Wireless Netw (2010) 16:65–78 DOI 10.1007/s11276-008-0115-4
Optimized asset planning for minimizing latency in wireless sensor networks Waleed Youssef Æ Mohamed Younis
Published online: 3 May 2008 Springer Science+Business Media, LLC 2008
Abstract Wireless Sensor Networks (WSNs) has been attracting lots of interest in recent years. In such networks sensors data are collected over multi-hop routes at one or multiple base-stations (gateway nodes) for processing. In many WSN applications such as disaster management and combat field surveillance, rapid response to detected events is necessary and thus data latency should be minimal. Given the sensor’s energy and radio range constraints, direct communication with the gateway is inefficient and often infeasible for most deployed sensors. An intuitive approach to limit data latency is to increase the population of gateways and place them in the vicinity of sensors. However, gateway nodes are typically costly and thus it is desired to limit their count. Therefore, there is a need to balance between such conflicting requirements. In this paper, we pursue an integrated approach to asset planning in WSNs so that the data latency is minimized. The goal is to determine the least number of gateways and identify where to place them in the network in order to achieve a certain delay bound on data delivery. We formulate an optimization model for the asset planning problem and present effective algorithms for solving it. The proposed solution scheme employs contemporary search heuristics such as k-means and genetic algorithms. Validation results confirm the effectiveness of our approach in achieving the desired design goals.
W. Youssef (&) M. Younis Department of Computer Science and Electrical Engineering, University of Maryland Baltimore County, Cantonsville, USA e-mail:
[email protected] M. Younis e-mail:
[email protected]
Keywords Wireless sensor networks Asset planning Gateway placement Gateway count estimation Network clustering
1 Introduction In recent years, wireless sensor networks (WSNs) have received lots of attention due to their potential use in many civil and military applications such as disaster management, border protection, combat field reconnaissance and secure installations [5, 10]. Most of these applications involve a large number of sensors that operate unattended in remote and often harsh environments. Sensors are miniaturized battery-operated devices equipped with radios. They probe their surroundings and report any abnormal events, often over multi-hop paths, to a gateway node for further processing. Gateway nodes are deployed in the monitored area along with the sensors and often have significantly more computation and communication resources than sensors. Gateways interface the network with multiple command nodes or user terminals via long haul communication links. Energy is consumed every time sensors send or receive packets. Once its onboard energy supply drains, a sensor stop functioning. In many setups, energy re-supply or energy scavenging from the environment is not available. Therefore, conservative usage of the sensors’ energy is a key for keeping the network operational for longer periods of time. One of the popular schemes for reducing energy consumption is to disseminate data over multi-hop paths. Since sensor data are forwarded to a gateway, the location of the gateway significantly influences the lifetime and performance of the network. When the gateway is located far from data sources, many sensors are involved in relaying data packets and hence energy consumption grows. In
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addition, longer paths boost data latency and risk an increase in packet drops. In many WSN applications such disaster management and combat field surveillance, rapid response to detected events is necessary and thus long delay and unreliable delivery of data would be unacceptable. To efficiently manage large WSNs, gateways often split the load by grouping sensors into clusters; each is handled by a gateway. Network clustering not only enables scalability but also boosts the network lifetime and packet throughput and minimizing data delivery delay [15]. Figure 1 depicts an example clustered WSN architecture in a disaster management application. Most of the published work in the literature focused on efficient grouping of sensors based on a known number of gateways and preset positions of gateway nodes. The number of deployed gateways is usually known and the set of initial gateway locations is often randomly picked or chosen based on a uniform distribution of the available gateways over the area of interest. The node assignment to gateways in that case can be based on proximity, gateway load, etc. [7, 15, 16]. Unlike that work, we study the problem of estimating the least number of gateways and the proper placement of these gateways in order to achieve some desired performance. We call this problem asset planning since the gateways are generally more expensive nodes compared to sensors and it is usually required to minimize their count. In this paper, we focus mainly on meeting a bound on the data delivery delay.
Fig. 1 A large scale sample multi-gateway WSN architecture for serving multiple command nodes and monitoring multiple events happening in an area of interest
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Optimal placement of a know number ‘‘N’’ of gateways is basically one of the un-capacitated facility location problems, which is a well-studied in the operation research literature. All variants of this problem for which N [ 1 is proven to be NP-Hard. The version that we study in the paper is placing N facilities (gateways) and assigning clients (sensors) to each facility so that maximum distance (number of hops) between a client and its associated facility is minimized. Such a problem is referred to in the literature as the ‘‘p-Center’’ problem and is often considered in urban planning. The P-Center problem is proven to be NP-hard [19]. Estimating the minimum number of centers (gateways) is also shown to be NP-hard by formulating it as iterative attempts for optimal placement of an increasing number of centers. Therefore, we pursue heuristics. In this paper we first present our Gateways’ Optimized placement Algorithm for enhanced data Latency, or GOAL for short. The objective of GOAL is to reduce the data latency through minimizing the average number of hops between a sensor and one of the gateways. GOAL employs genetic algorithms (GA) [14, 22], which are a stochastic search technique that mimics the natural evolution theorem. GA have been successfully applied to many problems, especially NP-hard ones and proved to be superior to many other heuristics. They often reach optimal or close to optimal solutions [11]. Since GA also involves substantial computation, we develop simplified versions that base the
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optimization on the Euclidean distance between communicating nodes rather than the hop count. We further extend our approach to estimate the minimal gateway count for achieving a preset bound on the data latency, defined in terms of the maximum allowable length of a data path. Most published schemes on estimating number of gateways tend to use a Brute force method to counter the high complexity of the problem. The Brute force method basically starts by one gateway and then keeps adding additional gateways till the desired performance is obtained [23]. We avoid such slow convergence by starting the search with a relatively accurate estimate. We present an efficient estimation function that significantly expedites the convergence rate to the optimal gateway count. The validation results in a simulated environment confirm the effectiveness of our approach and its superiority to contemporary schemes. The organization of this paper is as follows. The next section discusses related work. Section 3 presents our approach for efficient gateway placement. Section 4 describes how we estimate the least gateway count. The validation experiments are discussed in Sect. 5. Finally, Sect. 6 concludes the paper.
