sensors Article
A Type of Low-Latency Data Gathering Method with Multi-Sink for Sensor Networks Chao Sha 1,2,3,4, *, Jian-mei Qiu 1 , Shu-yan Li 1,5 , Meng-ye Qiang 1,5 and Ru-chuan Wang 1,2,3 1
2 3 4 5
*
College of Computer, Nanjing University of Posts and Telecommunications, Nanjing 210003, China;
[email protected] (J.Q.);
[email protected] (S.L.);
[email protected] (M.Q.);
[email protected] (R.W.) Provincial Key Laboratory for Computer Information Processing Technology, Soochow University, Suzhou 215006, China Jiangsu High Technology Research Key Laboratory for Wireless Sensor Networks, Nanjing 210003, China Nanjing University of Information Science & Technology, Nanjing 210044, China School of Engineering and Computation, New York Institute of Technology, New York 11568-8000, NY, USA Correspondence:
[email protected]; Tel.: +86-25-8349-2152; Fax: +86-25-8349-2152
Academic Editor: Mihai Lazarescu Received: 4 April 2016; Accepted: 16 June 2016; Published: 21 June 2016
Abstract: To balance energy consumption and reduce latency on data transmission in Wireless Sensor Networks (WSNs), a type of low-latency data gathering method with multi-Sink (LDGM for short) is proposed in this paper. The network is divided into several virtual regions consisting of three or less data gathering units and the leader of each region is selected according to its residual energy as well as distance to all of the other nodes. Only the leaders in each region need to communicate with the mobile Sinks which have effectively reduced energy consumption and the end-to-end delay. Moreover, with the help of the sleep scheduling and the sensing radius adjustment strategies, redundancy in network coverage could also be effectively reduced. Simulation results show that LDGM is energy efficient in comparison with MST as well as MWST and its time efficiency on data collection is higher than one Sink based data gathering methods. Keywords: Sensor Networks; mobile Sinks; low-latency; balance of energy consumption; redundancy on network coverage
1. Introduction For densely deployed Wireless Sensor Networks (WSNs), a typical way to send data is to the static Sink by multi-hop or points-to-point transmission [1–4]. However, nodes near the Sink tend to consume more energy as they are responsible for receiving and forwarding data from the whole network [5]. This easily leads to network disconnection and causes “hotspot problem” [6–10]. On the other hand, to reduce the end-to-end delay in data collection, Sink should be near the source of the event [11]. As the events occur at different regions within the network area, such an optimization cannot be achieved by using a static Sink [12]. Recently, how to use one or more mobile elements for data collection has become an important research topic [13]. With the help of one or more mobile Sinks, performance of WSNs in terms of energy consumption and coverage could be greatly improved. Francesco et al. [1] proposed that, due to the limited power of nodes, using one or more mobile Sinks for data collection in WSNs is an effective way to prolong network lifetime. Moreover, owing to the short communication distance between nodes and the mobile Sink, packet loss rate also decreases [14,15]. Besides, mobile Sinks may collect data from isolated regions which could improve the connectivity of the network. A real-time data collection method is proposed in [16]. Trajectories of the mobile Sinks are designed by modeling the problem as the Traveling Salesman Problem (TSP) to achieve a balance Sensors 2016, 16, 923; doi:10.3390/s16060923
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between energy consumption and data collection latency. While another type of data collection method with the help of multiple mobile Sinks is proposed by Ren et al. [17] which reduces not only the energy consumption of the whole network but also transmission delays. To further reduce energy consumption of data collection, Gao et al. [13] divided the sensor nodes into sub-Sink nodes which are in a direct communication area (DCA) or far-away nodes that are within the distance of the multi-hop communication area (MCA). Sink moves along the fixed path to gather as much data as possible. In [18], path constrained Sink mobility is used to improve the energy efficiency of the single-hop sensor networks which may be infeasible due to the limits of the path location and communication power. Nevertheless, how to find out the optimal moving paths for multiple Sinks and how to further reduce energy consumption and time delay on data uploading are still key problems that need to be discussed further. The remainder of this paper is organized as follows: the related works, as well as the network model are described in Sections 2 and 3 respectively. In Section 4, we analyze the sleep scheduling and sensing radius adjustment strategies in detail. Trajectories of the Sinks and the transmission path selection algorithm are also described in this section. Experimental results are shown in Section 5 and the conclusion is provided in the last section. 2. Related Works With the development of sensor networks, how to improve the efficiency of data collection has become one of the hot spots of research. Heinzelman et al. [19] described the Low-energy Adaptive Clustering Hierarchy (LEACH) protocol for data collection in WSNs. Each node randomly decides whether or not to become a Cluster Head (CH) and the parameter used in decision making is the percentage of desired CHs. The CHs assign to each sensor from their cluster, a time slot for reporting, aggregate data received from individual sensors and send them directly to the Sink. While the major problem with LEACH is that the Sink may be very far from many CHs, therefore direct reporting may be extremely energy-consuming, or even impossible. Another type of cluster based data gathering algorithm named Stable Election Protocol (SEP) has been proposed in [20,21]. The network is divided into several clusters to collect data respectively and only the cluster headers need to communicate with the static Sink. Simulation results have shown that SEP is suitable for WSNs with a non-uniform distribution but nodes near the Sink or the cluster header die quickly, which caused an unbalance of energy consumption. A type of Equalized Cluster Head Election Routing Protocol (ECHERP) for data collection in sensor networks is proposed by Nikolidakis, S.A. et al. [22]. It also pursues energy conservation through balanced clustering. ECHERP models the network as a linear system and using the Gaussian elimination algorithm, calculates the combinations of nodes that can be chosen as cluster heads in order to extend the network lifetime. Kandris, D. et al. focused on hierarchical routing in WSNs by using a new enhanced reactive protocol that aims at the achievement of power conservation through energy efficient routing [23]. This protocol performs the cluster leadership in a non-randomized way but takes into account the residual energy of nodes. Moreover, the data routing is based on a route selection policy which takes into consideration both the energy reserves of the nodes and the communication cost associated with the potential paths. In addition to the cluster based protocols, data uploading algorithms based on the tree-structure have also been widely used in WSNs. A type of data gathering method with the help of a Minimum Spanning Tree (MST) is proposed in [24]. Compared with other multi-hop data transmission methods, time delay in MST is lower and the efficiency on data aggregation is also enhanced. However, there is only a static Sink located at the edge of the network which could lead to unbalanced energy consumption. Sia, Y.K. et al. [25] presented a Spanning Multi-Tree Algorithm for Load Balancing (SMT-LB). SMT-LB aims to balance the load in multi-sink wireless sensor networks with heterogeneous traffic generating nodes. Simulation results show that SMT-LB is able to achieve a longer network lifetime with lower end-to-end delay by deploying sink nodes at the center of both left and right edges.
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In [26], the problem of building cluster-based topology for Sensor Networks with several sinks is also considered. The topology associated with each sink is modeled as an Independent Dominating Set with Connecting requirements (IDSC). Thus, the solution is a partition of a given graph into as many IDSC as there are sinks. In addition, several optimization criteria are proposed to implicitly or explicitly balance the topology. Network lifetime is improved since it benefits from a clustered structure and the number of hops control. Furthermore, it becomes necessary to choose an appropriate aggregation factor and transmission radius depending upon the requirement of the application for which the WSN has been installed. Ghosh, K. et al. [27] presented a Fermat point based data aggregating protocol which is distance vector protocol in nature. Moreover, Gavalas, D. et al. introduces a novel algorithmic approach for energy-efficient itinerary planning of Mobile Agents (MA) engaged in data aggregation tasks [28]. It adopts an iterated local search approach in deriving the hop sequence of multiple traveling MAs over the deployed source nodes. In recent years, the use of a mobile Sink which moves on a pre-specified trajectory has been extensively investigated by several researchers [13,14,29]. In the prospective of the mobility of mobile Sink, the works are divided into three categories [30,31]: Random Mobility; the movement of mobile Sink is on a random trajectory; Fixed Mobility, where the Sink moves on a fixed pre-specified path; Controlled Mobility, where the trajectory of the mobile Sink is controlled, depending on its position and density of data in its vicinity. 2.1. Random Mobility For the random mobility scheme, the mobile Sinks are often mounted on people or animals moving randomly to collect the required information [13]. However, due to its random mobility, it is difficult to bind the data transfer latency with the data delivery ratio [13]. Data is stored at the node temporarily to be transmitted when the mobile Sink is at the most favorable location in order to achieve the maximum network lifetime. Jain et al. [32] proposed a type of data gathering method with the help of one mobile Sink. Due to the randomness of trajectory, the Sink could communicate with each node with the same probability. However, this method may increase the load of hot spots and the random movement of Sink will cause frequent breakage as well as reconstruction of communication link for the network. Moreover, it will also increase extra energy consumption and time delay. A Virtual Circle Combined Straight Routing (VCCSR) protocol for data collection with a mobile Sink is proposed in [33]. VCCSR selects a set of cluster heads located near the virtual backbone. When the Sink issues a query in the network, a spanning tree is constructed to collect and complete data periodically. The goal of the proposed algorithm is to decrease the reconstruction cost and increase the data delivery ratio. However, a large number of nodes participate in routing, increasing network overhead. In addition, Yu et al. proposed an elastic routing algorithm to minimize the traffic and enhance the reliability of data uploading from nodes to the mobile Sink [34]. When a Sink moves, the new location information is propagated along the reverse geographic routing path to the source during data delivery. However, this hop-by-hop data transmission could also increase the latency in data collection. 2.2. Fixed Mobility A rendezvous-based data collection approach is proposed in [35] to select the optimal fixed path due to the delay limitation in WSNs with a mobile Sink. The mobile Sink visits exact locations called rendezvous points, according to the pre-computed schedule to collect data. The rendezvous points buffer and aggregate data originated from the source nodes through multi-hop relay and transfer to Sink on arrival. However, this method is only suitable for uniform distributed networks and the multi-hop relay mode will easily cause imbalances in energy consumption.
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Somasundara et al. [36] proposes another type of mobile sensor networks with a path-fixed Sink supporting multi-hop communication. A speed control algorithm of the mobile Sink is suggested to improve the energy performance and a Shortest Path Tree (SPT) is used to choose the cluster heads and route data, which may cause imbalance in traffic and energy dissipation. Seung-Wan and In-Seon proposed a Minimum Wiener index Spanning Tree (MWST for) as the routing topology network. Sensing data is collected by multiple mobile nodes [37] and the shortest path could also be found that effectively reduces energy consumption. Nevertheless, due to the multi-hop data transmission, nodes near the mobile Sinks run out of energy quickly. 2.3. Controlled Mobility As for a controlled mobility scheme, it is possible to guarantee the data delivery efficiency with the help of efficient communication protocols and data collection schemes while the trajectories of the mobile Sinks are constrained or controllable [13]. The primary objective to control the mobility is to improve data gathering performance of the mobile Sink, yet handling the mobility of the Sink in a controlled manner is much more challenging than that of a random scheme [38]. Thus, most of the current work in this case has focused on how to design the optimal trajectories of mobile Sinks to improve the network performance [13]. In [39], a routing protocol, called MobiRoute, is suggested for WSNs with a path predictable mobile Sink to prolong the network lifetime and improve the packet delivery ratio. The Sink sojourns at some anchor points and the pause time is much longer than the movement time. Moreover, in MobiRoute all nodes need to know the topological changes caused by the Sink mobility which is unrealistic [13]. Somasundara et al. [40] have studied the scheduling problem of mobile Sink in WSNs to optimize the path of the Sink to visit each node and collect data before buffer overflows occur. Furthermore, a partitioning-based algorithm is presented in [40] to schedule the movements of the mobile element to avoid buffer overflow. However, the mobile Sinks in [40] need to visit all nodes to collect data which causes huge energy consumption. A type of Mobile Sink based algorithm for Stable Election (MSE) is proposed by Wang et al. [16]. Sink moves back and forth along a certain designed trajectory which solves the energy hole problem. Moreover, MSE has also been proved to be used in a non-uniform network. However, nodes near the static trajectory die more quickly than others, especially in large networks. Kinalis et al. [41] propose a biased, adaptive Sink mobility scheme that adjusts to local network conditions, such as the surrounding density, remaining energy and the number of past visits in each network region. Sink moves probabilistically, favoring less visited areas in order to cover the network area faster, while adaptively staying longer in network regions that tend to produce more data. Nevertheless, the Sink usually takes a long time to finish a complete data gathering task that causes high latency problem. The contributions of this paper can be concluded as follows: Firstly, with the help of the minimum network coverage model in WSNs, the network is divided into virtue regions and the leaders are selected according to their residual energy as well as the average distance to all of the other nodes. Network lifetime could be prolonged by periodically selection of the leader and the number of traverse points in LDGM is less than in other mobile Sink strategies. Secondly, the sleeping scheduling and the sensing radius adjustment strategies are adopted in LDGM that not only reduce the number of active nodes in data collection but also decreases the energy consumption on sensing. Moreover, with the help of multiple mobile Sinks, the end-to-end delay in data uploading is greatly reduced. 3. Network Model As mentioned above, in sensor networks, random mobility and the fixed mobility schemes for data gathering are unable to balance energy consumption of nodes and the path for data gathering is not the optimal. While, the controlled mobility scheme in data gathering performs well in prolonging
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network lifetime as well as reducing time delay and could efficiently mitigate the energy hole problem. Sensors 2016, 16, 923 5 of 29 Thus, it is adopted as the mobile strategy in LDGM. It is assumed thatasthe network is a rectangular and width is M L respectively. network lifetime well as reducing time delayarea andwhose couldlength efficiently mitigate theand energy hole problem. Thus, it randomly is adopted as strategy LDGM. Nodes are deployed in the themobile area and meetinthe following conditions: It is assumed that the network is a rectangular area whose length and width is M and L
(1) respectively. Nodes are inNodes staticare and high-density deployment. number and density of them is defined as deployed randomly in the areaTotal and meet the following conditions: n and ρ respectively. (1) Nodes are in static and high-density deployment. Total number and density of them is defined (2) All nodes except the Sink have the same initial energy E0 . The transmission power as well as the as n and ρ respectively. sensing radius of each is also (2) All nodes except the node Sink have the adjustable. same initial energy E0. The transmission power as well as the sensing radius of each node also (3) There are several mobile Sinksisin theadjustable. network whose energy and storage space are unlimited. (3) There are several mobile Sinks in the network whose energy and storage space are unlimited.
