Industrial wireless sensor networks (IWSNs) have been widely used in many application scenarios, and data collection is an extremely significant part of IWSNs. Moreover, a mobile sink is widely used in industrial wireless sensor networks to collect sensory data and alleviate the “hot spot” problem effectively. However, usage of a mobile sink introduces some challenges, such as updating of a mobile sink’s location and planning of a mobile sink’s trajectory. Meanwhile, the impact of different distribution types of events on data collection has not been sufficiently valued in designing of data collection algorithm for IWSNs yet. To overcome these challenges, a virtual grid-based real-time data collection algorithm for applications with centrally distributed events (VGDCA-C) is proposed in this paper to gain a reliable data gathering for IWSNs . In the target application scenarios, the events are distributed centrally, so we mainly focus on how to shorten the routing paths and decrease the transmission delay. In our VGDCA-C, a mobile sink can adjust its movement dynamically according to the changes in event areas. The adjustment of a mobile sink movement strategy includes two aspects. The first one is the dynamic adjustment of a mobile sink’s parking time, and the second one denotes the moving toward event area of a mobile sink. Thus, a mobile sink adjusts its location such that it can get closer to the event area. Hence, the total length of routing is getting shorter so that source nodes can upload sensory data faster. Analysis and simulation results show that compared with the existing work, our VGDCA-C increases the network lifetime and decreases transmission delay. Keywords: Industrial wireless sensor networks, Data collection, Mobile sink, Centrally distributed events 1 Introduction used to collect sensory data from sensor nodes whose bat- With the development of industrial wireless communica- teries can be charged in some scenarios , and all source tion technologies, microelectronics, sensors, distributed nodes deliver sensory data to the static sink by via multi- information processing, and embedded computers, the hop transmission . This way of data collection always industrial wireless sensor networks (IWSNs) have been leads to a “hot spot” problem  that means nodes near widely used in many application scenarios such as poi- the sink or base station run out of energy very fast so that sonous gas boundary detection [1, 2], pollution mon- the network performance has been affected. Due to that, a itoring [3–5], and production monitoring [6, 7]. Data mobile sink is introduced to solve this problem. A mobile collected by sensor nodes need to be uploaded to a sink sink can alleviate “hot spot” problem efficiently. Namely, quickly and accurately via data routing to the sink. The plenty of researchers have revealed that mobile sink can stability and accuracy of data collection are the guarantees make the data collection energy efficient [13–27]. In their of IWSNs’ normal operations. Therefore, the data collec- researches, intelligent unmanned vehicle or unmanned tion and routing [8, 9] plays an important role in IWSNs. aerial vehicle is appointed to be a mobile sink, and all these In the traditional IWSNs, a static sink or a base station is vehicles are equipped with the industrial wireless com- munication device and data processor. A mobile sink can move to the locations of source nodes and collect sensory *Correspondence: email@example.com Department of Internet of Things Engineering, Hohai University, Changzhou, data directly from the source nodes. China © The Author(s). 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Zhu et al. EURASIP Journal on Wireless Communications and Networking (2018) 2018:134 Page 2 of 20 Moreover, a mobile sink can balance the energy con- 2 Related works sumption and prolong the lifetime of the network. 2.1 Overview However, the use of a mobile sink introduces two The VGDCA-C is a data collection algorithm based on new challenges in the data collection of IWSNs. The a virtual structure, which compensates the lack of data first one is the way the mobile sink’s latest location collection algorithms for non-virtual structures. However, is updated. The traditional way of this updating is the trajectory of a mobile sink and the corresponding loca- that a mobile sink broadcasts the updated informa- tion updating also need to be taken into consideration. tion on its location to the entire network. However, Recently proposed related algorithms can be classified a frequent broadcast may lead to high overheads and into two following categories: (1) non-virtual structure- shorten the lifetime of a network. Hence, it is challeng- based data collection algorithm and (2) virtual structure- ing to find a suitable way to update the information based data collection algorithm. of mobile sink with lower overheads. Another challenge is the way the trajectory of a mobile sink is planned 2.2 Non-virtual structure-based data collection algorithm . As the sensory data are delivered to a mobile A non-virtual structure-based data collection means that sink through multi-hops, the sensor nodes around the there is no auxiliary structure to assist the data collection, mobile sink run out of energy very fast. Moreover, the such as virtual grid, virtual honeycomb structure, and vir- number of transmission hops affects the transmission tual ring structure. In this kind of algorithms, mobile sink delay. Hence, the trajectory of a mobile sink affects the either moves randomly or along a pre-determined tra- balance of energy consumption and transmission delay jectory. When mobile sink moves randomly and beyond greatly. the communication range of its previous neighbor sen- Meanwhile, the impact of different distribution types of sor, a new neighbor sensor node of a mobile sink will be events on data collection has not been sufficiently valued appointed as an agent node. These agent nodes can help in designing of data collection algorithms for IWSNs. the routing of sensory data. If the mobile sink moves along In current studies, source nodes are always distributed a pre-determined trajectory, the sensory data will always evenly in the network. However, in some application sce- be routed to the sensor nodes near the trajectory. narios such as industrial fire detection, the monitored In , Han et al. proposed the minimum Wiener index targets are distributed in a local area. Therefore, here, spanning tree (MWST), which is designed for IWSNs with we focus on the scenarios wherein the source nodes a mobile sink. According to the characteristic of Wiener are distributed centrally. Taking into consideration the index, the MWST can provide efficient transmission paths challenges mentioned above and the distribution types for sensor nodes. However, finding a spanning tree with of source nodes, we propose a virtual grid-based real- a minimal Wiener index from a weighted graph is a non- time data collection algorithm for applications with cen- deterministic polynomial-time hardness (NP-hard) prob- trally distributed events for industrial wireless sensor lem. Therefore, the authors proposed a new way to solve networks. this problem; namely, through the extensive experiments, The contributions of this paper are summarized as they found that the Wiener index of a minimum span- follows. A real-time mobile data collection algorithm ning tree (MST) is similar to the Wiener index of MWST based on a virtual grid structure VGDCA-C is proposed. and that time complexity of finding the MST is low. The By constructing a virtual grid structure in the network, authors used the Wiener index of MST as an initial upper the information on a mobile sink location can be updated bound. On this basis, the authors proposed two algo- locally such that the energy consumption of a mobile sink rithms according to the network size. The first is a branch and data transmission delay can be reduced and network and bound algorithm for the small-scale sensor networks, lifetime can be extended. The algorithm proposed in this and the second is a simulated annealing algorithm for paper is suitable for scenarios wherein events are centrally the