2 Related work Careful placement of gateway nodes is an important problem that impacts the performance and operations of WSNs. Typically, the number of gateways to be deployed is known and the best positions for those gateways have to be found in order to maximize the network performance [8, 27] or the coverage of an area of interest [3]. To counter the high complexity most published approaches try to limit the search space, i.e. the cardinality of the set of candidate locations, in the hope of converging to some choices that achieve near optimal performance. For example, in [13] candidate locations are determined a priori by the application designers. Meanwhile, in [8] the feasible set is restricted to where sensors are. The latter case also applies when the gateway positioning is combined with the network clustering scheme. For example, it may be desirable for the gateways to be placed so that each sensor would reach a gateway in at most K hops, where K is predefined constant. By deciding to place gateways next to some sensors, the positioning/clustering problem becomes in that case finding the K-dominating set which has some polynomial time solution [13]. Unlike our proposed genetic algorithm based schemes, such prior work pursued approximation algorithms [8], integer programming [13] or k-means clustering [23]. In addition, these nonheuristic algorithms have been utilized for optimal senor nodes placement, as in [9]. Notable research related to gateway placement has also been conducted in the context of wireless local area networks
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and cellular infrastructure [12, 24]. The goal is to populate a building with the least number of access point (gateways) so that a user can directly reach at least one of them regardless where he is in the building. Meanwhile, the model considered in [2] and [4] is to use a gateway node as a direct router for a group of mobile nodes that would be otherwise unreachable due to topological reasons such as blockages. However the scope is limited to a single gateway system. In many setups, the number of gateways may not be known in advance and thus the number and positions of gateways are to be optimized. The selection of the most suitable goal for optimization is application dependent and may vary; however, reducing energy consumption and enhancing data latency are the most common objectives in WSNs. While the focus of [17, 21, 23, 25, 26] is on determining the gateway (relay node) count, the objective is different from ours. The authors geared their study for finding the least number of gateways necessary for achieving a certain network lifetime [17, 23, 26] or strong inter-node connectivity [21, 25]. The approach is to increment the number of relays until the desired goal is met. In [23], the k-means algorithm is used in grouping nodes and gateways are placed at the centroid of the individual clusters. The process is repeated with an increased gateways count until a desired minimal bound on network lifetime is achieved. We classify such approach as a Brute force method since the convergence rate is the worst. Our approach is more efficient because it uses an advanced estimator function to identify an initial solution that is very close to the optimal number of gateways needed. Genetic algorithms have been employed for optimizing the design and operation of WSNs. Most notable is the work of Khanna et al. [20], which addresses efficient topology maintenance in WSNs. The goal is to generate optimal number of sensor clusters that results in minimizing power consumption while maximizing sensors coverage. However, the focus is mainly on positioning sensor nodes. The problem considered in [1] is somewhat similar to the multigateway placement problem. The goal is basically to find the most suitable positions of radio transceivers in an industrial facility. However, the optimization objective is mainly coverage and throughput. In addition, the operation model is very different from that of WSNs. Genetic algorithms were also used for scheduling intra-cluster data gathering so that the inter-cluster interference is minimized [18]. We are not aware of prior work that addresses the asset planning problem, i.e., the identification of the least gateway count and their optimal positions, in an integrated way as we do in this paper. In [27] we presented a preliminary version of GOAL. In this paper, we propose an additional heuristic and highlight previously unexplored trade-off. We further extend the approach to find the least gateway count for achieving some desired performance.
