box indicate the upper quartile and lower quartile values, and the line inside of the box is the median value. The maximum and minimum values are also shown. In each density, we varied the number of nodes from 50 to 1000 in steps of 50. A. Required number of backbone nodes We first evaluate the representative node selection algorithms by comparing the numbers of selected representative nodes from the heuristic and the optimal ILP algorithms. Then we present the required number of backbone nodes to serve networks in fulfilling the threshold link quality requirement. While the ILP solution gives the optimal solution in a polynomial time, it does not scale well. Thus, for large-scaled networks, the heuristic algorithm is essential. Here, we try to evaluate how much the heuristic algorithm might deviate from the optimally minimal solution. The way we compare them is to study the ratio of the number of representative nodes used by the heuristic algorithm and the ILP algorithm for small-scaled and medium-scaled networks. We call this number the normalized number of representative nodes and report the results for sparse networks (density 0.1), medium density networks (density 0.3), and dense networks (density 0.5) in (a), (b), and (c) of Figure 5, respectively. The x-axis is the number of nodes in the network, and the y-axis is the ratio, the minimal number of representative nodes obtained from the heuristic approach that is normalized against the ILP-based approach. As shown in Figure 5, the heuristic algorithm calculates a bigger set of representative nodes in comparatively large sized and dense networks. For networks of 500 nodes, the increase is about 12% (density 0.1), 25% (density 0.3), and 35% (density 0.5) when we use the median over a set of simulations. These results confirm that obtaining the optimal representative nodes in dense networks is harder than in sparse networks, and thus the deviation in dense networks becomes larger than in sparse networks. However, those amounts might be acceptable, especially in light of the fact that the ILP algorithm cannot be applied to large networks. After selecting the representative nodes, we use their coordinate values as the initial values in solving our NLP formulation for the placement of backbone nodes. The graphs of Figure 6

(b) density 0.3 networks

(c) density 0.5 networks

Fig. 5.

Normalized number of minimum dominating set vs. Network size

present the required number of backbone nodes necessary to serve the network, so that every node has a higher reception rate than a predefined threshold value with its associated backbone node. In this paper, the predefined threshold is set to 80%. As expected, an increase in the number of nodes leads to a larger number of backbone nodes, which is required to serve their associated nodes with the guaranteed link quality. Figure 6 indicate that the number of backbone nodes increases linearly as the network size increases. The reason why the required number of backbone nodes in the sparse networks of (a) in Figure 6 is larger than in the dense networks of (b) in Figure 6 is because the size of a sparse network is larger than that of a dense network. For example, a thousand nodes of density 0.1 are deployed over an area of about 1002(m2 ), while a thousand nodes of density 0.5 covers only about 44.72(m2 ). The backbone nodes provide the lowpower nodes guaranteed communication quality. The low-


(a) density 0.1 networks (a) density 0.1 networks


Fig. 6.


Number of minimal backbone nodes vs. Network size Fig. 7.

power nodes are given a set of communication slots according to a time division method for direct communication to their assigned backbone nodes, and each of the low-power nodes can access a single backbone node with a link quality above the predefined threshold. B. Guaranteed service rate During the last phase, the backbone node assignment problem is solved by using the graph coloring heuristic algorithm we have described so that as many backbone nodes as possible can serve the maximum number of low-power nodes simultaneously. As a result, we obtain the total number of time slots, T , which is the number of time slots needed by all backbone nodes to send their messages once without any interference. Given a T value, we are interested in how much each lowpower node can communicate with its associated backbone node. In other words, we want to know the rates at which each node can be served by its associated backbone node, and we call this the guaranteed service rate. This guaranteed service rate can be denoted by a function of the number of low-power nodes under the control of backbone nodes. We obtain the guaranteed service rate under the assumption of backbone nodes equalizing the service time to their constituent nodes. The total number of time slots needed for all backbone nodes to transmit once is set to 1. Then, the service rate to 1 , where Ni is the each node can be denoted as the T ×N i number of constituent nodes under the control of backbone node Bi . We first evaluate the overall service rate at which a node can communicate with its associated backbone node. In

Average service rate vs. Network size

this calculation, the median value of the service rates is used, and the results are presented in Figure 7. We next examine the minimum service rate, and the results are presented in Figure 8. For example, in density 0.1 networks of a thousand nodes, each node is served at a minimum rate of 0.017 by an associated backbone node, while at least the rate of 0.005 is guaranteed in dense networks (density 0.5). These measurements are partially because a backbone node in networks of density 0.5 governs more than three times of nodes than in networks of density 0.1. These service rate results also lead to the possibility that during the rest of the service slots each node can go to sleep mode, or at least be able to turn its radio off so that it can save its energy. In addition, we estimate other parameters; for example, the number of nodes that can be served simultaneously in broadcasting service scenarios without causing any interference. In Figure 9, the upper box-plots show the number of low-power nodes that can be served at the same time, while the lower box plots show the minimum number of nodes served simultaneously. In (a) of Figure 6 and Figure 9, about 330 nodes can be simultaneously served with the construction of 150 backbone nodes for a thousand node networks of density 0.1. In dense networks of density 0.5, about 275 nodes can be simultaneously served with the construction of 45 backbone nodes. VI. C ONCLUSION We have studied a WSN that employs an infrastructuresupported hierarchical architecture and proposed algorithms


guideline for the operation of wireless networks to achieve efficient utilization of resources. For future work, we are interested in how to incrementally upgrade the existing infrastructure-based wireless network to account for additional nodes or traffic requirements. R EFERENCES

(a) density 0.1 networks


Fig. 8.

Minimum service rate vs. Network size

Fig. 9. Number of nodes served simultaneously vs. Network size in density 0.1 networks in a broadcasting service scenario

for a minimal construction of backbone nodes and network capacity optimization. Our technique consists of two primary phases. In the first phase, we place a minimal number of high capacity nodes to form a backbone network, which facilitates the interconnection of the backbone nodes across high power links. In the next phase, we schedule the backbone nodes to maximally serve the networks without causing any communication interference. We have studied how much each node can be served by its associated backbone node. These results are useful for network lifetime longevity because during the rest of the durations assigned to each node, nodes can deactivate the radio to save their batteries. Simulation studies of the proposed approach show that it allows nodes to turn the radios off up to 95% to 99% depending on network size and density. Finally, the presented approach gives a general

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