To establish the trajectories of the mobile Sinks and to reduce the amount of redundant data To establish the trajectories of the mobile Sinks and to reduce the amount of redundant data sensed by adjacent nodes, the network is divided into several virtual disks with radius R. Each of them sensed by adjacent nodes, the network is divided into several virtual disks with radius R. Each of is called Gathering Unit” (DGU). of disksof (white distributed on theon transverse them“Data is called “Data Gathering Unit”Centers (DGU). Centers disks dots) (whiteare dots) are distributed the or longitudinal line, as shown in Figure 1. transverse or longitudinal line, as shown in Figure 1.
Figure 1. Data gathering unit in the network. Figure 1. Data gathering unit in the network.
According to [1–3], data (especially the multimedia data) gathered by nodes closed to each other According to [1–3], data (especially multimedia data) gathered by nodes closed to each often show some similarity in the same the period. Thus, to decrease the amount of the redundant data,other oftenthe show some of similarity the sameArea” period. Thus, to decrease the amount of the redundant data, definition the “DatainGathering (DGA) is proposed as follows. As shown FigureGathering 1, the vertical distance from n3 to the line the definition of thein“Data Area” (DGA) is proposed as segment follows. n1n2 is just R. Thus, the region consisting of DGU n 1 , n 2 and n 3 is defined as a DGA, just as the gray area n in1 n Figure 1. As shown in Figure 1, the vertical distance from n3 to the line segment 2 is just R. Thus, the On the other hand, to reduce the probability of collecting redundant data, it is necessary region consisting of DGU n1 , n2 and n3 is defined as a DGA, just as the gray area in Figure 1. to minimize area of the overlapping region between these DGAs. Thus, in Figure 2, DGU n3, n4 and n5 On the other hand, to reduce the probability of collecting redundant data, it is necessary to need to meet the requirement of the minimum coverage model and O is the point where these DGUs minimize area of the overlapping region between these DGAs. Thus, in Figure 2, DGU n3 , n4 and n5 intersect. The distance between the centers of these adjacent DGUs is 3R . need to meet the requirement of the minimum coverage model and O is the point where these DGUs ? For the centers of some In LDGM, the virtual DGUs are uniformly distributed in the network. intersect. The distance between the centers thesethese adjacent DGUs is 3R. as in the same layer. DGUs, if their vertical coordinates are theofsame, DGUs are regarded In LDGM, DGUs arecoordinate uniformlyvalue distributed in the at network. For the Centers withthe thevirtual minimum vertical are just located the first layer. Thecenters numberof ofsome DGUs, if their vertical coordinates areasthe same,and these DGUsisare as the in the sameThen, layer.total Centers DGUs in the first layer is defined Num(L) Num(C) theregarded number of layers. of DGAsvertical (definedcoordinate as Num(R)) value is with number the minimum are just located at the first layer. The number of DGUs 1: Num(C) is even and 2 × Num(L)%3 = 0 (Figure 2). in the firstCase layer is defined as Num(L) and Num(C) is the number of the layers. Then, total number of
DGAs (defined as Num(R)) is 2 Num L Num C 2). R = 03 (Figure Case 1: Num(C) is even and 2 ˆ Num Num(L)%3 2 Num pRq “
2Num pLq Num pCq ˆ 3 2
(1)
(1)
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Figure 2. Distribution of DGAs (Case 1).
Figure 2. Distribution of DGAs (Case 1).
Case 2: Num(C) is even and Figure 2 × Num(L)%3 = 1 (Figure 3).(Case 1). 2. Distribution of DGAs
Case 2: Num(C) is even and 2 ˆ Num(L)%3 = 1 (Figure 3).
2 Num L 1 Num C Case 2: Num(C) is even andNum 2Figure × Num(L)%3 = 1 (Figure Distribution of DGAs 13). (Case 1). ˙ Rˆ 2.2Num 3 2 pLq ´ 1 Num pCq Num pRq “ 2 Num L 1 ` 1 Num ˆ C Case 2: Num(C) is even and 2 × Num(L)%3 =31 (Figure 2 Num R 13). 3 2 2 Num L 1 Num C Num R 1 3 2
(2)
(2) (2) (2)
Figure 3. Distribution of DGAs (Case 2).
Case 3: Num(C) is even and Figure 2 × Num(L)%3 = 2 (Figure 4).(Case 2). 3. Distribution of DGAs Figure 3. Distribution of DGAs (Case 2). 2 Num L 2 Num C Case 3: Num(C) is even andNum 2Figure × Num(L)%3 = 2 (Figure of DGAs 14). (Case 2). R 3.Distribution 3 Case 3: Num(C) is even and 2 ˆ Num(L)%3 = 2 (Figure4). 2 2 Num Num C 2 14). Case 3: Num(C) is even and 2 × Num(L)%3 = 2 L(Figure Num R ˆ ˙ 3 2 2Num pLq ´ 2 Num pCq Num pRq “ 2 Num L 2 ` 1 Num ˆ C 3 2 Num R 1 3 2
Figure 4. Distribution of DGAs (Case 3). Figure 4. Distribution of DGAs (Case 3). Figure 4. Distribution of DGAs (Case 3).
Figure 4. Distribution of DGAs (Case 3).
(3) (3) (3)
(3)
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Case 4: Num(C) is odd (Figure 5). Sensors 2016, 16, 923
2 Num L P 3 Case 4: Num(C) is odd (Figure 5). 2 Num L 1 Num R $ 2Nump Lq 1 P 3ˆ P ’ ’ 3 ¯ & ´ 2Nump Lq´1 Num pRq “ 2 Num3 L ` 2 1¯ ˆ P ´ ’ 1 P ’ % 2Nump3Lq´2 ` 1 ˆ P 3
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0 1
σ“0
σ“1 2 σ“2
(4) (4)
P “ Num2 C 1and σ “2ˆ2Num NumpLq L %3 %3 and P 2
NumpCq`1
Figure 5. Distribution of DGAs (Case 4). Figure 5. Distribution of DGAs (Case 4).
4. Data Gathering with the Help of Multi-Sink 4. Data Gathering with the Help of Multi-Sink 4.1. 4.1. Leader Leader Selection Selection Strategy Strategy in in DGA DGA In In LDGM, LDGM, it it is is assumed assumed that that one one or or more more “lead “lead nodes” nodes” exist exist in in each each DGA DGA which which receive receive data data from from other nodes in the same DGA and upload them to the mobile Sinks. During the network lifetime, other nodes in the same DGA and upload them to the mobile Sinks. During the network lifetime, the the mobile Sinks only need to communicate with these leaders, enhancing the efficiency of data gathering. mobile Sinks only need to communicate with these leaders, enhancing the efficiency of data gathering. For For the the DGA DGA consisting consisting of of three three DGUs, DGUs, the the node node located located at at the the triple triple coverage coverage region region (named (named as as “region C” for short) could be selected as the leader. Other nodes in the same DGA transmit to “region C” for short) could be selected as the leader. Other nodes in the same DGA transmit datadata to the the leader by hop. To prolong network lifetime, node with maximum residual energy leader hophop by hop. To prolong the the network lifetime, node with thethe maximum residual energy Er E inr in region C is selected as the leader, as S 1 shown in Figure 6. The value of Er must be greater than the region C is selected as the leader, as S1 shown in Figure 6. The value of Er must be greater than the threshold, sensing threshold, E Ethth.. When Whenthe theSinks Sinksare are far far away away from from the the DGA, DGA, all all of of the the nodes nodes carry carry out out their their sensing tasks their leaders. leaders. tasks and and upload upload data data to to their However, according to the of region region C C is is relatively relatively small. small. So However, according to the definition definition of of DGA, DGA, the the area area of So there there may be no nodes deployed in this region. In this case, the node with the maximum value of W in may be no nodes deployed in this region. In this case, the node with the maximum value of W in each each DGU selected as as the the leader, leader, as as node node SS2,, SS3 and S 4 shown in Figure 6. The value of W could be DGU will will be be selected and S shown in Figure 6. The value of W could be 2 3 4 calculated as follows: calculated as follows: In In Formula Formula (5), (5), ddioio is is the the Euclidean Euclidean distance distance between between node node ii and and center center of of region region C. and β β are parameters and and αα + + ββ == 1. C. α α and are the the adjustable adjustable parameters 1. 1 W Er 12 W “ αEr ` β dio
2
(5) (5)
dio Moreover, for the DGA consisting of less than three DGUs, the leaders will be selected directly Moreover, for the DGA consisting of less than three DGUs, the leaders will be selected directly in in each of its DGUs according to Formula (5), as S5, S6 and S7 shown in Figure 6. If there are just only each of its DGUs according to Formula (5), as S5 , S6 and S7 shown in Figure 6. If there are just only two DGUs in a DGA, dio is just the Euclidean distance between node i and the midpoint O of the line two DGUs in a DGA, dio is just the Euclidean distance between node i and the midpoint O of the line connecting the centers of the two DGUs. connecting the centers of the two DGUs.