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3 Optimized gateways placement In this section, we present a novel Gateways’ Optimized placement Algorithm for enhanced data Latency (GOAL). First, we start by defining the problem more formally and then discuss GOAL in detail. Some variations of the approach are also presented. In Sect. 4 we extend the approach to estimate the minimal gateway count required to achieve a preset bound on data latency. 3.1 Problem statement The problem we are studying in this paper is how to place a known number of gateways in an area, which has possibly 100s or 1,000s of deployed sensor nodes, such that the data collection latency is minimized. Data latency in this context is measured in terms of the average number of hops in each data path from source to destination. In typical WSN environments, sensors measure ambient conditions in their surroundings and send the collected data to a gateway either directly or through relaying nodes. Even if a sensor can reach the gateway directly, it usually uses multi-hop routes in order to minimize the total communication energy [5]. However, increasing the number of hops prolongs the delivery delay and thus balancing the energy consumption and data latency is subject to trade-off. As explained in Sect. 1, optimal placement of multiple gateways to minimize the maximum data latency of the data of the individual sensors is reducible to the P-Center problem which is known to be NP-hard [19]. Therefore, we pursue a heuristic approach. We observe that the placement of gateways can be viewed as a clustering problem, where the number of clusters equals to the number of available gateways. In other words, we strive to partition the sensors into disjoint clusters such that every cluster can be best served by one gateway. Given our goal of reducing data latency, the clustering criterion is to minimize the total number of data forwarding operations. Assume that N is the sensors’ count and M is the number of available gateways. Let the set P(Si, Gk) represents the nodes on the multi-hop path from a sensor Si : i B N to a gateway Gk : k B M. The objective is then to find an assignment A(Si, Gi,k) so that N P 1 PðSi ; Gi;k Þ is minimized. Since N stays constant, we N i¼1
simplify the calculation and minimize the total number of N P PðSi ; Gi;k Þ: hops on all paths instead, i.e., i¼1
Clustering sensors to minimize the total hop count requires establishing a routing tree to qualify every possible grouping arrangement. Even if optimized, a network layer analysis still complicates the clustering process. Therefore, we also explore trading off the complexity and
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the quality of the solution measured in terms of the achievable average delay. We alter the clustering criterion to become the minimization of the sum of all distances between a sensor and its assigned gateway, i.e. to minimize N P ðDðSi ; Gi;k Þ; where D(Si, Gi,k) is the distance between i¼1
the sensor Si, and its assigned gateway Gi,k. As will be shown later, this altered objective is easier to implement compared to the hops-based one. It involves no additional overhead for building intra-cluster routing trees in the optimization process. Details about the hop count minimization algorithm and its simplified versions are presented in the next subsections. 3.2 The detailed GOAL approach
As we discussed the gateway placement problem can be viewed as grouping the sensors into disjoint sets (clusters); each served by one gateway, so that the average number of data relaying operations is minimized. We employ genetic algorithms [14, 22] to achieve this objective. Our proposed approach, GOAL, encodes the area of interest into multiple clusters equal to the number of available gateways. Using this encoding, GOAL evolves until it finds the best cluster assignment for each sensor node. GOAL then optimizes the placement of gateways to better serve the sensors of the individual clusters. Basically, it employs Breadth First Search (BFS) to find a location that makes the gateway reachable to the largest number for sensors in the cluster. Figure 2 presents a high level pseudo code of the GOAL approach. Additional details of the approach are provided next.
Algorithm GOAL () Generate a random initial population P repeat Tournament_Selection(P) (m1, m2, m3) Perform Crossover (m1, m2) u mutate(u) um LocalOptimize(um) replace(u, m3, P) until (there is no improvement or max iterations count is reached) Clusters C best member of P; For each cluster c C Define b as a location; set to 0; Set Nb to 0, Calculate the centroid position CP; Form a (m × m) grid with CP at its center For each grid cell g loop Count sensors Ng that can reach CP If Ng > Nb then b = g End loop Place gateway at the center of b End For End;
Fig. 2 Pseudo code for the GOAL algorithm
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3.2.1 Encoding In GOAL, an individual member in the population represents a possible clusters’ assignment of all sensors in the deployment region. The length of the individual is equal to the number of deployed sensors, i.e. N. The individual member is represented as a one dimensional array indexed by the sensors number where the corresponding assigned cluster is stored. For example, in a network of two gateways and ten sensors, an individual member in the population is represented as: Index
0
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1
The above individual indicates that Cluster # 1 contains sensors (0, 3, 4, 5, 8, 9) and gateway # 1 while Cluster # 2 has sensors (1, 2, 6, 7) and gateway # 2. In GOAL, the size of the population remains constant throughout the execution of the genetic algorithm.
establishment of this type of routing information can enhance the performance of GOAL. It enables the algorithm to prepare this information only once and not to repeat the calculation every time a new gateway location is nominated. We employ the Floyd-Warshall algorithm [11] to build such generic routing table between any pairs of sensor nodes. 3.2.4 Evolution The following techniques are employed to help GOAL in reaching an optimal solution. •
•
3.2.2 Fitness The fitness of each individual member is calculated as the sum of the number of hops on all least-cost paths for all sensors in the network. This value can be calculated as follows. The fitness for each cluster is calculated then added up to represent the fitness of the individual. For each cluster, the fitness is the total number of hops from each sensor node to the centroid point for that cluster. The centroid point is used as an approximation for the gateway position. The smaller the value of the cluster fitness, the better the placement is. This process of calculating the fitness manipulates the process of building a minimum spanning tree with the gateway for each cluster located at the root of the tree. A link would be established between any two sensor nodes if and only if (1) they belong to the same cluster (2) they are within the communication range of each other. A value of one would be used to represent the cost of this link. It is worth noting that other costs functions can be employed in order to account for additional metric such as energy consumption.