large-scale sensor networks. These algorithms pro- distributed, such as the monitoring of a fire in the indus- vide a brand new idea for data transmission. However, the trial factories or malfunction monitoring of industrial method to find the location of mobile sinks was ignored. equipment. In , Shin and Kim proposed a milestone-based The remainder of this paper is organized as follows. predictive routing protocol that can solve the problem Firstly, the related works of data collection algorithms of finding a spanning tree with the minimum Wiener with a mobile sink are presented in Section 2. The details index from a weighted graph presented in . The pro- of the VGDCA-C are described in Section 3.InSection 4, posed protocol consists of two main parts: estimation of the simulation experiments and performance evaluations mobile sink future location (namely, when a mobile sink are provided. A brief conclusion is given in Section 5, finds some new sensor nodes entering its communication and abbreviations used in the manuscript are listed in the range, it broadcasts its updated location to them) and the “Abbreviation”section. establishment of milestone nodes and update of mobile Zhu et al. EURASIP Journal on Wireless Communications and Networking (2018) 2018:134 Page 3 of 20 sink’s location. The milestone nodes have to spread the 2.3.1 Random movement estimated future location of a mobile sink to nodes located Random movement of a mobile sink means that mobile near the recent trail of a mobile sink. If the direction of sink can move in any direction at any speed during data a mobile sink is changed, it chooses a new neighbor sen- collection. sor node as the next milestone node. All the sensory data In , Singh et al. proposed the EEGBDD algorithm. are delivered by these milestone nodes. The milestone In this algorithm, every source node establishes its own nodes are the tools of the source nodes to find the loca- virtual grid. Mobile sink moves randomly in the network, tion of a mobile sink. However, too many milestone nodes and sink initiates a query request when it needs data from are established if a mobile sink moves for a long time, the source node. The source node sends its data to the which leads to a longer routing path. Consequently, the sink via the virtual grid. All query request and data are control packets among milestone nodes consume more transferred through the dissemination nodes, and dissem- energy. Thus, the presented way to find the mobile sink is ination nodes are selected based on node residual energy inefficient. and the distance from the node to the intersection of the Astrategyofdoublecross to collectdata forindus- grid. This algorithm reduces the length of the transmis- trial wireless sensor networks was proposed by Shi et al. sion path so that it reduces the energy consumption of . In this strategy, the authors introduced the double- nodes. However, some nodes may belong to more than blind concept where the source nodes and mobile sink do one path so they could consume too much energy and die not know each other’s location. The authors provided the early. scheme of a random line walk (RLW), which is used to Tunca et al. proposed an energy-efficient routing pro- transmit the sensory data. When a source node needs to tocol to improve the network performance . In this upload the sensory data, it randomly chooses a direction protocol, a ring structure is used to maintain of mobile to establish the baseline. The source nodes transmit sen- sink location. After the network is deployed, a virtual ring sory data in two directions in that baseline. On the basis structure consisted of nodes is built. Sink sends its loca- of the RLW, the authors proposed the strategy of double tion information to the nodes on the ring. When a node cross. This strategy enables source nodes to be associated needs to send data, it first requests the location of a sink with a mobile sink. When a source node detects an event, from the nodes on the ring and then sends data to the sink. it selects one direction randomly and transfers the sen- To balance energy consumption, the nodes on the ring are sory data along that direction and its vertical direction periodically replaced. by the RLW mechanism. All sensor nodes on the trans- In , Wang et al. proposed a grid-based data dis- mission path cache the sensory data. When mobile sink semination routing protocol. In this protocol, source node needs sensory data, it transmits the query information. builds a grid to transmit data when an event is detected. The query information is also transmitted in two direc- Source node obtains the information on eight neighbor tions, which are perpendicular to each other, according grid vertices near the source node and then sends a packet to the RLW mechanism. The query path and the sensory to all its neighbors. Every neighbor node replies a packet data routing path intersect at a sensor node. If the inter- containing the information on node remaining energy. section sensor node receives both the query information Source node selects the best neighbor as a relay node and sensory data, the sensory data will be transmitted based on the residual energy of these neighbor nodes and to mobile sink. In this strategy, too many sensor nodes distance from the sink to the neighbor nodes. The relay need cache and relay sensory data to find the mobile node repeats this process until the data arrive at the sink. sink; thus, energy is wasted, and transmission delay When the mobile sink needs data, it initiates a query is large. request. The request arrives at the source node through the relay nodes, and the source node sends data to the sink 2.3 Virtual structure-based data collection algorithm via the query path. Data collection based on a virtual structure means that there is some auxiliary structure to assist the data gath- 2.3.2 Fixed-trajectory movement ering. The virtual structure contains the virtual grid, When a mobile sink moves along a fixed trajectory in virtual honeycomb structure, virtual ring structure, and data collection, then, sink always moves along a pre- so on. The establishment of a virtual structure can sim- defined trajectory regardless the network status and plify the location update of a mobile sink, data upload, application environment. Usually, the pre-defined tra- path planning of a mobile sink, and so on. In this kind jectory contains the straight line, rectangle, cycle, and of algorithms, the movements of mobile sinks can be so on. divided into three categories: random movement, fixed- Mottaghi et al. proposed the O-LEACH algorithm  trajectory movement, and dynamically adjusted trajectory that represents an improved version of the LEACH algo- movement. rithm. In the proposed algorithm, mobile sink moves Zhu et al. EURASIP Journal on Wireless Communications and Networking (2018) 2018:134 Page 4 of 20 along a fixed line, whereas the area near the linear tra- Ghafoor et al. proposed the efficient trajectory design jectory is called the convergence area. Nodes in the con- for mobile sink algorithm . In this algorithm, the vergence area are set as convergence nodes (RNs). The trajectory of a sink is based on a Hilbert curve, and network is divided into different clusters, and cluster trajectory of a mobile sink is adjusted dynamically accord- head nodes are selected for each cluster. Data from the ing to the density of nodes and network size. The order sensor nodes is sent to the cluster head nodes. Cluster of Hilbert curve is smaller when a mobile sink is mov- head node transmits the data to the sink if it is near ing toward the region with a smaller node density and the sink; otherwise, cluster head node sends data to the vice versa. This algorithm can dynamically adjust the tra- near convergence node, and the convergence node trans- jectory of mobile sink according to the network state mits data to the sink. This algorithm reduces the energy so that it can balance energy consumption of nodes. of nodes, but a fixed trajectory of a mobile sink leads However, this algorithm can only dynamically adjust to the high energy consumption of nodes near the tra- thetrajectoryinalargerange,but it is notsuitable jectory