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Figure 6. Leader nodes selection in each DGA. Figure 6. Leader nodes selection in each DGA. Figure 6. Leader nodes selection in each DGA. 4.2. Redundancy Reduction on Data Gathering 4.2. Redundancy Reduction on Data Gathering As mentioned before,on the leader may not be selected from region C if the density of nodes in the 4.2. Redundancy Reduction Data Gathering As mentioned before, the leader may be selected C if high the density of nodes in the network is too low. On the contrary, high not density of nodesfrom will region also cause redundancy on data Asismentioned before, the may density not be selected from region C if the density of nodes in network too low. On contrary, ofstrategy nodes will also cause high redundancy onthe data collection. Therefore, athe type of leader activehigh node selection and a sensing radius adjustment method network is too low. On the contrary, high density of nodes will also cause high redundancy on data collection. Therefore, a type of active node selection strategy and a sensing radius adjustment method are described in this section. a type active node selection strategy and a that sensing radius adjustment method arecollection. described in this ThereTherefore, are two section. types of of sleep scheduling strategies in WSNs, is centralized and distributed are described in this section. There are two types[19]. of sleep scheduling strategies in WSNs, that issmall centralized and distributed method, respectively The number of active nodes is relatively with the help of the There are two types of sleep scheduling strategies in WSNs, that is centralized and distributed method, respectively [19]. The number of active nodes is relatively small with the help of the centralized centralized sleep scheduling method which could effectively reduce network redundancy. While, method, respectively [19]. Thecould number of active nodes isdistributed relatively small with help of the sleep scheduling method which effectively reduce network redundancy. While, overhead time overhead of the centralized method is higher than the one. So, it isthe nottime suitable for centralized sleep scheduling method which could effectively reduce network redundancy. While, sensor networks with high requirement. of large-scale the centralized method is higher thanreal-time the distributed one. So, it is not suitable for large-scale sensor time To overhead of the centralized method is higher than the sleep distributed one. So, it is not suitable for improve efficiency in LDGM, the distributed scheduling strategy is executed in networks with hightime real-time requirement. large-scale sensor networks with high real-time requirement. each DGA. For example, there are two DGAs in Figure 7 (the white and the gray areas) and the active To improve time efficiency in LDGM, the distributed sleep scheduling strategy is executed in To(black improve time efficiency insensing LDGM,regions the distributed sleep scheduling strategy executed nodes as well as their in the7 white DGA are also shown in is this figure. Sin 10 each DGA. For dots) example, there are two DGAs in Figure (the white and the gray areas) and the active each DGA.active For example, there are twoDGA DGAs in Figure 7 (the white and the gray areas) and the active is another node in the adjacent (the gray one). It is obvious that, both S 8 and S9 are active nodes (black dots) as well as their sensing regions in the white white DGA DGAare arealso alsoshown shownininthis thisfigure. figure. S10 nodes dots) well as areas their sensing in the nodes (black although theassensing of DGA themregions havegray been completely covered by both the sensing area of active SS1010. is another active node in the adjacent (the one). It is obvious that, S and S are 8 9 is another active nodeofinthe thedistributed adjacent DGA (the gray one).strategy It is obvious that, both Sreduction 8 and S9 are active Therefore, the the effect sleep scheduling on redundancy may of not . nodes although sensing areas of them have been completelycovered covered bythe thesensing sensing area nodes although the sensing areas of them have been completely by area of S10S . 10 be the best. Thus, a sensing radius adjustment strategy is proposed as follows. Therefore, thethe effect of of thethe distributed sleep Therefore, effect distributed sleepscheduling schedulingstrategy strategyon onredundancy redundancyreduction reduction may may not not be thebebest. Thus,Thus, a sensing radius adjustment strategy is proposed asas follows. the best. a sensing radius adjustment strategy is proposed follows.
Figure 7. Distributed sleep scheduling strategy in each DGA. Figurein 7. Each Distributed sleep scheduling strategy in each DGA. 4.2.1. Active Node Selection DGAsleep Figure 7. Distributed scheduling strategy in each DGA.
is known that, energyinconsumption 4.2.1.ItActive Node Selection Each DGA on sensing for node Si (defined as eS(Si)) per unit time is 4.2.1. Active Node Selection in Eachradius DGA RS(Si) [42]. That is, related to the length of its sensing It is known that, energy consumption on sensing for node Si (defined as eS(Si)) per unit time is It is known that, energy consumption on is es (i)Ssensing ) Rs (Sifor ) is,node Si (defined as eS (Si )) per unit time (6) related to the length of its sensing radius RS(S i[42].1 That related to the length of its sensing radius RS (Si ) [42]. That is, (Si ) residual 1Rs (Si ) energy of Si is defined as Er(Si). To prolong λ1 and μ are the adjustable parameters whileesthe (6) network lifetime, we have, es pSi q “ λ1 Rs pSi qµ (6) λ1 and μ are the adjustable parameters while the residual energy of Si is defined as Er(Si). To prolong e s ( S i ) T λ 2 E r (S i ) (7) lifetime, we have,parameters while λ1 network and µ are the adjustable the residual energy of Si is defined as Er (Si ). To prolong e s ( S i ) T λ 2 E r (S i ) network lifetime, we have, (7) es pSi q ˆ T “ λ2 Er pSi q (7)
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T is the expected value of network lifetime and λ2 is the adjustable parameter whose value is
T is the expected value of network lifetime and λ2 is the adjustable parameter whose value is between 0 and 1. Thus, with the decrease of the residual energy, length of sensing radius of Si should between 0 and 1. Thus, with the decrease of the residual energy, length of sensing radius of Si should also be reduced to conserve its energy. Thus, according to Formulas (6) and (7) we get, also be reduced to conserve its energy. Thus, according to Formulas (6) and (7) we get, 1 E (S ) Rs (Si ) ˆ 2 r i ˙ 1 r pSiq µ λ2E1T
Rs pSi q “
(8)
(8)
λ T
For the convenience of calculation, the network is1divided into a number of virtual grids, whose length width are mofand l respectively, as shown is individed Figure 8.into It is a assumed m and l grids, could be For theand convenience calculation, the network numberthat of virtual whose divisible by M and L. gj is defined as the sensing area coverage degree of grid j, whose initial value is 0. length and width are m and l respectively, as shown in Figure 8. It is assumed that m and l could be At first, all the leaders in each DGA are selected as the active nodes and the length of their sensing divisible by M and L. gj is defined as the sensing area coverage degree of grid j, whose initial value is 0. radiuses could be calculated by Formula (8). Thus, the value of each gj now is shown in Figure 8.
Figure 8. Overlapping sensing area judgment based on grids.
Figure 8. Overlapping sensing area judgment based on grids.
Then, other nodes in the same DGA execute the following judgment one by one according to the
At first, theresidual leadersenergy in eachErDGA are selected as the active andin the length ofthe their sensing value of all their (Si) (from high to low). For each nodes grid j that the area of circle i and RS(Si(8). ), if Thus, the value of each gj now is shown in Figure 8. whose center radius are radiuses could beand calculated bySFormula Then, other nodes in the same DGA execute the following2 judgment one by one according to the 2 l y S R S 2 (9) circle m x S y value of their residual energy Exrj (S ) (from high to low). For each grid j that in the area of the i j i S i i 2 2 whose center and radius are Si and RS (Si ), if
Then, gj = gj + 1. xj and yj are the horizontal and vertical coordinates of the center of grid j, while ˆ ˙2 the value of gj are all greater than (x(Si), y(Si)) is the coordinate of Si. As for¯all ´ 2 the grids lin circle Si, if m 2 q q pSother x jsensing ˘ ´area ď RSby x pSof ` y ˘ ´ y pS 1, it is considered that the S i has been completely active nodes. Thus, i j i covered iq 2 2 Si goes into sleeping mode and in its sensing area, gj = gj − 1. Otherwise, Si becomes the active node.
(9)
Then, gj = gj + 1. xj and yj are the horizontal and vertical coordinates of the center of grid j, while 4.2.2. Sensing Radius Adjustment (x(Si ), y(Si )) is the coordinate of Si . As for all the grids in circle Si , if the value of gj are all greater than 1, It is known thatsensing the coverage redundancy the networkcovered could decrease with the nodes. help of Thus, the it is considered that the area of Si has beenofcompletely by other active Si active node selection method in Section 4.2.1. However, there are still some active nodes at the goes into sleeping mode and in its sensing area, gj = gj ´ 1. Otherwise, Si becomes the active node. boundary of each DGA that could go into sleeping mode, as S8 and S9 shown in Figure 7. Besides, the length of sensing radius RS(Si) calculated by Formula (8) may not be optimal. The redundant region 4.2.2. Sensing Radius Adjustment may still exist between the adjacent sensing areas. Therefore, sensing radius of the active nodes It is known that the coverage redundancy of the network could decrease with the help of the active should be further adjusted. For themethod grid whose coordinate meets the condition of are Formulas (9) and (10), itnodes is known that, it is node selection in Section 4.2.1. However, there still some active at the boundary not in the circle S i whose radius is RS(Si) − Δd, as the gray girds shown in Figure 9. In this case, gj = gj − 1. of each DGA that could go into sleeping mode, as S and S shown in Figure 7. Besides, the length 8
9
2 of sensing radius RS (Si ) calculated by Formula (8) may not2 be optimal. The redundant region may m x S y l y S R S d 2 (10) xj sensing i j i Sradius i still exist between the adjacent areas. Therefore, sensing of the active nodes should be 2 2 further adjusted. For the grid whose coordinate meets the condition of Formulas (9) and (10), it is known that, it is not in the circle Si whose radius is RS (Si ) ´ ∆d, as the gray girds shown in Figure 9. In this case, gj = gj ´ 1.
´
˙2 ¯2 ˆ m l x j ˘ ´ x pSi q ` y j ˘ ´ y pSi q ą pRS pSi q ´ ∆dq2 2 2
(10)
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Sensors 2016, 16,(10), 923 ∆d is a constant and it should meet In Formula a In Formula (10), Δd is a constant and ∆d it should ` m2 ą l 2meet
d
2
l m
2
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(11) (11)
Figure 9. Sensing radius adjustment.
Figure 9. Sensing radius adjustment.
If there is no grid satisfying gj = 0 in the annular region whose outer and inner radiuses are RS(Si) and R S(S − Δd respectively, i) = annular RS(Si) − Δd. Thiswhose judgement process repeats until one If there isi) no grid satisfyingwe gj set = 0RinS(Sthe region outer and inner radiuses areofRS (Si ) the two following conditions exist: and RS (Si ) ´ ∆d respectively, we set RS (Si ) = RS (Si ) ´ ∆d. This judgement process repeats until one of If there is conditions at least one exist: grid satisfying gi = 0, the current value of RS(Si) will be set as the sensing the two following radius. Then, we have gj = gj + 1 for all the grids in the annular region. If there is at least one grid satisfying gi = 0, the current value of RS (Si ) will be set as the sensing If the value of RS(Si) is 0, it is known that the sensing area of Si is completely covered by that of radius. Then, we have gj = gj + 1 for all the grids in the annular region. other active nodes (such as S8 and S9 shown in Figure 7). Then, Si will go into sleeping mode. If theNodes valuewhose of RS (S it is known that the sensing of adjust Si is completely by that of i ) is 0,areas sensing are at the boundary of thearea DGAs the length ofcovered their sensing otherradiuses active nodes as S8toand in For Figure Si willit go into sleeping mode. 9 shown firstly (such according the Sabove steps. ease7). of Then, description, is defined that node which Nodes sensing areas are at in the theitDGAs adjust the sensing located whose at the sensing region of S i and theboundary same DGAof with is the neighbor of Slength i. Thus, of thetheir number of neighbors (defined astoNei(S )) of thesteps. node located at of thedescription, boundary of it DGA is often that smaller than radiuses firstly according the iabove For ease is defined node which that thesensing node inside theof DGA. Then located atofthe region Si and in we thehave, same DGA with it is the neighbor of Si . Thus, the number
of neighbors (defined as Nei(Si )) of the node located at the boundary2 of DGA is often smaller than that Si n M L Nei Si RS Si (12) of the node inside the DGA. Then we have, If and only if Δρ(Si) is greater than a threshold Δρ, the sensing area of Si exceeds the boundary 2 pSi q “the n{M ˆ L ´ Nei pSi q{πR of that DGA. In this case, Si ∆ρ is called “boundary node”, just as S8i,qS9, S10 shown in Figure 7. The (12) S pS boundary nodes adjust the length of their sensing radiuses one by one according to the value of Δρ(Si) If andhigh onlytoiflow). ∆ρ(S ) isobvious greater than threshold ∆ρ, the sensing areaare of S the boundary (from Iti is that the a boundary node whose sensing areas completely by i exceedscovered other active (including nodesthe in other DGAs) goes intojust sleeping after this adjustment. of that DGA. Innodes this case, Si isthe called “boundary node”, as Smode , S , S shown in Figure 7. 8 9 10 Therefore, the redundancy of data gathered from the same DGA will be decreased. The boundary nodes adjust the length of their sensing radiuses one by one according to the value of Subsequently, in each the “non-boundary nodes” follow the same process. to ∆ρ(Si ) (from high to low). It isDGA obvious that the boundary node whose sensing areasMoreover, are completely save energy as much as possible and to achieve balance of energy consumption, the node with the covered by other active nodes (including the nodes in other DGAs) goes into sleeping mode after this lower residual energy takes priority to do the sensing radius adjustment.