•
•
3.2.3 Reducing complexity Fitness calculation is computationally expensive and is repeated multiple times during the evolution of GOAL. Therefore, in order to reduce complexity, we introduce a pre-processing step in order to facilitate the formation of the routing tree. The idea is to simply build a least cost generic routing table between each pair of sensor nodes in the environment. Since all sensor nodes locations are fixed and are known before the start of the algorithm, the
•
Tournament selection scheme: This scheme is used for parent selection. The scheme randomly selects four members of the population. Then, the best two members along with the worst member is returned; m1, m2, and m3, where m1 and m2 represent the two winners from the four members’ tournament and m3 denote the loser with the lowest fitness for replacement purposes. The crossover operator: A three-point crossover operator is applied for generating two new offspring. The fitness of the resultant offspring is calculated and only the offspring u with the best fitness is picked. The mutation operator: Mutation is used to introduce some randomness during the evolution of the algorithm and is performed on each newly created offspring as follows. For each offspring generated, the mutation operator is performed on chromosomes with probability p1, i.e. each is selected with probability p1. The cluster membership of the chromosome (which represents a sensor node) is then changed by randomly selecting a new cluster assignment. In GOAL, we used a value of p1 equal to 10% to avoid falling into the local optimal solution. Our choice for this value was based on experiments conducted at early stages to validate the best value for the mutation probability. The local optimization process: After mutation, the new offspring is optimized. Such a local optimization step is used mainly to speedup the convergence of the algorithm and reduce its time complexity. The local optimization process selects a random cluster in the environment (a specific value in the member) then it scans all sensor nodes to identify if any sensor should belong to this cluster or not. Upon completion, the new fitness value is calculated and retained if and only if it is better than the original value. The stopping criteria: The genetic algorithm stops after it reaches a predefined fixed number of iterations or if it evolves for a certain number of iterations with no progress or changes in the population. In GOAL, we set the maximum number of iterations to 20,000 and the maximum number of evolution with no progress to 2,000.
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3.2.5 Gateway placement After identifying the most appropriate cluster assignment, the next step for GOAL is to optimize the placement of each gateway in its cluster so that the average length of data path is reduced even further. In Goal, we employ a search technique similar to the Breadth First Search (BFS) to find the best location for the gateways of every cluster. The idea is to calculate the geometrical centroid of all nodes in a cluster and then use this position as a tentative location for the gateway. The area around the centroid is divided into two dimensional grid of size m 9 m. For each grid cell, the number of sensors that the gateway is within their transmission range is added together. The cell ‘‘b’’ with the maximum number of sensors count is selected. The gateway is then placed at the center of ‘‘b’’. The rationale for this strategy is to make the gateway directly reachable to the most number of sensors in the cluster so that the average length of data paths in a cluster becomes small. The dimension of the grid depends on the sensor’s density around the centroid. In GOAL, we calculate the number of cells based on the average distance ‘‘d’’ between a sensor node and the tentative location of the gateway assigned to the cluster, i.e., the centroid. The grid side S is set to 2 9 d and the gateway would be at the center of the grid. The size of each cell depends mainly on the sensor’s communication range. Intuitively, the side of a cell should be significantly smaller than the sensor’s range. 3.3 Light weight heuristics for GOAL For setups in which the computational resources are somewhat limited or the gateways are frequently repositioned due to changes in the sensor’s population, lighter heuristics may be preferred. In this section, we present two variants of GOAL with reduced complexity, namely GOAL-Simple (GOALS) and GOAL-Easy (GOALE). The GOALS approach is a simplified version of GOAL that is geared for reducing the complexity of the genetic algorithm, at the expense of the quality of the achievable solution. The simplification results from the use of the Euclidean distance between sensor nodes and their assigned gateways, instead of the hop count, as the cost factor for optimization. The rationale is that placing the gateway in the proximity of sensors would, with high probability, make it reachable to those sensors through few hops. Therefore, forming an intra-cluster topology is not needed to measure the quality of intermediate solutions and thus the complexity of the optimization is significantly reduced. In addition, the complexity of calculating the fitness value becomes simpler than GOAL. While genetic algorithms proved to be an effective optimization technique which often converges to global
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optima, it is somewhat computational intensive. Even with a simplified version like GOALS, the time complexity is still high. Therefore, we introduce GOALE which is an even lighter heuristic than GOALS and is more suitable for computationally constrained environments. GOALE employs the well-known k-means algorithm for cluster assignment [11]. The k-means algorithm is efficient in finding the best cluster assignment when dealing with small to medium size networks. However, it suffers from some drawbacks when networks get larger as it tends to cluster in circles, so clusters of oblong shapes may not be identified correctly. Furthermore, it falls easily into local optima. Nonetheless, the k-means algorithm rapidly converges. Moreover, its memory utilization is better compared to genetic algorithms. GOALE works as follows. It starts by randomly placing all gateways and then tries to associate each sensor to the closest gateway. Once all clusters are formed, the centroid of the sensors of each cluster is calculated and the gateway is relocated to that centroid position. The membership of each sensor is continuously checked to ensure that it stays associates with the closest gateway. The process stops when no membership changes for any sensor. The steps of the GOALE algorithm are shown in Fig. 3. In Sect. 5, we compare the performance and complexity of the three approaches, GOAL, GOALS, and GOALE, through simulation. 