because these nodes bear more data forwarding for data collection under the condition of uneven node task. density. In , Konstantopoulos et al. proposed a data collec- To solve the problem presented in , Yang et al. tion algorithm intended for an urban environment. In this proposed the adjustable trajectory design based on node algorithm, sink moves along a fixed trajectory and collects density for mobile sink algorithm . In this algorithm, data from the nodes near the trajectory. A virtual structure different orders of Hilbert curves are combined. By refin- called the cluster is established in the network. Cluster ing the established virtual grid structure and considering head node that is responsible for data fuse and data for- the density of nodes in a smaller region, Hilbert curves warding is selected in each cluster. Sensor nodes transmit with different orders are constructed according to the data to their own cluster head nodes. Cluster head nodes different densities of nodes. Besides the fact that this algo- send their data to those nodes near the trajectory of a rithm solves the problem stated in , it also makes the mobile sink. This algorithm reduces the energy consump- data collection algorithm suitable for the case of uneven tion of nodes. However, nodes near the trajectory of a node deployment. mobile sink bear more task and expend their energy early. Khan et al. proposed a data collect algorithm called the 3 Method VGDRA . In this algorithm, a network is divided into 3.1 Network model Mobile data collection can prolong the network life- virtualgrids,and thenumberofthe gridsisonlyrelated to the number of nodes. Namely, each grid selects a head time IWSNs. In most of mobile data collection algo- node, and the head node is in responsible for collecting rithm, the application scenarios are always with evenly data from nodes in its grid. Mobile sink moves along the distributed events. However, in some real application sce- network boundary, and during that movement, the rout- narios, source nodes are distributed centrally in a local ing of data is adjusted dynamically. Compared with the region, and the distributed region may change over the fixed line trajectory, the rectangle path of mobile sink bal- time. For instance, when the emergent events are moni- ances energy consumption of the network but nodes near tored, such as monitoring of a fire in the industrial factory the trajectory also consume a lot of energy. or monitoring the malfunction of industrial equipment, the source nodes are always distributed in a local region. 2.3.3 Dynamically adjusted trajectory movement As illustrated in Fig. 1, the sensor nodes within the event In this classification, a mobile sink is neither moving ran- area are source nodes. domly nor moving on the pre-defined trajectory. However, In the following, the network model and relevant the sink adjusts the trajectory dynamically according to assumptions are described in detail. The network is a rect- the collected data, distribution of nodes, remaining energy angle area with the size of L × D. The network consists of sensor nodes, and the number of travelling times in a of N sensor nodes, and these sensor nodes are deployed region. densely and randomly. All the sensor nodes are well con- In , Kinalis et al. proposed an algorithm named the nected, and the network is fully covered. The sensor nodes Biased Sink Mobility with Adaptive Stop Times. In this are static and location-aware (i.e., equipped with the GPS- algorithm, the virtual grid structure is established in the capable antennas). Sensor nodes have the same initial network, and the intersection point of the grid is a stop- energy, sensing radius r , and communication radius R. ping point of a mobile sink. If there is a higher density of Sensory data is delivered to the mobile sink by a multi- nearby sensor nodes near the point, a mobile sink will stay hop transmission. There is only one mobile sink in the network and is not constrained by energy, memory space, longer at that point. The adaptive stop time of a mobile sink can balance the energy consumption of nodes, but a and computing ability. The speed of the mobile sink v is long trajectory of a mobile sink increases network delay. fixed during in motion, and the mobile sink may park in Zhu et al. EURASIP Journal on Wireless Communications and Networking (2018) 2018:134 Page 5 of 20 Fig. 1 Source nodes located in a local region with emerging event. The gray circle in the figure indicates the area where the emerging event occurred the center point of the virtual grid cell for a while. The sen- (RCN) for each grid cell in step 2. To reduce the updat- sor nodes are densely deployed, and there are no obstacles ing range of a mobile sink’s location, we introduce the in the network, so we can assume that there are sensor directionnumber(DN)instep3. nodes in each grid. The notation and the corresponding 1) Calculation of side length of grid cells definition used in our algorithm are given in Table 1. As illustrated in Fig. 2, each grid cell has up to eight neighbor grid cells, and the sensor nodes in neighbor grid 3.2 Network initialization cells are called the neighbor nodes. To enable nodes to The first phase after the network is deployed is network communicate with the neighboring nodes, the relation of initialization. This phase includes three sub-phases: estab- communication radius R and a side length of grid cells a lishment of a grid-based virtual structure, election of head need to satisfy Eq. (1). When the side length a is calcu- nodes in the virtual grid cells, and establishment of the lated, mobile sink broadcasts some information in the net- neighbor tables. Since the deployment area is a rectangle, work to establish the virtual structure. The information we adopt the Cartesian coordinate system for conve- consists of a, L,and D. nience. The origin of this coordinate system is located at 2R the lower left corner of the network. a ≤ (1) 3.2.1 The establishment of grid-based virtual structure 2) Calculation of RCN of grid cells The establishment of a grid-based virtual structure After receiving the information broadcasted by a mobile includes three steps. The first step is to calculate the sink, sensor nodes calculate the number of grid cells length of a virtual grid cell. The grid cell is a square in in both horizontal direction and vertical direction. The our algorithm, and calculation of a grid cell’s length is the calculating process is defined by Eqs. (2)and (3). foundation of a virtual structure. To set an ID number for each grid cell, we calculate the row-column number n = (2) Table 1 Notations and definitions Notation Definition n = (3) L Transverse length of network Based on the received information and their own coordi- D Longitudinal length of network nates, nodes can get an RCN, which indicates the location N Number of sensor nodes of a grid cell that the node belongs to; the calculating R Communication radius of sensor nodes processisgiven in Eqs. (4)and (5). r Sensing radius of sensor nodes M = (4) v Speed of mobile sink r a Zhu et al. EURASIP Journal on Wireless Communications and Networking (2018) 2018:134 Page 6 of 20 Fig. 2 The relationship between communication radius and a side length of a grid cell. The distance between A and B is R, and it is easy to calculate the value of a 0, M = M & M = M ⎪ r r_sink c c_sink x 1, M > M & M > M i ⎪ r r_sink c c_sink M = (5) 2, M > M & M < M a ⎪ r r_sink c c_sink 3, M < M & M < M ⎨ r r_sink c c_sink Sensor nodes in the same grid cell have the same RCN DN = 4, M < M & M > M (8) r r_sink c c_sink value, and the RCN will not be modified. When RCN is ⎪ 5, M > M & M = M r r_sink c c_sink calculated, the network is as shown in Fig. 3. ⎪ 6, M = M & M < M r r_sink c c_sink 3) Calculation DN of grid cells 7, M < M & M = M r r_sink c c_sink Since the initial location of a mobile sink is in the grid ⎩ 8, M = M & M > M r r_sink c c_sink cell center, sensor nodes can get the RCN of the grid cell center according to the information they received. The 3.2.2 The election of head nodes in virtual grid cells calculating process is shown in Eqs. (6)and (7). In our VGDCA-C, the virtual grid cell head nodes