adjustment. Therefore, the redundancy of data gathered from the same DGA will be decreased. Subsequently, in each DGA “non-boundary 4.3. Energy Efficient Path for Datathe Transmission in DGA nodes” follow the same process. Moreover, to save energy as much as possible and to achieve balance of energy consumption, the node with the Compared with the leader selection and active nodes selection strategy mentioned above, lower residual energy takes priority to do the sensing radius adjustment.
finding the optimized paths for data uploading in each DGA is more important for balancing energy consumption and prolonging network lifetime. As shown in Figure 10, the circular region (length of 4.3. Energy Efficient Path for Data Transmission in DGA its diameter is just the straight line distance between Si and the leader) is regarded as “Region for Next-hop Node Selection” (“NSselection Region” forand short). Therefore, Si meets Formula it is obvious Compared with the leader active nodesifselection strategy(13), mentioned above,
finding the optimized paths for data uploading in each DGA is more important for balancing energy consumption and prolonging network lifetime. As shown in Figure 10, the circular region (length
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of its diameter is just the straight line distance between Si and the leader) is regarded as “Region for Next-hop Node Selection” (“NS Region” for short). Therefore, if Si meets Formula (13), it is obvious that there is no active node in “NS Region” and Si transmits its data to the leader by one hop. In Formula (13), d(Si ,leader) is the diameter length of the “NS Region” and and ρA is just the density of active nodes Sensors 2016, 16, 923 11 of 29 in this region. b d pS , leaderq ă
4{πρ
(13)
i that there is no active node in “NS Region” and Si transmitsAits data to the leader by one hop. In Formula (13),when d(Si,leader) is the diameter the Region” “NS Region” and ρA is just the density of Otherwise, an active node Sj length in the of “NS of Sand i , it is regarded as the candidate active nodes in this region. next-hop node for S if and only if it meets all the following requirements. i
Requirement 1: Residual energy of Sj dshould nodes in 4 Athan the average value of active(13) Si , leaderbe higher this “NS Region”, just as Formula (14) shows. This ensures that Sj has enough energy to transmit the Otherwise, when Ean active node Sj in the “NS Region” of Si, it is regarded as the candidate nextdata to the next receiver. r (S j ) and Er (Sk ) in Formula (14) are defined as the residual energy of Sj and hop node for S i if and only if it meets all the following requirements. any active node (e.g., Sk ) in this “NS Region” respectively. Num(NS) is the number of active nodes in Requirement 1: Residual energy of Sj should be higher than the average value of active nodes in this region and λ4 is an adjustable parameter whose value is between 0.5 to 1. this “NS Region”, just as Formula (14) shows. This ensures that Sj has enough energy to transmit the data to the next receiver. Er(Sj) and Er(Sk) in Formula (14) are as the residual energy of Sj and Num p NSdefined q ÿ ` ˘Region” respectively. λ4 any active node (e.g., Sk) in thisE“NS Num(NS) is Er pS q the number of active nodes in (14) r Sj ě Num pNSqvalue is betweenk 0.5 to 1. this region and λ4 is an adjustable parameter whose k “1
Num NS Requirement 2: Hop distance between be than the length of the (14) diameter, Er Sj S j and 4Sk should Er shorter Sk k 1 Thus, while both Sj and Sk are neighbors of Si in itsNum “NS NS Region”.
` Sj ˘and Sk should be shorter than the length of the diameter, Requirement 2: Hop distance between d S j , Sk ď λ5 d pSi , leaderq (15) while both Sj and Sk are neighbors of Si in its “NS Region”. Thus,
λ5 is an adjustable parameter whose value 0.5 to 1. d Sjis, Salso between d S , leader (15) k 5 i Requirement 3: The “step distance” form Sj to Sk should be longer than 0. As shown in Figure 10, λ5 isthe an projection adjustable parameter whose is also between 0.5 to 1. it is just of segment Sj Skvalue and its length is defined as, Requirement 3: The “step distance” form Sj to Sk should be longer than 0. As shown in Figure 10, Ñ its˘length` is defined it is just the projection of segment SjSk `and ˘ as, d1 S j , Sk “ d S j , Sk cosθ (16) d ' Sj , Sk d Sj , Sk cos (16)
Figure 10. Next-hop node selection in DGA.
Figure 10. Next-hop node selection in DGA.
As for all the candidate next-hop nodes (e.g., Sj, Sk, …), the weight of each path SjSk is defined as,
As for all the candidate next-hop nodes (e.g., Sj , Sk , . . 2. ), the weight of each path Sj Sk is defined as, W Sj , Sk 2 Eelec fs d Sj , Sk (17) ` ˘ ` ˘ 2 W S j , Sk “ 2Eelec ` ε f s d S j , Sk (17)
W(Sj,Sk) is just the energy consumption on transmitting one bit of data from Sj to Sk. Path SjSk is more likely to be one of the uploading paths from Si to the leader when this weight is relatively small. Thus, W(Sj ,Sk ) is just the energy consumption on transmitting one bit of data from Sj to Sk . Path Sj Sk is a weighted directed graph could be constructed in the “NS Region”, as shown in Figure 11. And the moreSingle-Source likely to be one of the uploading fromcould Si to also the leader when this weight relatively Shortest Path form Si topaths the leader be found (as the black solidisline in Figuresmall. Thus,11) a weighted directed graph could be constructed in the “NS Region”, as shown in Figure 11. And with the help of the Dijkstra algorithm. This is the energy efficient data uploading path for Si.
the Single-Source Shortest Path form Si to the leader could also be found (as the black solid line in Figure 11) with the help of the Dijkstra algorithm. This is the energy efficient data uploading path for Si .
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Figure 11. Weighted directed graph for data uploading. Figure 11. Weighted directed graph for data uploading.
4.4. Moving Path for Multi-Sink 4.4. Moving Path for Multi-Sink In LDGM, there is one Traverse Point (TP) in each DGA (the white dots in Figure 12) and the In LDGM, there is one Traverse Point (TP) in each DGA (the white dots in Figure 12) and the mobile Sinks stay at each TP for a period of time to receive data from the leader (the black dots in mobile Sinks stay at each TP for a period of time to receive data from the leader (the black dots in Figure 12). Then, they move to the next TP at a fixed speed v. So, the whole trajectory for one Sink in Figure 12). Then, they move to the next TP at a fixed speed v. So, the whole trajectory for one Sink in a a data collection cycle is composed of Num(R) − 1 segments. data collection cycle is composed of Num(R) ´ 1 segments. As for a DGA, when the leader is located at region C, the traverse point is just the center of this As for a DGA, when the leader is located at region C, the traverse point is just the center of this region. Therefore, distance between the leader and the mobile Sink is relatively shorter that decreases region. Therefore, distance between the leader and the mobile Sink is relatively shorter that decreases energy consumption on communication. energy consumption on communication. When the leaders are located at each DGU, the location of the traverse point could be calculated When the leaders are located at each DGU, the location of the traverse point could be calculated as follows: as follows: Case 1: If the DGA is composed of a single DGU, the traverse point is just the center of this DGU. As Case 1: point If the Z DGA showsisincomposed Figure 12.of a single DGU, the traverse point is just the center of this DGU. As point Z shows Figure Case 2: If there are only twoinDGUs in12. the DGA, it is known that two leaders exist in this DGA (just Si Case 2: and If there are only12). two in thethat, DGA, known leaders in this DGA Sj in Figure It DGUs is assumed Z’itisisthe TP ofthat thistwo DGA whileexist ki and kj are the (just data S and S in Figure 12). It is assumed that, Z’ is the TP of this DGA while k and k are the data being uploaded from the leaders to the mobile Sink. So, total energy consumption for Si and i j i j uploaded from the leaders to the as mobile Sink. So, total energy consumption for Si and Sj being on data uploading could be described follows. Sj on data uploading could be described as follows. ET Si ET Sj ki k j Eelec ki fs d 2 Si , Z ' k j fs d 2 Sj , Z ' (18) ` ˘ ` ˘ ` ˘ ` ˘ ET pSi q ` ET S j “ k i ` k j Eelec ` k i ε f s d2 Si , Z1 ` k j ε f s d2 S j , Z1 (18) To get the minimum value of ET(Si) + ET(Sj), the optimal location of Z’ could also be calculated with thethe help of the partial shown in (19), X(Si),Y(S i) and j),Y(S j), are the To get minimum value ofderivative, ET (Si ) + ETas (Sj ), the optimal location of Z’ couldX(S also be calculated coordinates of S i and S j respectively. with the help of the partial derivative, as shown in (19), X(Si ),Y(Si ) and X(Sj ),Y(Sj ), are the
coordinates of Si and Sj respectively.
ki X Si k j X Sj X Z ' ` ˘ k k XpkS q`k XpS j q X Z1 “ i i j ik `kj i j `ki Y ˘ Si ki YkpSj Yi q`Sk j YpS j q 1 Y Z ' Y Z “ k `k ki k j i j
(19) (19)
Case 3: If there are three DGUs in the DGA (e.g., Sl , Sm and Sn are the leaders), the coordinates of its Case 3: If there are three DGUs in the DGA (e.g., Sl, Sm and Sn are the leaders), the coordinates of its TP (e.g., Z”) could be calculated out by Formula (20). TP (e.g., Z’’) could be calculated out by Formula (20). ` 2 ˘ kl XpSl q`km XpSm q`kn XpSn q X kZl X S“l km X Sm knkXn Sn X Z '' ` ˘ k YpS q`kklm`YkpmS` (20) m q`k n Y pSn q Y Z2 “ lkl l kmk`kknm ` kn l (20) kl Y Sl kmY Sm knY Sn Y Z '' kl k m kn
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Figure 12. Location of the traverse point. Figure 12. Location of the traverse point. Figure 12. Location of the traverse point.
For a DGA (e.g., DGAi), if another DGA (e.g., DGAj) whose region is partly shared with the For aof DGA DGA another DGA (e.g., DGA ) So, whose region is at partly shared with the i ), iif region i,(e.g., these two DGAs regarded neighbors. each DGAishas most four neighbors. ForDGA a DGA (e.g., DGA ), if are another DGAas(e.g., DGAj)j whose region partly shared with the region of DGA , these two DGAs are regarded as neighbors. So, each DGA has at most four neighbors. Asregion shownofinDGA 13, the and neighbors colored So, with black and white, respectively. iFigure i, these twoDGA DGAs areitsregarded as are neighbors. each DGA has at most four neighbors. As shown in Figure 13,13, thetheDGA neighbors are colored and white, respectively. As shown in Figure DGAand and its its neighbors are colored withwith blackblack and white, respectively.
Figure TPs for forselection. selection. Figure13. 13.The Thenext next available available TPs Figure 13. The next available TPs for selection.
