Hybrid Rendezvous Clustering Model for Efficient Data Collection in Multi Sink Based Wireless Sensor Networks

Mobile sink based data collection has comparatively lower energy consumption compared to multi hop forwarding in wireless sensor networks. Energy efficiency is achieved by minimizing the hop count to sink in mobile sink based approaches. These approaches are of two types: Mobile sink collect stored data at rendezvous nodes or cluster heads forwarding data to mobile sink without storage by using its maximum transmission range. First approach provides higher energy gain at cost of delay. Second approach provides lower delay at cost of additional energy consumption. This work combines both the approaches with rendezvous node deciding to store or forward based on prediction of trajectory of multiple mobile sinks and packet latency deadlines.


Introduction
Wireless sensor network (WSN) is a network of sensor connected with a wireless infrastructure. In typical WSN, the sensor node senses various parameters and propagates it via multi hop to sink. This approach consumes higher energy. The nodes near to sink drains out of energy soon compared to other nodes and this reduces the life time of the WSN [1]. Among many approaches for optimizing the energy consumption in WSN, mobile sink provides considerably lower energy consumption [2]. Sink moves across the network to collect data. Mobile sink based approaches are of two categories: rendezvous [3] or cluster based [4]. In rendezvous based approach, a suitable sensor nodes are selected close to the mobile sink trajectory path. Sensor nodes nearby send their data to rendezvous node. The rendezvous node stores the data till sink arrives to collect the data. The energy consumption is lower compared to multi hop transmission in this approach at cost of delay in data collection. In clustering based approach, the network is clustered with cluster head selection based on energy distribution and mobile sink position. The cluster members send their data to cluster head, where the data is aggregated and forwarded to sink without storage. Since storage is avoided, delay is less but at the cost of higher energy consumption depending on position of the sink node. Rendezvous approach is more suited for longevity based applications. Cluster based approach is more suited for delay sensitive applications. The delay in rendezvous based approach and energy consumption in cluster based approach can still be minimized with use of multiple sinks for data collection.
This work proposes a hybrid rendezvous clustering model combining both rendezvous based and cluster based approach with multiple sinks to minimize both the energy consumption and delay. The solution is based on clustering topology. The cluster head selection is based on multiple criteria of node density, residual energy of nodes and proximity to sink trajectory. The decision to store or forward at cluster head is made based on the packet latency deadlines and prediction of sink arrival times. The solution tries to minimize the times of maximum distance forwarding at sink exploiting the packet latency and sink arrival predictions. Following are the contributions of the proposed solution.
1. A hybrid rendezvous clustering model combining both rendezvous and clustering based data collection with multiple sinks. 2. A novel path planning for multiple sinks by solving it as K-dominating set problem 3. Cluster head selection based on multi parameters of node density, residual energy and proximity to sink trajectory. 4. Decision at cluster head to use store or forward mode depending on the packet latency requirements and sink arrival predictions.
The rest of the paper is organized as follows. The survey on rendezvous and cluster based approaches are presented in Sect. 2. Section 3 presents the proposed hybrid rendezvous clustering model. The performance of the proposed model in terms of energy efficiency and delay is measured and compared to state of art existing works in Sect. 4. The conclusion remarks and future work scope are presented in Sect. 5.

Related Work
The survey is conducted in two categories of rendezvous and cluster based approaches.

Rendezvous Based Approaches
Wang et al. [7] proposed a rendezvous point (RP) based data collection algorithm. A spanning tree is constructed connecting all sensor nodes. RP node is selected on the spanning tree based on hop distance and amount of forwarding data from sensors. The path for sink is fine tuned to visit the RP in lesser time, so that the storage cache in RP does not overflow. The path needs to be frequently changed due to sensing rate of sensors and this creates higher packet loss. Fu et al. [9] proposed a energy balanced data collection scheme. The nodes are clustered and a RP is selected at center of each cluster. Using particle swarm optimization, the path for mobile sink connecting the RP is found.
Nodes in cluster send their data to RP and sink collects data from the RP. Re-clustering in form of splitting or merging is done to re-balance the energy. But the method creates buffer overflows at RP for larger network. Yarinezhad et al. [10] proposed a RP based scheme, in which RP only stores the information about the sink position. The nodes nearby to RP collect the sink position and decide to forward data to sink when it arrives in its transmission range. Though this approach reduces the energy consumption in advertising sink position to each node, it incurs additional delay for large networks with single mobile sink as node can send data to sink only when it is its transmission range. Zhang et al. [11] proposed a RP based data collection scheme. Optimal RP are selected and sensors send their data to RP via multi hop routing. An efficient spanning tree path connecting the RP is found using PSO algorithm with objectives of minimizing tree height. Mobile sinks travels along this path to collect data from RP nodes. The same RP node being part of data collection makes the RP node to drain out of energy soon. Wang et al. [12] clustered the sensor network and selected the node with maximal residual energy as cluster heads. Cluster heads are selected as RP. The mobile sink traverses in a path to collect data from cluster heads. The path for traversal is found using improved ant colony optimization algorithm. Cluster heads distance to path changes over time due to shift in CH role but path not adjusting to it. Due to this energy consumption is increased after certain period of time in this solution. Gharaei et al. [14] proposed a solution for energy efficient data gathering using two mobile sinks. A circular network model is splut to many sectors. Two sinks travel in a spiral path. Sink positions itself in sector for a certain period of time depending on the density of nodes to collect the data before it goes to next sector. Though the approach is energy efficient the delay for data collection is very high. Najjar et al. [15] proposed a energy efficient data gathering solution for WSN using mobile sink. The network is clustered using combined agglomerative clustering and ant colony optimization. In every round, the cluster is updated using genetic algorithm. Mobile sink travels along the cluster to collect data. The solution is able to ensure fair consumption of energy in clusters but it could not avoid delay in data collection. Wen et al. [16] proposed an algorithm to construct a energy aware path connecting a set of data collection points for mobile sink traversal. The path links are established based on the forwarding load of the sensor node. Konstantopoulos et al. [17] proposed a solution for reducing data collection delay in rendezvous based approach using multiple mobile sinks. The data gathering structure connecting mobile elements to the RP is created every time based on energy distribution change in the network. The approach has many overlapping paths which if avoided could result in lesser delay. Raj et al. [18] proposed a energy effective data collection technique combining game theory and enhanced ant colony optimization. Game theory is used to select the best set of RP. The best path between RP based on forwarding load at RP is found using enhanced ant colony optimization. The solution lacks policy for rotation of RP role due to which energy drains near RP. Chowdary et al. [19] proposed a multi criteria fitness function to select the cluster heads for RP. Mobile sinks travel around CH to collect in a single hop distance to CH. But delay is higher in the solution due to larger path length for sink traversal. Kumar et al. [20] proposed a new ant colony optimization algorithm to select the optimal RP in the sensor network and path though RP for data collection. The proposed algorithm also reselects RP after a period of time to balance the energy consumption. Thomas et al. [21] proposed a mobile sink travel path by solving as travelling salesman problem. The travel path is in terms of chords with alternating links. Sink stays in chord for variable times depending the data rate to be collected.