are D to collect sensory data from the same grid cell, deliver M = = (6) sensory data, and maintaining the DN of the grid cell. r_sink 2 2 In the first election, all the sensor nodes broadcast their coordinates and RCNs, and the radius of broadcasting is 2a. Thus, one sensor node can receive information from M = = (7) c_sink neighbor sensor nodes. Firstly, the sensor node compares 2 2 its RCN with the RCN from the received information. If the received RCN is equal to that of the receiver, the After calculating the initial RCN of mobile sink, sensor coordinates and RCNs information will be added to the nodes get the DN of grid cells that they belong to accord- election list of the receiver. If the received RCN is not ing to the relation of (M , M )and theirown RCN r_sink c_sink equal to that of the receiver, the receiver will drop the (M , M ). The comparing process is given in Eq. (8). r c coordinates and RCN information. After the information The grid cell where a mobile sink is located denoted the is processed, each sensor node adds the source node of the grid of sink (GS), and the relation between grid cell DN information into its election list. and GS is shown in Table 2 and Fig. 4. Zhu et al. EURASIP Journal on Wireless Communications and Networking (2018) 2018:134 Page 7 of 20 Fig. 3 The RCN of virtual grid cell. It shows the RCS of virtual grid cell After the operation of adding, sensor nodes sort their mark sending node as a head node of that cell. Accord- election lists. The election lists are sorted in ascending ing to the sorted election list, the nodes in the grid are order by the abscissa, and if some sensor nodes have the successively selected as the head nodes. same abscissas, the lists are sorted in ascending order by If some sensor nodes cannot broadcast CellHead, a wait- the ordinate. After the sorting operation, the sensor nodes ing mechanism is introduced. If other nodes in the same in thesamegridcellhavethe same election list.Ifasensor grid cell cannot receive CellHead after a threshold period node finds itself at the top of the election list, the sen- Th , the next sensor node in the election list tries to time sor node broadcasts information of CellHead within the broadcast CellHead . radius of 2a. The broadcasted CellHead consists of the 3.2.3 The establishment of neighbor tables indexes of sensor node in the election list. The other sen- As each grid cell has up to eight neighbor grid cells, one sornodes in thesamegridcellreceive theCellHeadand head node has up to eight neighbor head nodes. In the process of establishing the neighbor tables, each head Table 2 The relation between grid cells DN and GS node broadcasts its coordinate and RCN in the commu- nication range. Meanwhile, each head node can receive DN Relation between corresponding grid cell and GS information from other head nodes. Each head node 0 The corresponding grid cell is GS compares its RCN (M , M ) with RCN of another head r c 1 (up side of GS)&&(right side of GS) node M , M . According to the relation of (M , M ) and r c r c 2 (up side of GS)&&(left side of GS) M , M , neighbor head nodes can be added to the corre- r c 3 (down side of GS)&&(left side of GS) sponding rows of the neighbor table. The neighbor table and corresponding criterion are shown in Table 3 and 4 (down side of GS)&&(right side of GS) Fig. 5,respectively. 5 (same column with GS)&&(up side of GS) 6 (same row with GS)&&(left side of GS) 3.3 Data routing 7 (same column with GS)&&(down side of GS) After the network initialization, sensor nodes could rely 8 (same row with GS)&&(right side of GS) on a virtual grid structure to upload sensory data to the Zhu et al. EURASIP Journal on Wireless Communications and Networking (2018) 2018:134 Page 8 of 20 Fig. 4 The DN of virtual grid cell. The grid cell 0 is the cell wherein a mobile sink is located mobile sink.Whensourcenodehas collected thesen- 3.4 Trajectory planning of mobile sink sory data, it encapsulates its RCN and sensory data into In our VGDCA-C, the moving region of a mobile sink is a data packet and transmits it to the corresponding head composed of a transverse moving belt and a longitudi- node in the same grid cell, and the head node forwards the nal moving belt. The two moving belts are presented as a data packettoaneighborheadnodeaccordingtothe DN gray region in Fig. 7. The two moving belts may switch to of the former. The data packet also includes other infor- another column or row when target events change. Before mation, and the detail will be described in the following the switching of a moving belt, the mobile sink will com- sections. The relation of the DN of head nodes and the plete Num moving cycles in the moving belt. In Fig. 7, cycle corresponding transmission direction are shown in Fig. 6 the grid cells in the gray region are called the moving and Table 4. belt grids. In one moving cycle, the mobile sink parks in Table 3 The neighbor table and corresponding criterion Rows of neighbor table Definition Criterion LU Head node in the upper left corner M = M + 1 & M = M − 1 r c r c RU Head node in the upper right corner M = M + 1 & M = M + 1 r c r c LD Head node in the lower left corner M = M − 1 & M = M − 1 r c r c RD Head node in the lower right corner M = M − 1 & M = M + 1 r c r c UG Head node in the grid above M = M + 1 & M = M r c r c DG Head node in the grid below M = M − 1 & M = M r c r c LG Head node in the left grid M = M & M = M − 1 r c r c RG Head node in the right grid M = M & M = M + 1 r c r c Zhu et al. EURASIP Journal on Wireless Communications and Networking (2018) 2018:134 Page 9 of 20 Table 4 The rules of selecting next hop head node DN of current head node Transmission direction Row selected table in neighbor 1 Bottom left LD 2 Bottom right RD 3Topright RU 4 Top left LU 5Down DG 6Right RG 7Up UG 8Left LG 0 (Broadcast in local grid) / Fig. 5 The neighbor grid cells and corresponding rows in neighbor table. Node A is the head node 3.4.1 Trajectory of mobile sink in moving cycle In our target application scenarios, the event region appears randomly. To adapt to this kind of application sce- narios, we design a “cross” moving trajectory for a mobile different moving belt grids for different durations accord- sink. As illustrated in Fig. 7, the grid cell intersected by ing to the collected sensory data. The mobile sink assigns two moving belts is called the intersecting grid (IG). In weight values to the moving belt grids, and the weight val- one moving cycle, the mobile sink starts from IG and ues affect the parking time of a mobile sink. When the moves toward the direction whose DN is 5. After the mobile sink completes Num moving cycles in the cur- cycle mobile sink arrives at the grid cell whose M is (n − 1), r D rent moving belts, it estimates the location of the event it starts to move in the opposite direction. The mobile region. Subsequently, the moving belts switch according sink can move back to the IG, and then, the moving direc- to the corresponding strategy. tion switches to the direction whose DN is 8. When the mobile sink arrives at the grid cell whose M is (n − 1), c L the mobile sink switches the moving direction to the opposite direction. The mobile sink moves in the direc- tion whose DN is 7 after moving back to the IG. When the mobile sink arrives at the grid cell whose M is 2, it starts to move toward the IG again. After moving back to theIG, themobilesinkstartstomovetothe direction whose DN is 6 until it reaches the grid cell whose M is 2, then the mobile sink starts to move to the IG. When the mobile sink arrives at the IG, one moving cycle is completed. 