ForFor any mobile two consecutive consecutiveTPs TPsisistoo toolong, long, energy any mobileSink, Sink,ififthe thedistance distance between between its two itsits energy For any mobile Sink, if the distance between its two consecutive TPs is too long, its energy consumption ononmoving length of ofthe thetrajectory trajectorywill willalso also increase and consumption movingwill willhigher. higher.In In this this case, case, the length increase and consumption on moving willproblems”. higher. In As this case, the length ofthe the trajectory also increase and may cause “buffer overflow problems”. As shown shown 12, mobile Sink at at Z’’ and its its may cause “buffer overflow in Figure Figure 12, the mobile Sinkiswill isnow now Z’’ and next is Thus, thenext nextperiod periodof ofAs time, the leaders leaders in DGAs ofof the DGA may cause overflow problems”. shown in Figure 12,neighbor the mobile Sink is now atwhere Z”where and its next TPTP is“buffer Z.Z. Thus, ininthe time, the in the the neighbor DGAs the DGA Z’’ is may have nochance chance upload data toleaders this Sink. Therefore, some constraints Z’’TP is located may have totoupload data this mobile mobile Sink. Therefore, some constraints are next islocated Z. Thus, in theno next period of time, theto in the neighbor DGAs of the DGAare where described as follows. described as follows. Z” is located may have no chance to upload data to this mobile Sink. Therefore, some constraints are described as 1: follows. Constraint 1: There arek kmobile mobileSinks Sinksin inthe the network. network. Constraint There are
Constraint 2:For For a SinkatatDGA DGAi, thenext next TP of of it it could could only inin the neighbors Constraint a Sink onlybe beselected selectedfrom fromthe theTPs TPs the neighbors Constraint 1:2: There are k mobilei, the Sinks inTP the network. DGA. DGA. Constraint 2: 3: For a Sink DGA TPT,ofeach it could only move be selected from the TPs in the i , the next Constraint During oneatdata gathering period Sink should to each TP once and only Constraint 3: During one data gathering period T, each Sink should move to each TP once and only neighbors DGA. once. once. ConstraintAs 3: forDuring one data gathering period T, each Sink should move to each TP once and a mobile Sink (e.g., Sink(i)) locating at TP(m), the weight that Sink(i) moves to the next TP As for a only mobile Sink (e.g., Sink(i)) locating at TP(m), the weight that Sink(i) moves to the next TP once. (e.g., TP(n)) at current time t is defined as follows. (e.g., TP(n)) at current time t is defined as follows. Num DGA As for a mobile Sink (e.g., Sink(i)) locating at TP(m), the weight that Sink(i) moves to the next TP DGA RS 2 Si ui (21) PTP m _ TP nas t t p t0 Num t follows. (e.g., TP(n)) at current time t is defined i 1 (21) PTP m _ TP n t t t p t0 RS 2 Si ui n
`
PTPpmq_TPpnq ptq “ t ´ t p ´ t0
n
i 1
DGAn q ˘ Numpÿ i “1
πRS 2 pSi q ui
(21)
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In Formula (21), tp is the time when TP(n) was visited by another Sink last time. Num(DGAn ) is regarded as the number of active nodes in the DGA where TP(n) locates at. πRS 2 (Si )ui is just the data gathering rate of each active node Si whose sensing radius is RS (Si ). When Sink(i) stays at TP(m) for a period time slot t0 , other TPs in the neighbor DGAs calculate the value of their weight. The TP with the maximum value of PTP(m)_TP(j) and has not yet being visited by Sink(i) is selected as the next TP of Sink(i). If there is no such traversal points, Sink(i) moves back to the previous traverse point TP(k) and chooses one of the unvisited TPs with the maximum weight value from the neighbor DGAs as its next TP. Thus, the hop distance of the mobile Sink will not be too long and the probability that TPs in the neighboring DGAs being visited by Sink(i) will also be increased. Moreover, the amount of data waiting for uploading in one DGA is another important factor in determining which TP Sink(i) will visit next, just as Formula (21) shows. Therefore, the possibility of buffer overflow on leaders could be effectively decreased. It is also known that the longest period of time that the leader could cache data in DGAn could be calculated as follows. Numpÿ DGAn q Tth pnq “ Cache{ πRS 2 pSi q ui (22) i “1
Without loss of generality, the value of the parameter Cache is set to 4 KB (just the buffer size of MicaZ). Thus, for the network with k mobile Sinks, the period T for one round of data collection is defined as follows. ˇ ¨ ˛ Numÿ p Rq´1 ˇ ˇ 1 T “ MAX ˝ Num pRq t0 ` l j ˇˇ η “ 1, 2, ...k‚ (23) vη ˇ j “1 Parameter t0 is defined as the time slot that Sink stays at each TP and vη is the moving speed of Sink(η). While lj is the straight line distance between two adjacent TPs on the trajectory of one Sink. So the value of T in Formula (23) is just the longest time that the Sink spends on visiting all the TPs. For one DGA, if the time intervals between any two successive arrivals of different Sinks could be approximately equal, the efficiency of LDGM could be further improved and the burden on the leader could also be reduced. In this case, the time interval To ’ is, ˇ ¨ ˛ Numÿ p Rq´1 ˇ ˇ 1 1 To1 “ MAX ˝ Num pRq t0 ` l j ˇˇ η “ 1, 2, ..., k‚ (24) k vη ˇ j “1 To avoid buffer overflow, the value of To ’ should meet, To1 ď MAX p Tth pnq| n “ 1, 2, ..., Num pRqq
(25)
So, with the help of Formulas (22)–(24), we get, ˜ MAX kě
Num pRq t0 ` ˜
Cache{MAX
Numpř DGAn q i “1
1 vη
Numř p Rq´1 j “1
ˇ ¸ ˇ ˇ l j ˇ η “ 1, 2, ..., k ˇ
ˇ ¸ ˇ ˇ πRS 2 pSi q ui ˇ n “ 1, 2, ..., Num pRq ˇ
(26)
However, in LDGM, trajectories of the mobile Sinks are not fixed and their moving paths could also be affected by the value of PTP(m)_TP(n) (t). Thus, To ’ is just the optimal value of time interval. In the worst case, no Sinks visit the DGA during the time of T-kt0 , so the longest time interval Tm ’ is,
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¨ 1 Tm “ MAX ˝ Num pRq t0 `
1 vη
Numÿ p Rq´1 j “1
ˇ ˛ ˇ ˇ l j ˇˇ η “ 1, 2, ..., k‚´ kt0 ˇ
(27)
In this case, if and only if Tm ’ satisfies the following conditions, the cache overflow does not occur. 1 Tm ď MAX p Tth pnq| n “ 1, 2, ..., Num pRqq
(28)
Accordingly, from Formulas (22), (27) and (28), we could also get, ˜ kě
1 t0 MAX
Num pRq t0 `
´
˜ t0 MAX
1 vη
Numř p Rq´1 j “1
ˇ ¸ ˇ ˇ l j ˇ η “ 1, 2, ..., k ˇ
(29)
Cache
NumpDGA ř nq i“1
ˇ ¸ ˇ ˇ πRS 2 pSi qui ˇn“1,2,...,Nump Rq ˇ
With the help of Formulas (26) and (29), the optimal number of mobile Sinks deployed in the network could be calculated out. 5. Simulation Results To evaluate the performance of LDGM on balancing energy consumption, prolonging network lifetime as well as reducing coverage redundancy and transmission delay, a series of simulations are carried out with the help of VC++6.0 and Matlab 8.5. We also compared LDGM with some typical cluster based data gathering methods with mobile Sinks, e.g., MST, MWST and so on. Values of the parameters in these experiments are shown in Table 1. Table 1. Parameter values in simulation. Parameter
Symbol
Value
Unit
Network Size Radius of DGU Number of Nodes Number of Mobile Sinks Weight Coefficient Weight Coefficient Adjustable Parameter Sensing Rate Data Collection Rate of the Mobile Sink Moving Speed of the Mobile Sink Initial Energy of Nodes Threshold of the Residual Energy Buffer Size of One Node Energy Consumption of Sending and Receiving Circuit Energy Consumption of Amplifier in Free-Space Model Energy Consumption of Amplifier in Multi-Path Fading Model
MˆL R N Ns α β λ1 uik v’ v E0 Eth Cache Eelec µfs µamp
100 ˆ 100~200 ˆ 200 5~20 100~800 1–4 0.2 0.8 2 ˆ 10´6 0.05~0.5 100 5–20 2.0 0.7 4 50 10 0.0013
m2 m
J/(m2 ¨ s) bit/(m2 ¨ s) Kbps m/s J J KB nJ¨ b´1 pJ¨ (b/m2 )´1 pJ¨ (b/m4 )´1
5.1. Network Coverage and Redundancy To evaluate the performance of LDGM on reducing redundancy on coverage, experiments are carried out in the following cases. Network size is 100 m ˆ 100 m and the results of these experiments are shown in Figure 14. Case 1: Case 2: Case 3:
Nodes are deployed randomly in the network without doing any optimization. Nodes in the network carry out sleep scheduling strategy after being deployed. Nodes in the network execute both of the sleep scheduling and the sensing radius adjustment algorithms.
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Network coverage rate under different number of nodes is shown in Table 2. As mentioned in Section 4, LDGM does not change the network coverage rate. So when the number of nodes is fixed, the coverage rates in the above three cases are the same. Without loss of generality, the “virtual grids” described in Section 4.2 is used to calculate the network redundancy on coverage (defined as η). Qi = 1 when gi > 1, otherwise Qi = 0. Sensors 2016, 16, 923
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¨
pM{mqˆp N {nq
˛
described in Section 4.2 is used to calculate theÿ network redundancy on coverage (defined as η). η “ ˝m ˆ l ˆ Qi ‚{ pM ˆ Lq (30) Qi =1 when gi > 1, otherwise Qi = 0. i “1
M m N n m l Qi M L i 1 Table 2. Network coverage rate (100 m ˆ 100 m).
(30)
Table 2. Network coverage rate (100 m × 100 N = 100 N = 200 N m). = 300
Number of Nodes
Number of Nodes N = 200 Coverage Rate 0.798059 N = 1000.970983 Number of Nodes N = 500 0.798059N =0.970983 600 Coverage Rate Coverage Rate 0.995491 N = 5000.996863 Number of Nodes N = 600 Coverage Rate 0.995491 0.996863
N = 400
N 0.988334 = 300 N = 400 0.999804 N = 700 0.999804 N = 800 0.988334 N 0.999902 = 700 N = 800 1.000000 0.999902 1.000000
In Figure 14, it is known that with the rise of the number of nodes, redundancy on coverage also In Figure 14, it is known that with the rise of the number of nodes, redundancy on coverage also increases. Moreover, the increasing rate is faster when the number of nodes increases from 100 to 400. increases. Moreover, the increasing rate is faster when the number of nodes increases from 100 to 400. At the time, the the coverage rate from79.8% 79.8%toto 99.9%. This is main the main reason Atsame the same time, coverage ratehas hasalso alsoenhanced enhanced from 99.9%. This is the reason why why the redundancy increases sharply. However, after doing sleep scheduling as well as sensing the redundancy increases sharply. However, after doing sleep scheduling as well as sensing radius adjustment, thethe redundancy ononcoverage lot(in (insome some cases, more than 10%). radius adjustment, redundancy coverage decreases decreases aalot cases, more than 10%).
Redundancy on Coverage (%)
100
Without Sleep Scheduling and Sensing Radius Adjustment After Sleep Scheduling but without Sensing Radius Adjustment After Sleep Scheduling and Sensing Radius Adjustment
80
60
40 100
200
300
400
500
600
700
800
Number of Nodes Figure 14. Redundancy on coverage (100 m × 100 m).
Figure 14. Redundancy on coverage (100 m ˆ 100 m).
Figure 15 shows the number of active nodes before and after sleep scheduling. According to the
Figure 15 shows the4,number of that active before and after scheduling. description in Section it is known the nodes node whose sensing area issleep completely coveredAccording by other to nodes will be sleep mode network as shown in by the description in in Section 4, it iswithout knownreducing that the the node whosecoverage sensingrate. areaTherefore, is completely covered Figure 15, the number of active nodes is significantly decreased after sleep scheduling. Moreover, this other nodes will be in sleep mode without reducing the network coverage rate. Therefore, as shown in number nearly stable (no more thanis260 in this experiment) when the sleep number of nodes increases. Figure 15, theis number of active nodes significantly decreased after scheduling. Moreover, this It is necessary to mention that by carrying out a series of experiments, we found that the number number is nearly stable (no more than 260 in this experiment) when the number of nodes increases. of active nodes was not significantly reduced. This is because only the nodes near the boundary of It is necessary to mention that by carrying out a series of experiments, we found that the number the DGA would go into the sleeping mode during the sensing radius adjustment process. Thus in of active nodes was not significantly reduced. This is because only the nodes near the boundary of Figure 15, the two broken-lines with circular mark and diamond mark almost coincide. the DGA Experiment would go into theinsleeping mode the sensing radius adjustment results the 200 m × 200during m network are shown in Figures 16, 17 process. and TableThus 3 in Figure 15, the two broken-lines with circular mark and diamond mark almost coincide. respectively. Compared with the result shown in Figure 15, it is known that the decrease of the redundancy on coverage in Figure 16 is not obvious. Because in this case density of nodes is lower and the initial redundancy is also lower than that in the network whose size is 100 m × 100 m. In addition, coverage rate of the network does not decrease in LDGM. So, there are still many active nodes in this network (see Figure 17).