4 Estimating minimal gateway count Multiple approaches for gateways placement have been introduced so far. Although, these approaches vary mostly in computational complexity, they all assume that the number of gateways to be deployed is known upfront. While this assumption is valid in some setups, in many applications the network designer needs to determine the most appropriate gateway count. As we mentioned in Sect. 1, finding the optimal number of gateways involves a tradeoff. On the one hand, a large gateway population would yield a better network topology by shortening the data paths and thus increase network lifetime, reduce data Algorithm GOALE () Place gateways randomly While no changes for all A(s,g) For each sensor s A(s,g) Assign s to closest G C Calculate centroids (all clusters) i 0 For the ith gateway g(i) g(i).location C(i) End;
Fig. 3 GOALE is an implementation of the popular k-means clustering algorithm
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collection latency and boost the throughput and the delivery reliability of packets. On the other hand, gateways tend to be significantly more expensive than sensors and a large count of gateways would limit the practicality of WSNs. In addition, gateways may require manual placement or involve sophisticated means for deployment. To strike a balance, a designer usually sets some minimum performance bounds and architects the WSN with as few gateways as possible in order to achieve these bounds. The problem we are studying in this section is how to estimate the least number of gateways needed to serve an area of interest, which has possibly 100s or 1,000s of deployed sensor nodes, such that the data collection latency is below certain desired value. In this context, data latency is measured in terms of the length (number of hops) of the data dissemination paths. We present an approach for the Latency-based Estimation of Gateways’ Optimal count, or LEGO. LEGO consists of two main modules; LEGOEstimator and LEGO-Refiner. LEGO-Estimator is an algorithm for finding a close estimate for the least number of gateways to ensure that the longest data path in the network meets the desired data latency bound. The LEGORefiner module further improves the estimate. 4.1 LEGO gateway count estimator As we mentioned earlier assessing the optimal gateway count is an NP-hard problem. One of the intuitive approaches to finding the least count is to iteratively try a growing list of values, starting from one gateway. For each count, the gateways are placed and the network topology is checked. The process will then stop when meeting the data latency requirement. We have classified this approach as a Brute force method since the convergence rate can be radically slow, especially for large networks. LEGO opts to avoid such unpredictable performance by starting the search with a relatively accurate estimate. LEGO-Estimator identifies the factors that impact the number of deployed gateways and then forms an estimation function that captures the relationship between these factors. This function can be used to provide an initial count that is close to optimal and can thus expedite the convergence. We have experimented with the GOAL approach in order to find such factors. We mainly studied the relationship between the gateway count and the maximal path length, measured as the largest number of hops for a sensor to reach its closest gateway. The results are shown in Fig. 4 for multiple network sizes deployed in the same region. We have observed that the relationship nearly fits an exponential function. Therefore, a function of the form: y ¼ a ebx þ c was used, where y represents an estimate for the number of gateways needed to achieve the input x (maxHops) for the latency bound.
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Fig. 4 The relationship between the number of gateways and the longest data path that was observed when optimizing the gateway placement through the GOAL approach
The value of c is a constant and can be derived from the initial conditions as follows. When x grows towards infinitely, i.e. there is no constraint on the length of data paths, a single gateway would be sufficient and thus y = c = 1. To determine a and b, we derive an estimate for a gateways count for x = 1 and 2 using geometry. Let h and l be the dimensions of the deployment region, N is the number of sensors and r is the communication range of a sensor node. We call the square with a diagonal r a reachable zone. Assuming a uniform node distribution in the area, it is fair to assume that every node can reach a gateway if there is a gateway less than r unit away. Thus, to form a network in which each sensor can directly reach one gateway, i.e. maxHops = 1, it would be sufficient to place one gateway for every 4 zones (see the dotted squares in the Fig. 5(a)). Of course, this may not be a necessary The l m lcondition. m h l number of zones is: jzonesj ¼ pffiffi2r pffiffi2r : Through simple calculation, the number of gateways for maxhop = 1 can be approximately estimated as: y ¼ minðN; djzonesj=4e: Obviously if the N \ |Zones| there is no need to have a gateway to cover each zone. An estimate for the gateways count when maxhop = 2, can be approximated in a similar way but making the side of a zone equals r, as depicted in Fig. 5(b). The expected number of sensors NR in a zone that can directly reach the gateway is: NR ¼
N pr 2 =4 p N N 2 ¼ 0:8 : r 4 jzonesj jzonesj jzonesj
Assuming N is sufficiently large to allow multiple sensors to be positioned in each zone, we argue that every sensor node will be reaching his cluster assigned gateway in a maximum of 2 hops. The two conditions, where x = 1 and 2, can be used for evaluating the values of a and b. We have experimented with methods of forming the function y to be very close to
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Algorithm LEGO (maxHops) LEGO-Estimator (maxHops) EG do Execute GOAL/GOALS/GOALE Form a least-cost intra-cluster routing tree
r G
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Link Cost
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//Estimator Adjustment Subfunction // If tree depth Td > maxHop then EG EG + ((Td - maxHops) Else EG EG - (maxHops - Td) End if
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Until Delay bound is met End;
(a)
Fig. 6 A highlight of the general flow of LEGO
r
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terminates when EG cannot get lower while keeping Td B maxHops. The overall steps are shown in Fig. 6.