3.4.2 Calculation of weight value for moving belt grids According to Section 3.3, all the sensory data are routed to the moving belts. Different moving belt grids are respon- sible for different areas. As illustrated in Fig. 8,grid A has 13 responsible grid cells and grid B is responsi- ble for 6 grid cells. Hence, different moving belts grids have different workloads. When a mobile sink starts the first moving cycle in the current moving belts, it calcu- lates the weight value for each moving belt grid. Here, Fig. 6 The DN of current head node and corresponding transmission W is used to represent the weight value. The RCN of direction. Node A is the current head node, and the others are IG is (M , M ), and the RCN of moving belt grid r_IG c_IG neighbor head nodes is (M , M ). The process of calculation is as follows: r_m c_m Zhu et al. EURASIP Journal on Wireless Communications and Networking (2018) 2018:134 Page 10 of 20 Fig. 7 The moving region of mobile sink in a moving cycle. The dashed line with arrow is the trajectory of sink M > M && M = M : r_m r_IG c_m c_IG W M , M = min − M , M − 1 r_m c_m r_m c_m D + min M − 1 , M − 1 r_m c_m W M , M = min M − 1 , − M r_m c_m c_m r_m (12) L D + min −M −M c_m r_m M > M && M = M : a a r_m r_IG c_m c_IG (9) W M , M = min M − 1 , − M r_m c_m c_IG r_IG M = M && M > M : r_m r_IG c_m c_IG + min − M , r_IG D L W M , M = min −M , −M r_m c_m r_m c_m a a − M L c_IG + min −M , M − 1 c_m r_m + min − M , M −1 (10) c_IG r_IG + min M − 1 , M − 1 r_IG c_IG M < M && M = M : r_m r_IG c_m c_IG (13) W M , M = min − M , M − 1 3.4.3 Allocation of parking time for mobile sink in the first r_m c_m c_IG r_m moving cycle + min M − 1 , M − 1 c_m r_m When the mobile sink starts the first moving cycle in (11) the current moving belt, it allocates parking time for the moving belt grids according to the corresponding weight M = M && M < M : r_m r_IG c_m c_IG values. In one moving cycle, the moving time of a mobile Zhu et al. EURASIP Journal on Wireless Communications and Networking (2018) 2018:134 Page 11 of 20 Fig. 8 The moving belt grids and corresponding responsible areas. S, A,and B are the moving regions of mobile sink in one moving cycle. A represents the region which grid A is responsible for and B represents the region which grid B is responsible for sink is calculated by Eq. (14). We assume that in a mov- berofparking in different typesofgridcells is differentin ing cycle, the parking time t is equal to the moving time a moving cycle. If a grid cell is a top grid, a mobile sink can pa t . Therefore, the total time of a moving cycle is park in this grid cell only once. We assume that the RCN moving_sink calculated by Eq. (15). of a moving belt grid is i, j . The number of times the mobile sink parks in different types of moving belt grids is 2 × a × (n + n − 6) L D t = (14) moving_sink calculated as follows: If a grid i, j is a top grid, then: 4 × a × (n + n − 6) L D T = t + t = (15) moving_sink pa We allocate t to each moving belt grid according to the W i, j pa t = × t (17) p pa corresponding weight values, and the allocated time is the all corresponding parking time. Thus, we need to get the sum of weight values, which is defined in Eq. (16). If a grid i, j is IG, then: n −1 W = W i, M all c_IG W i,j ( ) × t pa i=2 all t i, j = (18) (16) p n −1 L 4 + W M , j − W M , M r_IG r_IG c_IG j=2 • If a grid i, j is the other moving belt grids, then In the allocation process, the moving belt grids need to W (i,j) be classified into three categories. The first category is a × t pa all top grid, and it refers to the moving belt grids that are t i, j = (19) adjacent to the boundary grids. The second category is IG, and the third category consists of other moving belt In the first moving cycle, a mobile sink starts to collect grids. The reason for grids classification is that the num- sensory data in the current moving belt according to the Zhu et al. EURASIP Journal on Wireless Communications and Networking (2018) 2018:134 Page 12 of 20 n −1 parking time given above. When a mobile sink collects C = C M , j gma gm r_IG the sensory data, it counts the sensory data in the cor- j=2 responding counters. Therefore, in the following, we will n −1 (20) talk about the counters in the mobile sink. + C i, M gm c_IG 3.4.4 Counters of mobile sink i=2 In the process of sensory data routing to the mobile − C M , M gm r_IG c_IG sink, the sensory data carry the information on source nodes and routing. According to that information, the n −1 mobile sink counts the corresponding counters. When C = C M , j gra gr r_IG the sensory data are sensed, the source nodes attach j=2 their RCNs to the sensory data. When the sensory data n −1 (21) are routed to the moving belt grid for the first time, + C i, M gr c_IG then RCN of this moving belt grid is attached to the i=2 sensory data. The counters the mobile sink has are as − C M , M gr r_IG c_IG follows: • When the recalculated parking time is discussed, the C i, j : In the sensory data, if the RCN of a moving gm moving belt grids need to be classified into three cate- belt grid that is first met is i, j , then the amount of gories: top grids, IG, and other moving belt grids. We sensory data is added to this counter. • assume that the RCN of a moving belt grid is i, j .The C i, j : This counter is used to record the number gm time that mobile sink parking in different types of mov- of the moving belt grids which the sensory data pass ing belt grids is calculated as follows (the calculated time and the amount of sensory data are added to the is the time of one parking in the grid): counters corresponding to these passed moving belt grids. When a grid i, j is a top grid the time is defined by C (i): The value of i is from 1 to 3. As the horizontal RCN of the source node is in the sensory data, M of C i, j t C i, j t gm gr pa pa the source node can be obtained. If M of the source t i, j = × + × C 2 C 2 node is larger than IGs, the value of i is 1, and the gma gma amount of sensory data is added to C (1).If horizontal C i, j C i, j gm gr a×(n + n − 6) L D = + × M of the source node is equal to IGs, the value of i is C C v gma gra 2. The value of i is 3 when the M of the source node (22) is smaller than IGs. C (i): The value of i is from 1 to 3. As the RCN vertical When a grid i, j is IG the time is defined by of the source node is in the sensory data, M of the source node can be obtained. If M of the source C i, j C i, j t t gm pa gr pa node is larger than IGs, the value of i is 1 and the t i, j = × + × amount of sensory data is added to C (1).If M C 2 C 2 gma gra vertical c of the source node is equal to IGs, the value of i is 2. C i, j C i, j a × (n + n − 6) gm gr L D The value of i is 3 when the M of the source node is = + × C C 4 × v gma gra smaller than IGs. (23) 3.4.5 Dynamic adjustment of parking time When a grid i, j is the other moving belt grid the After completing the first moving cycle and moving back time is defined by to the IG, a mobile sink readjusts the parking time for the next moving cycle according to its counters. Due to that, C i, j t C i, j t gm gr pa pa t i, j = × + × different grid cells handle different amounts of sensory p C 2 C 2 gma gra data in the moving belts, so the mobile sink needs to park C i, j C i, j a × (n + n − 6) longer in the moving belt grid, which handles more sen- gm gr L D = + × sory data. We divide the time of a moving cycle into two C C 2 × v gma gra parts on average, of which is allocated by C i, j ,and gm (24) another is allocated by C i, j . The summing process of gr C i, j is defined by Eq. (20), and the summing process gm After the redistribution of parking time, a mobile sink of C i, j is defined by Eq. (21). gr starts a new moving cycle according to the allocated Zhu et al. EURASIP Journal on Wireless Communications and Networking (2018) 2018:134 Page 13 of 20 parking. Before the start of a new moving cycle, all the The second category refers to the situation that the counters of a mobile sink are set to zero. After the moving belts switch to another column or row. When a mobile sink completes Num moving cycles, it esti- transverse moving belt switches to another row, both pre- cycle mates the location of the event area according to the vious row and current row need to update their DNs. counters. The moving belt then moves toward the event When a longitudinal moving belt switches to another col- area. umn, both previous column and current column need to update their DNs. The updating is relevant to the grid 3.4.6 Moving trajectory of moving belts cell where the mobile sink is located before moving. The As the source nodes are distributed centrally, the mobile relationship of grid cell DN and GS is shown in Fig. 4. sink needs to move toward the event area as close Namely, when mobile sink