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Experiment results in the 200 m ˆ 200 m network are shown in Figure 16, Figure 17 and Table 3 respectively. Compared with the result shown in Figure 15, it is known that the decrease of the redundancy on coverage in Figure 16 is not obvious. Because in this case density of nodes is lower and the initial redundancy is also lower than that in the network whose size is 100 m ˆ 100 m. In addition, coverage rate of the network does not decrease in LDGM. So, there are still many active nodes in this network (see Figure 17). Table 3. Network coverage rate (200 m ˆ 200 m). Number of Nodes
N = 100
N = 200
N = 300
N = 400
Coverage Rate Number of Nodes Coverage Rate
0.374174 N = 500 0.904532
0.5835 N = 600 0.946486
0.717433 N = 700 0.955843
0.826786 N = 800 0.973194
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900
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900
600 600
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Without Sleep Scheduling and Sensing Radius Adjustment After Sleep Scheduling butand without Without Sleep Scheduling Sensing Radius Adjustment Sensing Radius Adjustment After Sleep Sleep Scheduling Scheduling but andwithout After Sensing Radius Radius Adjustment Adjustment Sensing After Sleep Scheduling and Sensing Radius Adjustment
300 300
0 100
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300
400
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Number of Nodes
0 10015. Number 200 300active400 500LDGM 600 800 Figure of nodes in (100 m700 × 100 m).
Figure 15. Number of active nodes LDGM (100 m ˆ 100 m). Number of in Nodes
Redundancy on Coverage (%) (%) Redundancy on Coverage
100 15. Number of active nodes in LDGM (100 m × 100 m). Figure 100 80 80 60 60 40
Without Sleep Scheduling and Sensing Radius Adjustment After Sleep Scheduling butand without Without Sleep Scheduling Sensing Radius Adjustment Sensing Radius Adjustment After Sleep Sleep Scheduling Scheduling but andwithout After Sensing Radius Radius Adjustment Adjustment Sensing
40 20 20 0 100
200
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After Sleep 400 500 Scheduling 600 and 700 Sensing Radius Adjustment
800
Number of Nodes
0 100 200Redundancy 300 400 500 (200 600 700m). 800 Figure 16. on coverage m × 200
Number of Nodes
rumber of Active NodesNodes of Active
900 Figure 16. Redundancy on coverage (200 m × 200 m). Without Sleep Scheduling and (200 m ˆ 200 m). Figure 16. Redundancy on coverage Sensing Radius Adjustment 900 After Sleep Scheduling butand without Without Sleep Scheduling Sensing Radius Radius Adjustment Adjustment Sensing After Sleep Sleep Scheduling Scheduling but andwithout After 600 Sensing Radius Radius Adjustment Adjustment Sensing 600
300
After Sleep Scheduling and Sensing Radius Adjustment
Red
After Sleep Scheduling but without Sensing Radius Adjustment After Sleep Scheduling and Sensing Radius Adjustment
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0 100
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Number of Nodes
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Figure 16. Redundancy on coverage (200 m × 200 m).
Number of Active Nodes
900 Without Sleep Scheduling and Sensing Radius Adjustment After Sleep Scheduling but without Sensing Radius Adjustment After Sleep Scheduling and Sensing Radius Adjustment
600
300
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0 Table 3. Network coverage rate (200 m × 200 m). 100 200 300 400 500 600 700
800
Number of Number of Nodes N = 100 N Nodes = 200 N = 300 N = 400 Coverage Rate 0.374174 0.5835 0.717433 0.826786 Figure 17. Number of active nodes in LDGM (200 m × 200 m). Figure 17. Number of active nodes in LDGM (200 m ˆ 200 m). Number of Nodes N = 500 N = 600 N = 700 N = 800 Coverage Rate 0.904532 0.946486 0.955843 0.973194
As shown in Table 2, the network coverage rate is up to 97% when 200 nodes are randomly shown in Table 2, thesize network up to 97% when 200 nodes are randomly deployedAs in the network whose is 100coverage m ˆ 100rate m. is Accordingly, we further analyze the coverage deployed in the network whose size is 100 m × 100 m. Accordingly, we further analyze the coverage degree of the network in LDGM by using the same values of these parameters and the result is shown degree in LDGM by using the sameover values of these parameters andarea the result shown in Figure 18.ofItthe is network known that the coverage degree most of the redundant (over is 60%) is more in Figure 18. It is known that the coverage degree over most of the redundant area (over 60%) is more than three when the nodes are randomly deployed, while this percentage is obviously reduced after than three when the nodes are randomly deployed, while this percentage is obviously reduced after carrying out the sleep scheduling algorithm. Moreover, the coverage degree of more than 70% of the carrying out the sleep scheduling algorithm. Moreover, the coverage degree of more than 70% of the redundant areaarea in the network is is nonomore sensingradius radius adjustment. redundant in the network morethan thanthree three after after sensing adjustment.
Percentage about the Coverage Degree (%)
40 Coverage Degree = 1 Coverage Degree = 2 Coverage Degree = 3 Coverage Degree = 4 Coverage Degree = 5 Coverage Degree > 5
30
20
10
0
Without Sleep Scheduling After Sleep Scheduling After Sleep Scheduling but without Sensing and Sensing but without Sensing Radius Adjustment Radius Adjustment Radius Adjustment
Figure 18. Percentage about the coverage degree (100 m × 100 m, 200 nodes). Figure 18. Percentage about the coverage degree (100 m ˆ 100 m, 200 nodes).
Lengths of the sensing radius after adjustment are shown in Table 4. The initial sensing radius
Lengths ofset thetosensing after arethese shown in Tableand 4. The radius lengths are 5 m, 6 m,radius 7 m and 8 madjustment respectively in experiments eachinitial value sensing of λ2 could be are calculated Formula (7). It is obvious thatinno matter what the value of the initial lengths set to 5out m, by 6 m, 7 m and 8m respectively these experiments and each value ofsensing λ2 could be radiusout is, there are always 50% that nodes shorten their sensing thesensing adjustment calculated by Formula (7).more It is than obvious nothat matter what the value radius of the after initial radius is, process in LDGM. Among them, more than 70% nodes shorten their sensing radius by 1–3 m in there are always more than 50% nodes that shorten their sensing radius after the adjustment process effectively reducing the amount of redundant sensing data as well as energy consumption on sensing. LDGM. Among them, more than 70% nodes shorten their sensing radius by 1–3 m effectively reducing the amount of redundant sensing data as well as energy consumption on sensing. Table 4. Lengths of the sensing radius after adjustment. Value of λ2
Number of Active Nodes
6.4 × 10−5
252 (Initial Value of Rs(Si) is 8 m)
4.9 × 10−5
284 (Initial Value of Rs(Si) is 7 m) 317
Rs(Si) after Amended 7m 6m 5m 6m 5m 4m 5m
Number of Nodes with Different Rs(Si) 155 51 11 179 28 3 168
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Table 4. Lengths of the sensing radius after adjustment. Number of Active Nodes
Rs (Si ) after Amended
Number of Nodes with Different Rs (Si )
6.4 ˆ 10´5
252 (Initial Value of Rs (Si ) is 8 m)
7m 6m 5m
155 51 11
4.9 ˆ 10´5
284 (Initial Value of Rs (Si ) is 7 m)
6m 5m 4m
179 28 3
3.6 ˆ 10´5
317 (Initial Value of Rs (Si ) is 6 m)
5m 4m 3m
168 22 2
2.5 ˆ 10´5
382 (Initial Value of Rs (Si ) is 5 m)
4m 3m 2m
182 12 0
Value of λ2
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5.2. Average Average Residual Residual Energy Energy of of Nodes Nodes 5.2. The Average Average Residual ResidualEnergy Energy(ARE) (ARE)ofof 500 nodes a 100 m network is shown in The 500 nodes in ain100 m×m 100ˆm100 network is shown in Figure Figure 19 and there are four mobile Sinks in this network for data gathering. It is shown that the 19 and there are four mobile Sinks in this network for data gathering. It is shown that the residual residualdecrease energy decrease when no optimization algorithms are carried out.the Attime the time energy quickly quickly when no optimization algorithms are carried out. At of 2of× 210ˆ4 4 seconds this value is already below the threshold, 0.7 J. Because in this case, all nodes are active 10 seconds this value is already below the threshold, 0.7 J. Because in this case, all nodes are active and and they collect their initial sensing radius which maylead leadtotohigh highenergy energy consumption. consumption. they collect datadata withwith their initial sensing radius which may Moreover, the number of redundant datadata to the SinkSink that Moreover, theleaders leadersshould shouldupload uploada aconsiderable considerable number of redundant to mobile the mobile also shortens the network lifetime. that also shortens the network lifetime. While after after sleep sleep scheduling, scheduling, the the number number of of active active nodes nodes significantly significantly decreases, decreases, so so the the value value of of While ARE increases. Moreover, after after sensing sensing radius radius adjustment, adjustment, network network life life in in LDGM LDGM could could be be further further ARE increases. Moreover, 4 s, the value of ARE is closed to 0.8 J which ensures that prolonged. For example, at the time of 3 ˆ 10 4 prolonged. For example, at the time of 3 × 10 s, the value of ARE is closed to 0.8 J which ensures that most of of the the nodes nodes could could still most still work work for for aa long long time. time.
Average Residual Energy of Nodes (J)
1.8 Without Sleep Scheduling and Sensing Radius Adjustment After Sleep Scheduling but without Sensing Radius Adjustment After Sleep Scheduling and Sensing Radius Adjustment
1.4
1.0
-
0.6
0.2 0.5
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Network Running Time (s)
x 10
4
Figure 19. 19. Average residual energy energy of of nodes nodes (100 (100 m mˆ × 100 Figure Average residual 100 m, m, 500 500 nodes). nodes).
5.3. Time Delay in Data Gathering As mentioned above, in LDGM each Sink is required to move to each traverse point once and only once during one round of data gathering period. Thus for any TPj, the maximum time interval (defined as TPj(Δtmax)) between two consecutive visits is,
TPj tmax MAX tij1 tij i 1, 2,...k 1
(31)
tij refers to the time when Sink(i) moves to TPj while k is the number of Sinks. Therefore, the maximum time delay on data gathering could be defined as,
T
MAX TP t
j 1, 2,...Num R
(32)
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5.3. Time Delay in Data Gathering As mentioned above, in LDGM each Sink is required to move to each traverse point once and only once during one round of data gathering period. Thus for any TPj , the maximum time interval (defined as TPj (∆tmax )) between two consecutive visits is, ´ ¯ j j TPj p∆tmax q “ MAX ti`1 ´ ti |i “ 1, 2, ..., k ´ 1
(31)
ti j refers to the time when Sink(i) moves to TPj while k is the number of Sinks. Therefore, the maximum time delay on data gathering could be defined as, ` ˘ ∆Tmax “ MAX TPj p∆tmax q |j “ 1, 2, ..., Num pRq
(32)
Similarly, average time delay on data collection is defined as, ∆Tavg “
Num ÿpRq
TPj p∆tmax q{Num pRq
(33)
j “1
Maximum Time Delay on Data Gathering (s)
Experiment results of ∆Tmax and ∆Tavg with different R and Ns in a 100 m ˆ 100 m network are shown in Figures 20 and 21. When Ns is fixed, the value of ∆Tmax decreases with the increase of R. This is because when R is larger, there will be fewer DGAs in the network and the number of TP will decrease. spent Sensors 2016, Thus, 16, 923 the total time spent by delaying at these traverse points also decreases time20 of 29 during data gathering. of of R isRfixed, timetime delay in a multi-Sink basedbased network is much On the the other otherhand, hand,when whenthe thevalue value is fixed, delay in a multi-Sink network is smallersmaller than thethan network that has only in time delayinis time not obvious when much the network that one has Sink. only However, one Sink. decrease However, decrease delay is not the number of the Sinks increases fromincreases three to four. there arewhen morethere Sinksare moving the obvious when number of Sinks fromBecause three towhen four. Because more in Sinks moving thepossibility network, the that different the same TPtime at the time or during network,inthe thatpossibility different Sinks visit theSinks samevisit TP at the same orsame during a short time ainterval short time intervalThat increases. of TP j (Δ t max ) increases according to Formula (31). As increases. is, the That valueis,ofthe TPvalue (∆t ) increases according to Formula (31). As a result, max j a∆T result, Δ T max is stable. is stable. max When the value of R is larger, there will be less traverse traverse points in the network. Thus, the effect on reducing time delay delay is not very very obvious obvious no no matter matter how how many many Sinks Sinks are are moving moving in in the the network. network. As shown in Figure 20, when R is 20 m, the maximum time delays on data gathering with different Sinks are nearly the same. Therefore, Therefore, the the time time efficiency efficiency of LDGM will be better when the network size is large and R is small. 350 Ns = 1 Ns = 2 Ns = 3 Ns = 4
300 250 200 150 100 50 0
5
10
15
20
The Value of R (m) Figure 20. 20. Maximum Maximum time time delay delay on on data data gathering gathering (100 (100 m mˆ × 100 Figure 100 m, m, 200 200 nodes). nodes).