r G
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(b) Fig. 5 Dividing pffiffiffi the deployment region into square zones with sides equals (a) 2 r/2 for maxHops = 1 and (b) r for maxHops = 2 and then placing a gateway for each 4 zones
the obtained results. As we show in section V, using LEGO-Estimate expedites the convergence significantly. 4.2 The LEGO-Refiner module The LEGO-Estimator module recommends an initial gateway count EG. The LEGO-Refiner module starts by validating whether the estimated number of gateways EG would achieve the desired level of performance in terms of data latency, and refines the estimate accordingly. First, we employ GOAL or any of its simplified versions in order to appropriately place these gateways. Then, a least-cost intra-cluster routing tree is formed with the link cost set to 1 to yield minimal path lengths. If the depth of the tree Td exceeds maxHops, this means that not enough gateways have been employed and consequently LEGO increases EG by a value proportional to (Td - maxHops). If maxHops C Td, this indicates that there is room for more optimization. In that case, EG is decremented by a value proportional to (maxHops - Td). LEGO successfully
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5 Experimental validation All the approaches presented in this paper are validated in a simulated WSN that serves a target tracking application. In this section, we provide the performance results for the presented gateway placement schemes, GOAL, GOALS, and GOALE, and for the LEGO gateway count estimation approach. In the simulation experiments we compare the three placement approaches to a uniform distribution of gateways, which serves as a baseline and to COLA [3], which strives to maximize the gateway coverage while reducing the latency for collecting the sensor data. Meanwhile, an implementation of the Brute force method of [23] is used as a baseline when validating the effectiveness of the LEGO approach in estimating the least number of gateways that achieves the desired data latency performance. The next subsections describe the simulation environment setup, performance metrics, and experimental results. 5.1 Experiment setup The simulation environment adopts the node parameters and the network operational model of [3]. A free space propagation channel model is assumed with the capacity set to 2 Mbps [6]. Packet lengths are 10 Kbit. Packets are generated at a constant rate of 1 packet/sec.1 Each data packet is time-stamped when it is generated to allow the calculation of average delay per packet. In addition, each packet has an energy field that is updated during the packet 1
‘‘Data sheet for the Acoustic Ballistic Module’’, SenTech Inc., http://www.sentech-acoustic.com/Page4.htm.
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transmission to calculate the average energy consumed per packet. We have adapted the radio model of [16] to estimate communication-related energy. The transmission range of sensors is assumed to be 50 m (see footnote 1). In each experiment, the network consists of fixed number of sensor nodes and an estimated number of gateways that is fixed through the experiment. All sensors are randomly placed in an area of 1,000 9 600 m2 and have an initial energy of 5 joules [16]. Unless the effect of the sensor population is studied, the number of sensors stayed fixed in the experiments (equal to 500 sensors). In all experiments, we assume that targets travel across the area of interest from randomly selected locations. All Targets are characterized by having a constant speed chosen uniformly from the range 4–6 m/s and a constant direction chosen uniformly depending on the initial target position. Data packets are generated by sensor nodes that are in the vicinity of the target. All conducted experiments were executed on a Pentium M 1.73 GHz computer with 512MB RAM. Experiments were run for several network topologies, generated through different seed values, until the results approximately reached the 90% confidence level while staying within 6–10% of the sample mean. In addition, we have run the placement experiments for varying number of gateways (ranging from 2 to 10 gateways). For the LEGO approach, we varied the upper bounds on the hop count between 4 and 15 nodes. 5.2 Performance metrics Two sets of performance metrics were used to validate the gateway placement and count estimation approaches. The first set measures the network performance based on the topology achieved by GOAL and its two variants GOALS and GOALE. We used contemporary metrics such as average delay per packet, average energy consumed per packet, packet drop rate and average node lifetime to measure the effectiveness of these approaches compared to both the uniform distribution of the gateways and to COLA. In the second set of experiments we study the following metrics to assess the performance of LEGO: (1) the estimated number of gateways to achieve the desired bound on hop count (2) the efficiency of the LEGO estimation algorithm in terms of convergence rate and computational complexity (3) the average hop count in the network, and (4) the average distance between sensor nodes and their corresponding gateways. We used a Brute force based method as the baseline for comparing results in this set.