updates a grid cell’s DN, it only as possible such that the total length of the sensory needs to update the head node of the grid cell. Thus, the data transmission is reduced and the energy consump- local updating not only reduces the update area but also tion is decreased. Before the moving belts switch to reduces the number of the updated sensor nodes. another column or row, the mobile sink first com- pares C (1), C (2),and C (3).If horizontal horizontal horizontal 3.6 Re-election of head nodes C (1) has the largest value, the transverse mov- horizontal To prolong the network lifetime and balance the energy ing belt switches to a neighbor row above. If C (3) horizontal consumption of sensor nodes in each grid cell, the head has the largest value, the transverse moving belt switches nodes need to be regularly re-elected. First, the ratio of the to a neighbor row below. If C (2) is the largest, horizontal residual energy of the current head node and its energy or two of three counters are equal, or all three coun- when it was elected is calculated. If that ratio is below ters are equal, the transverse moving belt does not switch a threshold Th, the head node broadcasts Re-Election to to another row. Similarly, the mobile sink compares start re-election of the corresponding grid cell. The Re- C (1), C (2) and C (3).If C (1) has vertical vertical vertical vertical Election includes the ordinal number of the head nodes the largest value, the longitudinal moving belt switches in the election list Index. The sensor nodes in the same to a neighbor column on the right. If C (3) is vertical grid cell can receive the Re-Election and query the sen- the largest, the longitudinal moving belt switches to a sor node whose the ordinal number in the election list is neighbor column on the left. In other cases, the lon- (Index + 1). If a sensor node A finds that the sensor node gitudinal moving belt does not switch. According to queried itself, the sensor node A sends CellHead_01 to the this strategy, the mobile sink can get closer to the current head node. After receiving CellHead_01, the cur- event area. rent head node sends its neighbor list to the sensor node A.Whensensornode A receives the neighbor list of the 3.5 Local updating of mobile sink current head node, it broadcasts CellHead_02. When the When a mobile sink moves from one grid cell to another, other sensor nodes receive CellHead_02, the sensor node the DN of grid cells needs to be updated to main- A becomes the new head node of the current grid cell, and tain a reliable data routing. According to Section 3.3, the previous head node is retired. According to Eq. (1), the sensory data are routed to the mobile sink accord- all eight neighbor head nodes can receive CellHead_02, ing to DN of grid cells. Hence, the updating of DN of and the neighbor head nodes then add sensor node A to grid cells denotes the updating of the location infor- their neighbor lists. Before the new head node is ready, mation of a mobile sink. For further discussion, the the sensory data are also transmitted to the previous head updating operations need to be classified into two node. When the other sensor nodes are waiting for Cell- categories. Head_02, if the waiting time exceeds the threshold Th , time The first category refers to the situation that the mov- they query the sensor node whose the ordinal number is ing belts do not switch. In this situation, DNs of two grid (Index + 2). If the current head node is the last one on cells need to be updated when the mobile sink enter into a the election list, then the sensor nodes will query the first new grid cell. The first grid cell is the one that the mobile sensor node on the election list in the next election. sink is located in before entering the new one. The second grid cell is the one that the mobile sink entered, and this 4 Results and discussion grid cell sets its DN to 0. The former grid cell sets its DN 4.1 Simulation model according to the moving direction. If mobile sink moves To evaluate the performance of our proposed algorithm, toward the direction whose DN is 5, the DN of the former we designed the simulation experiment using the MAT- grid cell is set to 7. If the direction DN is 8, the former’s LAB platform. The simulation parameters are listed in DN is set to 6. If the direction has DN is 7, the former’s Table 5 and the values of the parameters are listed in DN is set to 5. If the direction DN is 6, the former’s DN is Table 6. In our simulation, the target monitoring area was set to 8. a rectangle area with the size of L × D. The network Zhu et al. EURASIP Journal on Wireless Communications and Networking (2018) 2018:134 Page 14 of 20 Table 5 Simulation parameters To simulate the centrally distributed event, we assumed Parameters Definition event area is a circular area and all sensor nodes in this area are appointed as source nodes. The network L Transverse length of network lifetime was determined by the time when the first D Longitudinal length of network node runs out of its energy. In our VGDCA-C, the N Number of sensor nodes real-time data collection means that the source nodes r Communication radius of sensor nodes upload sensory data immediately when the sensory data r Radius of event area is sensed. In this context, we mainly focused on the E Initial energy of sensor node balance of energy consumption to prolong the network lifetime. Thus, we focused on the lifetime performance d Threshold of communication and energy consumption balance, while the delay of sen- l Size of control packet sory data transmission was not considered. We used the l Size of sensory data packet following aspects as performance metrics of simulation E Digital electronics elec experiments: E Communication (d < d ) fs 0 Network lifetime: defined by the time when the first E Communication (d ≥ d ) mp 0 node runs out of its energy Th Threshold of re-election Average residual energy: the mean value of residual Num Threshold of movig cycle cycle energies of all the sensor nodes v Velocity of mobile sink sink A variance of residual energy: the variance of residual energies of all the sensor nodes consisted of N sensor nodes, and these sensor nodes had An average number of transmission hops: the mean the same communication radius r and initial energy E. value of transmission hops from a source node to the The size of the control pocket was l ,andthesizeof mobile sink. the sensory data packet was l .Weadopted theenergy model wherein if a sensor node receives n bit sensory 4.2 Performance analysis under different system data, the consumed energy is (n × E ) J;ifasensor b elec parameters node sends n bit sensory data, the consumed energy can In the simulation experiments of VGDCA-C, we first be classified into two categories. We assumed the trans- studied the impact of system parameters Th and Num cycle mission distance is d, and the threshold of transmission on network performances, where Th denotes the thresh- distance is d .If d < d , the consumed energy is 0 0 old of the re-election of head nodes, which affects the n × E + E × d )J;if d ≥ d , the energy is equal b elec fs 0 equilibrium of energy consumption in a single grid cell, to n × E + E × d J. b elec mp and Num affects the energy consumption in the entire cycle network and network lifetime. In these experiments, the number of sensor nodes was 1000, and the location of Table 6 Values of simulation parameters event area changed every 1000 s. The values of Th were Parameters Values 10, 30, 50, 70, and 90%, and the values of Num were 2, cycle L 200 m 4, 6, 8, and 10. D 200 m N 800~1600 4.2.1 Network lifetime r 75 m As illustrated in Fig. 9, the network lifetime was mini- mal at Th of 10%, and the lifetime increased with the r 30 m increase of Th. In the case of Th of 10%, the head node E 2J could start re-election when the residual energy became d 75 m 10% of the energy at the election time. It means that l 200 bit sensor nodes that had been head nodes had little resid- l 800 bit ual energy. However, the sensor nodes that had not been E 50 nJ/bit elec elected had higher residual energy. Thus, the energy con- sumption within the grid cell was unbalanced, and the first E 10 pJ/bit/m fs 4 sensor node that ran out of energy appeared soon. There- E 0.0013 pJ/bit/m mp fore, the network lifetime was short when Th was 10%. Th 10~90% With the increase of Th, the sensor nodes in the grid cell Num 2, 4, 6, 8, 10 cycle assumed the task of the head node more frequently, and v 10 m/s sink the energy consumption within grid cell became more and Zhu et al. EURASIP Journal on Wireless Communications and Networking (2018) 2018:134 Page 15 of 20 Fig. 9 The network lifetime under different system parameters (Th and Num ). When Th was 90% and Num was 8, the network lifetime could cycle cycle reach the maximum value more balanced. We found that the network lifetime had increase was caused by the increase of Th. Thus, the aver- the highest growth rate when Th varied between 70 and age residual energy decreased. When Th was unchanged, 90% because in that case, energy consumption within grid the average residual energy was the lowest at Num of cycle cell was the most balanced. 