Figure 21 shows the average time delay on data gathering. In the majority of cases, the effect on multi-Sink based network is better than that with only one Sink. Moreover, when the value of R is small, this advantage is more obvious. While if R is larger, ΔTavg increases slightly, as shown in Figure 20. 160
Maximum T
100 50 0
5
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The Value of R (m)
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Figure 20. Maximum time delay on data gathering (100 m × 100 m, 200 nodes).
Average Time Delay on Data Gathering (s)
Figure 21 shows the average time delay on data gathering. In the majority of cases, the effect Figure 21 based showsnetwork the average time than delaythat on data In theMoreover, majority of cases, the effect on multi-Sink is better withgathering. only one Sink. when the value ofon R multi-Sink based network is better than that with only one Sink. Moreover, when the value of R is small, is small, this advantage is more obvious. While if R is larger, ∆Tavg increases slightly, as shown in this advantage is more obvious. While if R is larger, ΔTavg increases slightly, as shown in Figure 20. Figure 20. 160 Ns = 1 Ns = 2 Ns = 3 Ns = 4
140 120 100 80 60 40 20
5
10
15
20
The Value of R (m) Figure 21. 21. Average Average time time delay delay on ondata datagathering gathering(100 (100m mˆ × 100 m, 200 nodes). Figure
In addition, experiments about the maximum and average time delay in a 200 m × 200 m network are shown in Figures Figures 22 22 and and 23. 23. Similar Similar to to Figure Figure 20, 20, the the maximum maximum time time delay delay decreases decreases with with the the are shown in increase of of R R when whenthe thenumber numberofofSinks Sinksisisfixed. fixed.However HoweverininFigure Figure when R increases from 15 20, to 22,22, when R increases from 15 to 20, value decreases which is different from result in Figure This is because number thisthis value stillstill decreases which is different from thethe result in Figure 20.20. This is because thethe number of of in Figure is obviously thaninthat in the 100 m network. In the thispossibility case, the TPsTPs in Figure 22 is22 obviously more more than that the 100 m ˆ100 100m m ×network. In this case, possibility that two different Sinks sameaTP during short time interval that two different Sinks visiting the visiting same TPthe during short timeainterval is not large. is Sonot thelarge. valueSo of the value of Δstill Tmaxdecrease. could still decrease. ∆Tmax could Maximum Time Delay on Data Gathering (s)
addition, SensorsIn2016, 16, 923 experiments about the maximum and average time delay in a 200 m ˆ 200 m network 21 of 29
1200 Ns = 1 Ns = 2 Ns = 3 Ns = 4
1000 800 600 400 200 0
5
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20
The Value of R (m)
Figure 22. Maximum time delay on data gathering (200 m × 200 m, 500 nodes). Figure 22. Maximum time delay on data gathering (200 m ˆ 200 m, 500 nodes).
Similarly, the average time delay in a multi-Sink based network is obviously shorter than that in the single Sink based one, as shown in Figure 23. The value of it decreases slowly with the increase of R.
hering (s)
600 500
Ns Ns Ns Ns
=1 =2 =3 =4
Maxi
0
5
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15
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The Value of R (m)
Figure 22. Maximum time delay on data gathering (200 m × 200 m, 500 nodes).
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Similarly, the average time delay in a multi-Sink based network is obviously shorter than that in the single Sinkthe based one, time as shown 23. Thebased valuenetwork of it decreases slowly with the Similarly, average delayininFigure a multi-Sink is obviously shorter thanincrease that in of Rsingle . the Sink based one, as shown in Figure 23. The value of it decreases slowly with the increase of R.
Average Time Delay on Data Gathering (s)
600 Ns Ns Ns Ns
500
=1 =2 =3 =4
400 300 200 100 0
5
10
15
20
The Value of R (m)
Figure 23. Average time delay on data gathering (200 m × 200 m, 500 nodes). Figure 23. Average time delay on data gathering (200 m ˆ 200 m, 500 nodes).
Experiment results about the maximum and average time delay with different moving speeds Experiment results the24maximum and average When time delay moving the speeds of of Sinks are shown in about Figures and 25 respectively. the with valuedifferent of v increases, delay Sinks are shown in Figures 24 and 25 respectively. When the value of v increases, the delay decreases decreases in LDGM. However, this decreasing rate becomes slower and slower when the speed of in LDGM. However, this decreasing ratethe becomes the speed at of each Sink further Sink further increases. This is because length slower of timeand the slower mobile when Sink is staying TP is a increases. This is because the length of time the mobile Sink is staying at each TP is a constant value in constant value in LDGM. In this case, the increase of speed could only shorten the time spent on LDGM. In this case, the increase of speed could only shorten the time spent on moving. In addition, no moving. In addition, no matter how fast the moving speed is, time efficiency of the multi-Sink based matter how fast thehigher moving speed efficiency of the multi-Sink based network is always higher network is always than thatis,oftime single Sink based network. Sensors 2016,of 16,single 923 Sink based network. 22 of 29 than that
Maximum Time Delay (s)
250 Ns = 1 Ns = 2 Ns = 3 Ns = 4
200
150
100
50
0
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Moving Speed of Sinks (m/s) Figure 24. Maximum Maximum time delay with different moving speeds of Sinks.
rage Time Delay (s)
120
100
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60
Ns = 1 Ns = 2 Ns = 3 Ns = 4
0
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Moving Speed of Sinks (m/s) Sensors 2016, 16, 923
Figure 24. Maximum time delay with different moving speeds of Sinks.
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Average Time Delay (s)
120 Ns = 1 Ns = 2 Ns = 3 Ns = 4
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Moving Speed of Sinks (m/s) Average time time delay delay with with different different moving movingspeeds speedsof ofSinks. Sinks. Figure 25. Average
5.4. Efficiency Efficiency of of Data Data Gathering Gathering 5.4. In LDGM, LDGM, the the leader leader carries carries aa big big load load its its energy energy consumption consumption is is much much higher higher than than any any other other In node. However, However,there thereare areno no differences differencesin insize sizeof ofcache cacheas as well well as as the the ability ability to to transmit transmit data data between between node. these two twotypes typesofofnodes. nodes. how to speedily upload to mobile the mobile Sinkhow andtohow to aavoid these SoSo how to speedily upload datadata to the Sink and avoid buffera buffer overflow on leaders also important problems requiring resolution. overflow on leaders are alsoare important problems requiring resolution. Firstly, we analyze the time interval of the two consecutive data uploading process process of of each each leader leader Firstly, we analyze the time interval of the two consecutive data uploading with the size of the networks set to 100 m × 100 m and 200 m × 200 m, as shown in Figures 26 and with the size of the networks set to 100 m ˆ 100 m and 200 m ˆ 200 m, as shown in Figures 26 and 27. 27. In the the single single Sink Sink based based network, network, each each TP TP could could only only be be visited visited once once during during one one round round of of data data In gathering time. time. So, is is nearly uniform. It should be pointed out gathering So,the thedistribution distributionofofthese thesetime timeintervals intervals nearly uniform. It should be pointed thatthat the the different moving paths of of Sinks could but after after out different moving paths Sinks couldalso alsoinfluence influencethe thelength lengthof of time time intervals intervals but many experiments, experiments, it it was was found found that that the the impact impact is is limited. limited. While While with with the the increase increase of of N Nss,, the the time time many interval between two consecutive times of data uploading is obviously shorter for example, in the interval between two consecutive times of data uploading is obviously shorter for example, in the 100 m mˆ× 100 100 m m network networkwith withfour fourmobile mobileSinks Sinksfor for more than 80% of the leaders, intervals 100 more than 80% of the leaders, the the timetime intervals are are shorter than 120 s. Thus, LDGM could greatly increase the frequency of data uploading and shorter than 120 s. Thus, LDGM could greatly increase the frequency of data uploading and therefore therefore the probability of buffer overflow. reduce thereduce probability of buffer overflow. Moreover, Percentage of Valid Data collected by Sinks (PVD) is another important indicator to show the efficiency of data gathering. PVD in LDGM is defined as the ratio between the amount of data received by all the mobile Sinks and the total amount of data collected by all active nodes in a round of data gathering time. Experimental result is shown in Figure 28. With the increase of uik , the value of PVD decreases. In LDGM, the cache size of each node is set to 4KB so it will overflow when the sensing rate is too high. On the other hand, PVD will be higher when Ns is larger, e.g., when Ns = 4, even if uik is up to 0.5 bit/(m2 ¨ s), the value of PVD is still nearly 90%.
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0~40s 0~40s 40~80s 40~80s 80~120s 0~40s 80~120s 120~160s 40~80s 120~160s 80~120s 120~160s
10 10 10 5 5 5 0 0
1 1
2
3
4 4
2 3 Number of Sinks Number of Sinks
0
Figure 26. Time interval of two 1 consecutive 2 times of data 3 upload (1004 m × 100 m, 200 nodes). Figure 26. Time interval of two consecutive times data upload(100 (100 ˆ 100 m, 200 nodes). Figure 26. Time interval of two consecutive timesofof ofSinks data upload mm × 100 m, 200 nodes). Number 30
Figure 26. Time interval m × 100 m, 200 nodes). 0~40s 30 of two consecutive times of data upload (100 40~80s 0~40s 80~120s 40~80s 120~160s 80~120s 160~200s 120~160s 0~40s 200~240 160~200s 40~80s >240s 200~240 80~120s >240s 120~160s 160~200s 200~240 >240s
Number of Leaders Number Leaders Number ofof Leaders
25 30 25 20 25 20 15 20 15 10 15 10 105 5 50 0
1 1
2
3
4
Percentage of Valid Data Collected by Sinks (%) Percentage Valid Data Collected Sinks (%) Percentage ofof Valid Data Collected byby Sinks (%)
2 3 4 Number of Sinks Number of Sinks 0 Figure 27. Time interval of two 1 consecutive 2 times of data 3 upload (2004 m × 200 m, 500 nodes). Figure 27. Time interval of two consecutive timesofof ofSinks data mm × 200 m, 500 nodes). Number Figure 27. Time interval of two consecutive times dataupload upload(200 (200 ˆ 200 m, 500 nodes).
100 Figure 27. Time interval of two consecutive times of data upload (200 m × 200 m, 500 nodes). 100 Ns = 1 Ns = = 21 Ns 100 Ns = = 32 Ns 95 Ns == 13 Ns 95 =4 Ns == 24 Ns Ns =3 95 Ns = 4 90 90 90 85 85 85 80 800.1 0.1
0.2 0.2
0.3
uik (bit/s) Value of 0.3 Value of uik (bit/s)
0.4 0.4
0.5 0.5
80 Figure 28. Percentage of valid 200 nodes). 0.1 0.2data collected 0.3by Sinks (100 0.4m × 100 m, 0.5 Figure 28. Percentage of valid dataValue collected Sinks (100 m × 100 m, 200 nodes). of u by(bit/s) ik
Figure 28. Percentage of valid data collected by Sinks (100 m × 100 m, 200 nodes).
Figure 28. Percentage of valid data collected by Sinks (100 m ˆ 100 m, 200 nodes).
even if uik is up to 0.5 bit/(m ·s), the value of PVD is still nearly 90%.