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performance based on the network topology set by these approaches and compare it to that achievable through uniform placement of the gateways and to the positions recommended by the COLA approach. Figure 7 shows the average delay per packet in seconds for a varying gateway count. The delay per packet is highly affected by the closeness of the sensor nodes to their assigned gateway, which, for a fixed sensors location, depends on two factors; the number of available gateways, and the proper placement of the gateways. The results in Fig. 7 indicate that our three new placement approaches deliver superior delay performance. The improvement in the data latency compared to both the uniform placement and the COLA approach emphasizes the effectiveness of the new techniques in appropriately placing the gateways. It is worth mentioning that COLA is geared for enhancing both the gateway’s coverage and the data collection latency. The results obtained through COLA represent a local optimal solution since the optimization is made at the level of individual clusters, which are formed at network setup time through the uniform placement of gateways. Meanwhile, for GOAL, GOALS, and GOALE, the optimization step is performed at the global level. Hence, additional complexity is incurred. GOAL and GOALS are close in results. The difference is minimal and in favor of GOAL due to the sophistication of the approach, which is reflected as a better optimal solution for the placement problem. In summary, the figure clearly indicates that the quality of the performance results is traded for complexity. The figure also indicates that the delay per packet decreases as the number of gateways increases. This is due to the increased gateway to sensor ratio which results in close gateway’s proximity to the sensors of its cluster. We also note that the deployment of many gateways makes
5.3 Performance of the gateway placement approaches This section reports on the experimental results for GOAL, GOALS, and GOALE. We basically study the WSN
Fig. 7 Average delay per packet in seconds versus number of gateways deployed when comparing GOAL/GOALS/GOALE to the uniform placement strategy and to the COLA approach
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the effect of the optimized positioning less significant since the density of gateways is high. Even though the goal of the three presented placement techniques—GOAL, GOALS, and GOALE—is not to minimize the communication energy (we only strive to enhance the data latency), a significant improvement in energy consumption was observed. Basically, due to the proper placement of gateways, packets were able of reaching their destinations using shorter routes. Figure 8 reports the average energy consumed per packet for a varying number of gateways. Overall the figure shows that our approaches achieve better average energy consumption per packet than uniform placement. Meanwhile, COLA has been able to achieve low level of energy consumption due to the good coverage characteristic of the approach. Nonetheless, the performance of GOAL still surpasses that of COLA. Moreover, the results further quantify the effect of the reduced algorithm complexity on performance with GOAL enabling a lower communication energy than its two other variants. Similar to the average delay per packet, when the density of gateways becomes higher, the average energy consumed per packet decreases and the effect of placement optimization diminishes due to the resultant increased sensor to gateway proximity. The performance results obtained not only have confirmed the positive impact of the proposed placement approaches on data latency and average energy consumption, but also have shown a boost in traffic reliability, measured in terms of the percentage of dropped packets in the network and in network longevity, assessed by tracking the time for first sensor node to die. Figure 9 depicts the percentage of dropped packets for different number of deployed gateways. The figure indicates that the gateway positions picked by our proposed approaches achieve a big decline in packet drop. Such decline is more significant for
low gateway densities. We also note that even for increased gateway count the proper placement of gateways could achieve a major reduction in reducing the frequency of packets drop. Meanwhile, Fig. 10 reports on the time for first sensor to die and shows the positive impact that our approaches make on network longevity. The results indicate that GOAL achieves the best performance and that GOALS and GOALE sustains acceptable level of performance gains despite the reduced complexity. In addition, the time for first sensor to die also grows with the increase in gateway count due to shortened data paths and distribution of the packets load to a larger pool of sensors during the transmission and reception processes. Figure 11 compares the runtime complexity of GOAL and GOALS. It is clear from the figure that GOALS is faster than GOAL since it is the least complex approach. However, other figures before indicate that GOAL is slightly superior to
Fig. 8 Average energy consumed per packet in joules for a varying number of deployed gateways
Fig. 10 Impact of the gateway placement strategies on the network lifetime, in terms of the time for first sensor node to die, under varying gateway count
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Fig. 9 Average percentage of dropped packets when running all approaches for 240 min
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GOALS. In the next section, we used GOAL as the base for genetic algorithm based approaches and GOALE as the k-means approach and compared these two approaches with the Brute Force method. 5.4 LEGO’s performance results The previous subsection presented results when the number of gateways to be deployed is known. In this section, we evaluate the other part of our integrated asset planning for WSNs, namely the estimation of the optimal gateway count through the LEGO approach. We compare LEGO to the Brute force method [23]. We consider two variants of LEGO that are based on employing either GOAL or GOALE as the underlying gateway placement module within LEGO. The inclusion of GOALE in the performance study will be useful since it, similar to the Brute force method, employs the k-means clustering algorithm and it will thus enable us to assess the effectiveness of the LEGO-Estimator module. As we mentioned earlier, we opt to validate the effectiveness of LEGO in obtaining the least gateway count and its efficiency in terms of convergence rate and computational complexity. We also report on the properties of the formed network topology by measuring the node’s proximity to a gateway in terms of both Euclidean distance and number of hops. Figure 11 shows the relationship between the desired maximum number of hops and the number of gateways obtained. The results clearly show that the version with GOAL is more effective by employing significantly fewer gateways when the maximum number of hops is small. The performance of the GOALE version resembles that of the Brute force since both are based on the k-means algorithm. The figure also indicates that when the maximum hop count is increased, the number of gateways decreases since the problem becomes less constrained. In addition,
Fig. 11 Runtime comparison between GOAL and GOALS