8, which means that the energy utilization rate was the When we analyzed the situation from the vertical axis, best in that case. In Fig. 10, it can be seen that when we found that for the same Th, network lifetime was min- Num was equal to 2, the average residual energy was cycle imal when Num was 2. When Num was 2, the lower than the average residual energy at Num of 4. cycle cycle cycle mobile sink needed to determine whether to switch the However, when Num was 2, the network lifetime was cycle moving belts after every two completed moving cycles. shorter than that when Num was4.Thisisbecause the cycle According to the distribution of event area and the strat- moving belts needed to be constantly switched, and much egy of switching the moving belts, two moving belts energy was consumed to update the corresponding grid switched in general circumstances. Hence, the grid cells cells. Thus, the energy utilization rate was not high when of two rows and two columns needed to be updated. Num was 2 because much energy was wasted. On the cycle Therefore, much energy was consumed and network life- other hand, when Num was 8, the energy utilization cycle time was shortened. With the increase of Num ,the rate was the highest. cycle network lifetime also increased. When Num reached cycle 4.2.3 Variance of residual energy 8, the network lifetime had the maximum value because The variance of residual energy indicates the balance of the updating operation did not consume much energy energy consumption. As illustrated in Fig. 11,the variance when the moving belts did not switch frequently. When was minimal at Th of 10% because only a small number Num was 10, the network lifetime began to decrease cycle of sensor nodes had consumed energy when the network because all the sensory data were routed to the moving ended. Most sensor nodes had almost the same residual belts. If the moving belts were not switched for a long energy. With the increase of Th, most sensor nodes began time, the sensor nodes in the moving belts could cause the to consume energy, and the variance increased. When the “hot spot” problems, which would shorten the network Num was 2 and 4, the network lifetime was short, and cycle lifetime. Thus, when Th was 90% and Num was 8, the cycle the variance was low. Although the energy consumption network lifetime could reach the maximum value. was balanced in that state, that was not an excellent sit- 4.2.2 Average residual energy uation. When the Num was 10, the variance reached cycle The average residual energy indicates the energy utiliza- the maximum value because in that case, the moving belts tion rate of the network. As illustrated in Fig. 10,with stayed in the same area for a long time, and the sen- the increase of Th, the average residual energy decreased sory data converged in that area. Hence, the sensor nodes continuously. According to Fig. 9, the network lifetime of that area consumed all energy very fast. The energy Zhu et al. EURASIP Journal on Wireless Communications and Networking (2018) 2018:134 Page 16 of 20 Fig. 10 The average residual energy under different Th and Num .WhenNum ycle was 8, the energy utilization rate was the highest cycle consumption of network was unbalanced. When Num Num of 8. There we set Th to 90% and Num to cycle cycle cycle was 6 and 8, the variance values were close, and the net- 8 and compared the performance of the VGDCA-C and work had a better performance regarding the lifetime and VGDD . average residual energy. According to the analysis of network lifetime, aver- 4.3 Comparison with VGDD age residual energy, and residual energy’s variance, the In this section, we compare the performance of the network had the best performance at Th of 90% and VGDCA-C and VGDD for different numbers of sensor Fig. 11 The variance of residual energy under different system parameters (Th and Num ). When Num was 6 and 8, the variance values were cycle cycle close, and the network had a better performance regarding the lifetime and average residual energy Zhu et al. EURASIP Journal on Wireless Communications and Networking (2018) 2018:134 Page 17 of 20 Fig. 12 The comparison of VGDD and VGDCA-C in network lifetime. It shows that network lifetime of the VGDCA-C was longer that VGDD in our simulation model nodes. The numbers of sensor nodes were 800, 1000, 1200, distributed events, the VGDCA-C could allocate parking 1400, and 1600, respectively, and the time interval of event time dynamically according to the counters of a mobile area change was 1000 s. sink. The mobile sink would park longer time in the virtual grids with more sensory data. This method could reduce 4.3.1 Network lifetime energy consumption and a total length of transmission. As illustrated in Fig. 12, we compared the network life- Meanwhile, two moving belts would switch dynamically time for different numbers of sensor nodes. With the according to the counters of a mobile sink. These counters increase of the number of sensor nodes, the network life- indicated the location of event area, and the moving belts time of the VGDCA-C was always larger than that of switched toward the event area. However, in the VGDD, a the VGDDs. In the application scenarios with centrally mobile sink moved by the predefined trajectory. When the Fig. 13 The comparison of VGDD and VGDCA-C in average residual energy. It indicates that the VGDCA-C could work longer when the same energy was consumed, which further means that the VGDCA-C had higher energy utilization ratio Zhu et al. EURASIP Journal on Wireless Communications and Networking (2018) 2018:134 Page 18 of 20 Fig. 14 The comparison of VGDD and VGDCA-C in a variance of residual energy. The energy consumption balance of the VGDCA-C was slightly better than that of the VGDD event area changed, the mobile sink of the VGDD could 4.3.2 Average residual energy not adjust its trajectory to the event area. Hence, network As mentioned above, the average residual energy indicates lifetime of the VGDCA-C was longer. When the number the energy utilization ratio. As illustrated in Fig. 13,with of sensor nodes increased, the number of source nodes the increase of the number of sensor nodes, the average also increased. Moreover, there was no major fluctuation residual energy of the VGDCA-C was slightly lower than in the network lifetime due to the increase of the number that of the VGDD, which indicates that energy utiliza- of sensor nodes. tion ratio of the VGDCA-C was higher than that of the Fig. 15 The comparison of VGDD and VGDCA-C in an average number of transmission hops. The VGDCA-C decreases transmission hops in the applications with centrally distributed events Zhu et al. EURASIP Journal on Wireless Communications and Networking (2018) 2018:134 Page 19 of 20 VGDD. In Fig. 12, it can be seen that network lifetime and automatically. Afterward, the trajectory planning of of the VGDCA-C was two times greater than that of the a mobile sink is proposed such that the mobile sink can VGDD. However, the average residual energy of VGDCA- move closer to the event area and park in the virtual C was only slightly below than that of the VGDD, which grids longer, which increases the amount of sensory data. indicates that