5.5. Costs on Data Gathering
Total Length of Path for Data Transmission (m)
To further verify the performance of LDGM on total length of data transmission path as well as network energy consumption, we compared it to MST (a shortest path based data gathering method) Sensorsand 2016,MWST 16, 923 (a type of backbone based data collection strategy with the help of randomly moving 25 of 29 Sink). Figure 29 shows the total length of Path for Data Transmission (PDT) during one round of data gathering time. It is known that the length of PDT in MST is the longest. Because each node in the 5.5. Costs on Data Gathering network needs to do a continuous sensing task and upload data directly to Sink. Thus, MST performs well if and only if there are not too many nodes in network. the transmission density of nodes is larger, To further verify the performance of LDGM onthe total lengthWhen of data path as well as the length of PDT obviously increases. network energy consumption, we compared it to MST (a shortest path based data gathering method) MWST is another efficient data gathering method by finding out the shortest uploading path. and MWST (a type of backbone based data collection strategy with the help of randomly moving With the help of the mobile Sink, not all nodes need to transmit data to the receiver directly. Thus, Sink). Figure 29 shows the total length of Path for Data Transmission (PDT) during one round of data the length of PDT in MWST is shorter than that in MST. However, the mobile Sink moves randomly gathering It is known thenodes length of PDT in MST is the longest. Because or each node in the along time. the backbone path.that Other need to upload data to Sink by single-hop multi-hop network needs do a in continuous sensing task upload dataare directly to Sink. MSTneeds performs manner. Asto shown Figure 30, rectangles withand different colors the mobile Sinks.Thus, Each Sink well if if there arehave not the toosame manycolor nodes in theSo network. density nodes larger, toand visitonly the nodes that as itself. its lengthWhen is stillthe much longerofthan thatisof LDGM. the length of PDT obviously increases. While in our algorithm, node only needsby to upload theshortest leader closest to it, so path. MWST is another efficienteach dataactive gathering method findingdata outtothe uploading ofthe PDTmobile in LDGM is not the all shortest. trajectories of mobile Sinks in LDGM areThus, With the thelength help of Sink, nodesMoreover, need to transmit data to the receiver directly. controllable. These Sinks visit each TP and receive data from the leader that shorten the distance of the length of PDT in MWST is shorter than that in MST. However, the mobile Sink moves randomly single-hop transmission. In addition, the advantage of LDGM on the length of PDT is more obvious along the backbone path. Other nodes need to upload data to Sink by single-hop or multi-hop manner. when the number of nodes is over 200, as shown in Figure 29. In this case, the number of active nodes As shown in Figure 30, rectangles with different colors are the mobile Sinks. Each Sink needs to visit is still stable with the help of the sleep scheduling and sensing radius adjustment processes. Thus, the nodes that haveofthe same as itself. So in itsLDGM lengthdoes is still longerincrease. than that of LDGM. the total length paths forcolor data transmission notmuch significantly 3.5
x 10
3
5
LDGM MST MWST
2.5 2 1.5 1 0.5 0 50
100
150
200 250 Number of Nodes
300
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Figure 29. Total length pathfor fordata datatransmission transmission (100 100100 m, m, 200200 nodes). Figure 29. Total length of of path (100mm× ˆ nodes). Sensors 2016, 16, 923
25 of 29
Figure30. 30. Data Data collection MWST. Figure collectionpath pathofof MWST.
Average energy consumption of nodes is shown in Figure 31. It is known that, the advantage on energy saving in LDGM is not very obvious when there are a small amount of nodes deployed in the network because the total lengths of PDT in MST and MWST are short when there are not too many nodes in the network (see Figure 30). Moreover, in this case, the hop distances between nodes and Sink are also short in both of these two algorithms. Thus, according to the data transmission model proposed by Heinzelman[19], it is known that, energy consumption on communication in MST and MWST is low.
Sensors 2016, 16, 923
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Average Energy Consumption of Nodes (J)
While in our algorithm, each active node only needs to upload data to the leader closest to it, so the length of PDT in LDGM is the shortest. Moreover, trajectories of mobile Sinks in LDGM are controllable. These Sinks visit each TP and receive data from the leader that shorten the distance of single-hop transmission. In addition, the advantage of LDGM on the length of PDT is more obvious when the number of nodes is over 200, as shown in Figure 29. In this case, the number of active nodes is still stable with the help of the sleep scheduling and sensing radius adjustment processes. Thus, the Figure 30. Data collection path of MWST. total length of paths for data transmission in LDGM does not significantly increase. Average energy consumption Figure 31. 31.ItItisisknown knownthat, that,the the advantage Average energy consumptionofofnodes nodesis is shown shown in in Figure advantage onon energy saving ininLDGM there are are aasmall smallamount amountofofnodes nodes deployed energy saving LDGMisisnot notvery veryobvious obvious when when there deployed in in thethe network because and MWST MWSTare areshort shortwhen whenthere there are not many network becausethe thetotal totallengths lengthsof ofPDT PDT in in MST and are not tootoo many nodes in in the network this case, case, the thehop hopdistances distancesbetween between nodes and nodes the network(see (seeFigure Figure30). 30). Moreover, Moreover, in this nodes and Sink also shortininboth bothofofthese thesetwo twoalgorithms. algorithms. Thus, model Sink areare also short Thus, according accordingtotothe thedata datatransmission transmission model proposed Heinzelman[19], known that, energy in in MST and proposed byby Heinzelman [19], itit isis known energy consumption consumptionon oncommunication communication MST and MWST is low. MWST is low. 0.25
0.2
LDGM MST MWST
0.15
0.1
0.05
0 50
100
150
200
250
300
350
400
Number of Nodes Figure Averageenergy energyconsumption consumption of of nodes nodes (100 nodes). Figure 31.31.Average (100 m m ׈100 100m,m,200 200 nodes).
In LDGM, there are fewer nodes in each DGA when the number of nodes is less than 200. In this In LDGM, there are prefer fewer to nodes in each number of nodes is less than enhances 200. In this case, most of the nodes upload data DGA to the when leaderthe by using a single-hop way which case, most of the nodes prefer to upload data to the leader by using a single-hop way which their energy consumption. However, with the help of the sensing radius adjustment strategy, enhances energy their energy consumption. with thefor help of the sensing adjustment strategy, energy consumption on sensing isHowever, greatly decreased most active nodes.radius So, total energy consumption of consumption onofsensing is level greatly decreased most active nodes. So, total energy consumption of LDGM is still the same as that of MSTfor and MWST. LDGMWith is stillthe ofincrease the same as thatofofnodes, MST and MWST. of LDGM on energy saving is more and of level the density the advantage With the increase of the density of nodes, the advantage on energy more and more obvious and the average energy consumption of nodesofisLDGM also stable becausesaving in thisiscase, the more obvious and nodes the average energy consumption of nodes is also stable strategy. because Moreover, in this case, number of active increases slowly by carrying out the sleep scheduling thethe optimalofpath for nodes data transmission in eachbyDGA couldout alsothe be sleep foundscheduling out, which restrains increase ofthe number active increases slowly carrying strategy.the Moreover, energypath consumption LDGM. optimal for data in transmission in each DGA could also be found out, which restrains the increase of energy consumption in LDGM. Average residual energy of nodes in the three types of data gathering algorithms is shown in Figure 32. Similar to Figure 31, when the density of nodes in the network is large, the transmission paths in MST and MWST are longer. Thus, residual energy of nodes is lower. With the help of one mobile Sink, the residual energy of some nodes decreases slowly in MWST. But this Sink moves randomly in the network. It may move to a hotspot area that could increase the energy consumption on nodes in this region. However, in LDGM, each active node only needs to upload data to the leader in the same DGA. So, total length of the transmission paths is not too long. In addition, the leader selection and the sleep scheduling strategies further balance energy consumption in our algorithm. Thus, average residual energy of nodes in LDGM is higher than MST and MWST.
paths in MST and MWST are longer. Thus, residual energy of nodes is lower. With the help of one mobile Sink, the residual energy of some nodes decreases slowly in MWST. But this Sink moves randomly in the network. It may move to a hotspot area that could increase the energy consumption on nodes in this region. However, in LDGM, each active node only needs to upload data to the leader in the same DGA. So, total length of the transmission paths is not too long. In addition, the leader and the sleep scheduling strategies further balance energy consumption in our algorithm. Sensorsselection 2016, 16, 923 27 of 29 Thus, average residual energy of nodes in LDGM is higher than MST and MWST.
Average Residual Energy of Nodes (J)
2.00 LDGM MST MWST
1.99 1.98 1.97 1.96 1.95 1.94 1.93
0
500
1000 1500 2000 Network Running Time (s)
2500
3000
Figure 32. Average residual energy of nodes (100 m × 100 m, 200 nodes).
Figure 32. Average residual energy of nodes (100 m ˆ 100 m, 200 nodes).
6. Conclusions
6. Conclusions
To achieve energy balance in sensor networks, a type of multi-Sink based data gathering method
is proposed in this paper. By selecting optimal leader in each DGA, the energy efficient data To achieve energy balance in sensorthe networks, a typenode of multi-Sink based data gathering method uploading paths could be established and trajectories of Sinks are also optimized improving time is proposed in this paper. By selecting the optimal leader node in each DGA, the energy efficient in paths data collection. withand the help of the sleep scheduling and optimized the sensing improving radius data efficiency uploading could beMoreover, established trajectories of Sinks are also adjustment strategies, redundancy in network coverage and energy consumption in sensing and time efficiency in data collection. Moreover, with the help of the sleep scheduling and the sensing communication could also be effectively reduced. radius adjustment strategies, redundancy in network coverage and energy consumption in sensing Currently in the big data era, time efficiency is topic under close review. The time delay in data and communication could also be effectively reduced. gathering has been reduced with the help of multiple Sinks in LDGA, but different Sinks may move Currently the bigpoint datasimultaneously, era, time efficiency is topic under close review. The time delay in data to the same in traversal extending the time delay in data uploading in some DGA. gathering has been reduced with the help of multiple Sinks in LDGA, but different Sinks may move to It should be further improved in our future work. the same traversal point simultaneously, extending the time delay in data uploading in some DGA. Acknowledgments: The subject sponsored by the National Natural Science Foundation of P. R. China It should be further improved in isour future work. (61373017), Jiangsu Provincial Research Scheme of Natural Science for Higher Education Institutions
(14KJB520029), Natural Science Foundationby ofthe Jiangsu Province (BK20130882), Open Project of R. Provincial Key Acknowledgments: The subject is sponsored National Natural Science Foundation of P. China (61373017), Laboratory for Computer of Soochow University (KJS1327), Open(14KJB520029), Project of Jiangsu Provincial ResearchInformation Scheme ofProcessing Natural Technology Science for Higher Education Institutions Jiangsu HighFoundation Technology Research Key Laboratory for Wireless Sensor (WSNLBZY201517), A Project for Natural Science of Jiangsu Province (BK20130882), OpenNetworks Project of Provincial Key Laboratory Funded by the Priority Academic Program of Development of Jiangsu (KJS1327), Higer Education Computer Information Processing Technology Soochow University Open Institutions(PAPD), Project of Jiangsu High Technology Key Innovation LaboratoryCenter for Wireless Sensor Networks (WSNLBZY201517), A Project Funded by the JiangsuResearch Collaborative on Atmospheric Environment and Equipment Technology(CICAEET) Priority Development JiangsuProvince Higer Education Institutions(PAPD), Jiangsu Collaborative andAcademic InnovationProgram Project for Postgraduate of Jiangsu (SJLX15_0382, SJLX15_0383, KYLX15_0842). Innovation Center on Atmospheric Environment and Equipment Technology(CICAEET) and Innovation Project Author Contributions: Sha proposed the main ideas of the LDGM algorithm while Jian-mei Qiu designed for Postgraduate of JiangsuChao Province (SJLX15_0382, SJLX15_0383, KYLX15_0842). and conducted the simulations of the protocol. Shu-yan Li and Meng-ye Qiang analyzed the data, results and
Author Contributions: Chao ShaWang proposed main ideas the LDGM algorithm while Jian-mei Qiu designed verified the theory. Ru-chuan servedthe as advisor to theof above authors and gave suggestions on simulations, and conducted the simulations of the protocol. Shu-yan Li and Meng-ye Qiang analyzed the data, results performance evaluation and writing. The manuscript write up was a combined effort from the five Authors. All and verified the theory. Ru-chuan Wang served as advisor to the above authors and gave suggestions on simulations, authors have read and approved the final manuscript. performance evaluation and writing. The manuscript write up was a combined effort from the five Authors. All authors have read andThe approved the final Conflicts of Interest: authors declare nomanuscript. conflict of interest. Conflicts of Interest: The authors declare no conflict of interest.
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