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the figure shows that the number of gateways deployed and the upper bound for data latency has an exponential relationship, which is consistent with the LEGO-Estimator module presented in the previous section. Figure 12 shows the number of iterations that each approach takes until converging to an optimal solution. The results confirm the effectiveness of the LEGO-Estimator module, particularly when comparing the version with GOALE to the Brute force method since they both employ the k-means algorithm. For the Brute force method, the number of reruns increases substantially as the desired maximum number of hops decreases. LEGO-Estimator significantly accelerates the convergence rate of the approach. When the maximum hop count is large, the problem becomes mostly unconstrained and all approaches converge quickly. In addition, the results show that the LEGO version with GOAL outperformed that with GOALE. Such superior performance is expected given the extensive optimization that GOAL conducts. Meanwhile, Fig. 13 shows how the convergence rate relates to the sensor count. The figure shows the number of iterations when fixing the desired maximum number of hops at 5 and 10. Generally, the results indicate the superiority of LEGO, especially for small network sizes, i.e., for low node density. Increasing the node density tends to expedite the convergence rate of the GOALE-based version of LEGO since it is a distance based clustering heuristic. Loosening the path length constraint accelerates the convergence even more. Figure 14 also captures the performance when the sensor population grows by comparing the gateway count achieved by the GOAL and GOALE versions of LEGO. The maximum number of hops is kept constant during this experiment. The figure shows sample results when the desired path length is less than 4 and 7 nodes. The results indicate that GOAL is clearly worth the computational
Fig. 12 Number of iterations taken by the tested approaches to achieve the desired maximum path length
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Fig. 13 Number of iterations for converging to optimal solution for varying sensors’ population
Fig. 14 Comparing the effectiveness of GOAL and GOALE as the underlying placement module for LEGO under varying network sizes
overhead for low density networks and under tight delay constraints. GOALE appears to better suite large networks when the data latency is less constrained. Figure 15 shows the impact of using LEGO on the average number of hops and the average distance between any sensor node and its assigned gateway. These metrics assess the efficiency of the post-deployment layout of the network. The results confirm the effectiveness of LEGO in reducing the numbers of hops and reducing the Euclidean distances. The results of the Brute force methods are very
Fig. 15 The average hop count (Left) and the average Euclidean distances (Right) between sensor nodes and gateways
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comparable to LEGO, yet by employing significantly larger number of gateways as shown earlier in Fig. 16. Such results imply, and have also been confirmed by other simulation experiments, that LEGO and the Brute force method would perform similarly in terms of delay and energy per packet, throughput and average node lifetime; again with lower cost incurred when LEGO is used. Such observation also stresses the importance of careful asset planning in WSNs and further supports the significance of the contribution of this paper.
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maximum number of hops on a data path. LEGO applies an estimation function to find a close to optimal initial solution and iteratively converges to the optimal gateway count. The validation results have confirmed the effectiveness of our approach and its superiority to contemporary schemes in the literature. Our future plan includes extending the approach to include other factors that impact the selection of number of deployed gateways, such as energy consumption, cost of deployment, and mission type. Acknowledgement This work is supported by the National Science Foundation, contract # 0000002270.
Fig. 16 Number of gateways obtained versus the desired maximum hop count, which is provided as an input
6 Conclusions and future work Wireless Sensor Networks are making their way to numerous applications such combat field reconnaissance, border protection, security surveillance, etc. A WSN employs a large number of miniaturized and batteryoperated sensors that probe their surrounding and report their findings to significantly more capable gateway nodes. In mission critical setups, the network designer is usually faced with conflicting requirements that mandate a trade-off. On the one hand, employing many gateways can shorten data paths and will thus reduce data latency, increase packet throughput and lower energy consumption at the individual sensor nodes. On the other hand, minimizing the gateway count is highly desirable in order to limit the cost, avoid increased visibility to adversaries, etc. We call determining the optimal number of gateways and their positions the asset planning problem. Asset planning is reducible to the P-Center problem which is NP-hard. In this paper, we have presented a very effective approach for asset planning in WSNs. We have introduced GOAL, which finds the most suitable spots for placing a known count of gateways so that the length of data paths is minimized. GOAL employs heuristics and artificial intelligence techniques in order to group sensors into disjoint clusters and then identifies optimized positions for the gateways to better serve the intra-cluster networks. We have also presented two lightweight variants of GOAL that trade the quality of the results for decreased complexity. We have further introduced LEGO for estimating the least gateway count for achieving a desired bound on data latency, measured in terms of the
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Author Biographies Waleed Youssef received his M.S. degree from the Department of Computer Science at Pennsylvania State University, Capital College in 2004. He is currently a Ph.D. Candidate in the Department of Computer Science and Electrical Engineering at the University of Maryland Baltimore County (Degree expected Fall 2007). His research interests include Wireless Sensor Networks (WSN), Artificial Intelligence (AI), Application of AI Techniques in WSN, Cognitive WSN approaches, and genetic algorithms. Dr. Youssef has published over 15 technical papers in refereed conferences and journals. Mohamed Younis received B.S. degree in Computer Science and M.S. in Engineering Mathematics from Alexandria University in Egypt in 1987 and 1992, respectively. In 1996, he received his Ph.D. in Computer Science from New Jersey Institute of Technology. He is currently an Associate Professor in the Department of Computer Science and Electrical Engineering at the University of Maryland Baltimore County (UMBC). Before joining UMBC, he was with the Advanced Systems Technology Group, an Aerospace Electronic Systems R&D organization of Honeywell International Inc. While at Honeywell he led multiple projects for building integrated fault tolerant avionics, in which a novel architecture and an operating system were developed. This new technology has been incorporated by Honeywell in multiple products and has received worldwide recognition by both the research and the engineering communities. He also participated in the development the Redundancy Management System, which is a key component of the Vehicle and Mission Computer for NASA’s X-33 space launch vehicle. Dr. Younis’ technical interest includes network architectures and protocols, embedded systems, fault tolerant computing and distributed real-time systems. Dr. Younis has four granted and three pending patents. He served on multiple technical committees and published over 85 technical papers in refereed conferences and journals.