the VGDCA-C could work longer when the Using the proposed algorithm, the total length of rout- same energy was consumed, which further means that the ing paths and the transmission delay are decreased. To VGDCA-C had higher energy utilization ratio. reduce the energy consumption of updating of a mobile sink location, we propose the local updating. Finally, we 4.3.3 Variance of residual energy proposed the re-election of head nodes in the virtual As illustrated in Fig. 14, when the number of sensor nodes grid cells to balance energy consumption. Compared with was 800 and 1600, the variance value of the VGDCA-C the VGDD algorithm, the VGDCA-C algorithm prolongs was slightly larger than that of the VGDD. However, when network lifetime and decreases transmission delay in the the number of sensor nodes was 1000, 1200, and 1400, applications with centrally distributed events. the variance value of the VGDCA-C was slightly lower Abbreviations than that of VGDD. The performances of two algorithms IWSNs: Industrial wireless sensor networks; VGDCA-C: Virtual grid-based regarding the balance of energy consumption ware simi- real-time data collection algorithm for applications with centrally distributed lar. As the network lifetime of the VGDCA-C was larger events; MWST: Minimum Wiener index spanning tree; MST: Minimum spanning tree; RLW: Random line walk; EEGBDD: Energy efficient grid-based data than that of VGDD, the energy consumption balance of dissemination routing mechanism; O-LEACH: Optimizing LEACH clustering the VGDCA-C was slightly better than that of the VGDD. algorithm; RNs: Convergence nodes; VGDRA: Virtual grid-based dynamic routes adjustment scheme; VGDD: Virtual grid-based data dissemination scheme; ID: Identification; RCN: Row column number; DN: Direction number; GS: Grid of 4.3.4 Average number of transmission hops sink; LU: Head node in the upper left corner; RU: Head node in the upper right As illustrated in Fig. 15, when the number of sensor nodes corner; LD: Head node in the lower left corner; RD: Head node in the lower right varied from 800 to 1600, the average number of trans- corner; UG: Head node in the grid above; DG: Head node in the grid below; LG: Head node in the left grid; RG: Head node in the right grid; IG: Intersecting grid mission hops was about 4 hops in the VGDCA-C. The corresponding number of the VGDD was greater than 7. Funding The average number of transmission hops indicated that The work is supported by “the Fundamental Research Funds for the Central Universities, no. 2017B14714”, supported by “the National Natural Science when the VGDCA-C was used, and source node sent data Foundation of China under grant no. 61572172”, and supported by to the mobile sink, the hops of the packet could be reduced “Changzhou Sciences and Technology Program, no. CE-20165023 and no. by 3 hops compared to the VGDD, which was because the CE20160014” and “six talent peaks project in Jiangsu Province, no. XYDXXJ-S-007”. trajectory of a mobile sink was adjusted dynamically and moved toward the event area. Meanwhile, when mobile Availability of data and materials sink allocated the parking time, the sink parked longer in The values of simulation parameters are listed in Table 6. the grids, which processed more sensory data. By con- Authors’ contributions stantly adjusting the movement trajectory and parking CZ, XL, GH, JJ-N, and SZ designed the study, performed the research, analyzed time, mobile sink could get closer to the source nodes, the data, and wrote the paper. All authors read and approved the final and the sensory data could be uploaded to the mobile manuscript. sink faster. However, the mobile sink had a predeter- Authors’ information mined trajectory in the VGDD, so the mobile sink could Chuan Zhu received the Ph.D. degree from the Department of Computer not adjust its moving status according to the changes in Science, Northeastern University, Shenyang, China, in 2009. And in December 2017, he finished his work as a Postdoctoral Researcher with Hohai University. the event area. Thus, the VGDCA-C had better real-time He is currently a Lecturer in the Department of Information and performance than the VGDD. Communication System, Hohai University, China. He has authored over ten papers in related international conferences and journals. His current research interests are sensor networks, cloud computing, and computer networks. 5Conclusions Xiaohan Long is a Master degree candidate of the Department of Internet of In this paper, the algorithm for real-time data collection things and its Application at Hohai University, China. His current research for applications with centrally distributed events, called interests are wireless sensor networks, underwater wireless sensor networks, cloud computing, and Android security software development. the VGDCA-C, is proposed and analyzed. Firstly, a vir- Guanjie Han is currently a Professor in the Department of Information and tual grid virtual gird structure is introduced to initialize Communication System, Hohai University, Changzhou, China. In 2004, he the network. The virtual grid structure can divide the received the Ph.D. degree from Northeastern University, Shenyang, China. From 2004 to 2006, he was a Product Manager for the ZTE Company. In network into several virtual square areas with the same February 2008, he finished his work as a Postdoctoral Researcher in the size, where virtual grids of different areas have differ- Department of Computer Science, Chonnam National University, Gwangju, ent RCN and DN. The structure is the basis of sensory Korea. From October 2010 to 2011, he was a Visiting Research Scholar in the Osaka University, Suita, Japan. He is the author of over 230 papers published in data routing. Then, the routing of sensory data is dis- related international conference proceedings and journals and is the holder of cussed. With the help of a virtual grid structure, the 100 patents. His current research interests include sensor networks, computer sensory data can be routed to the mobile sink easily communications, mobile cloud computing, and multimedia communication Zhu et al. EURASIP Journal on Wireless Communications and Networking (2018) 2018:134 Page 20 of 20 and security. Dr. Han has served as a Co-chair for more than 50 international 16. K Shin, S Kim, Predictive routing for mobile sinks in wireless sensor conferences/workshops and as a Technical Program Committee member of networks: a milestone-based approach. J. Supercomput. 62, 1519–1536 more than 150 conferences. He had been awarded the ComManTel 2014, (2012) ComComAP 2014, Chinacom 2014, and Qshine 2016 Best Paper Awards. He is 17. G Shi, J Zheng, J Yang, Z Zhao, Double-blind data discovery using double amemberofIEEE andACM. cross for large-scale wireless sensor networks with mobile sinks. IEEE Jinfang Jiang is currently a Lecturer in the Department of Information and Trans. Vehicular Technol. 61, 2294–2304 (2012) Communication System at Hohai University, China. She received her Ph.D 18. P Singh, R Kumar, V Kumar, An energy efficient grid based data degree in Information and Communication Engineering from Hohai dissemination routing mechanism to mobile sinks in Wireless Sensor University, China, in 2015. Her current research interests are security and Network, International Conference on Issues and Challenges in Intelligent localization for sensor networks. Computing Techniques, 401–409 (2014) Sai Zhang received the Master degree from the Department of Information 19. C Tunca, M Dönmez, S Isik, C Ersoy, Ring routing: an energy-efficient and Communication System at Hohai University, China, 2017. He has routing protocol for wireless sensor networks with a mobile sink. IEEE published 1 paper in related international conferences and journals. He is Trans. Mobile Comput. 14, 1947–1960 (2015) working at Huawei Technologies Co., Ltd. currently. 20. N Wang, Y Chiang, Power-aware data dissemination protocol for grid based wireless sensor networks with mobile sinks. 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EURASIP Journal on Wireless Communications and Networking – Springer Journals
Published: May 29, 2018
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