Cluster Based Approaches
Wei et al. [5] proposed a cluster based energy optimization algorithm with single mobile sink. The LEECH clustering algorithm is extended to select cluster head based on adaptive adjustment of energy density function and motion performance function. The energy density function scores the nodes based on node density and residual energy of the nodes. The motion performance function scores the nodes based on location of mobile nodes. Combining these two scores in a weighted manner, an adaptive score is created for each node. Instead of random cluster head selection in LEECH, nodes are selected based on this adaptive score. But this approach works only for small networks and not scalable for large networks. Toor et al. [6] proposed a Mobile Energy Aware Cluster Based Multi-hop routing protocol. The network is clustered with nodes having highest residual energy is selected as cluster heads. The network is further divided to sectors and a mobile data node collects data from cluster heads ithin that sector. But the approach does not consider the packet latency deadlines during forwarding from cluster heads. This incurs additional energy consumption. Wang et al. [8] divided the network into sectors of equal size and a cluster head is selected for each sector. A chain is created among the cluster heads. Mobile sink moves in circular pattern and announce its angular velocity prior to cluster head. The cluster head arrange their chain to forward data mobile sink. For a larger network, the hop count from peripheral region to central region of sector is high and this incurs high energy consumption for intra cluster routing. Wang et al. [13] selected the nodes close the mobile sink are selected as forwarder for the packets. Though this approach is able to reduce the hot spot problem, it could not mitigate it. Without information of mobile sink trajectory, best forwarders were not selected and this increased the energy consumption in this approach. Krishnan et al. [22] proposed a dynamic clustering and optimal routing mechanism for data collection. The dynamic clustering approach finds the most suitable cluster head to avoid hot spot problem. The most effective path with low latency connecting the CH is found using ant colony optimization algorithm. Bencan et al. (2020) used evolutionary game theory to select the next place of visit for the sink node. A utility function is designed based on average energy of the cluster, inter cluster and intra cluster energy consumption. The location with highest utility value is selected as position for sink. Cluster heads sends data directly to the new position of sink without storage. The method is not scalable for larger networks.
From the survey, it could be seen that rendezvous based approaches perform well in terms of energy conservation, since they store the data till sink arrives to pick it up. But they introduce a higher delay and this becomes intolerable for packet with strict deadline time. Cluster head approaches have higher energy consumption compared to rendezvous due to their decision to forward without storing the data. But they are able to reduce the delay. If the store or not decision is made dynamic based on the delivery deadline and mobile sink trajectory, the energy consumption can be reduced and at time delivery deadlines can be met. If the path of mobile sinks can be planned based on clusters, energy consumption and delivery deadline can be further improved. The proposed solution is based on this observation.

Hybrid Rendezvous Clustering Model
The proposed hybrid rendezvous clustering model integrates the rendezvous and clustering based data collection with multiple mobile sinks. The network layout of the proposed solution is given in Fig. 1.
In the figure, sensor nodes are clustered based on density. For each cluster, a point close to center of cluster is selected as strategic points. From the strategic points, Steiner points optimally connecting the strategic points are found applying graph theory. These Steiner points are grouped based on minimization of delay using particle swarm optimization (PSO) algorithm. For each group of Steiner points, a mobile sink is allocated for data collection. Each mobile sink allocated to group visits the strategic points within group in shortest path to collect the data. A decision is made by cluster head to wait till mobile sink visit nearby to collect data or Group 1

Cluster Head
Normal Node Mobile SInk Steiner point Fig. 1 Proposed network topology forward the packet in multi hop manner to the mobile sink. Each mobile sink forwards the collected data to a single collection point for data processing (Fig. 2).
The hybrid solution is scalable and it works with goal of energy consumption minimization and same time meet up the delivery deadlines for critical packets by reducing the delay for them. The proposed solution has following important stages: (i) Clustering the network, (ii) selecting the Steiner points, (iii) Grouping the Steiner points and (iv) Mobile sink data collection. Each of the stages are detailed below.

Clustering the Network
LEECH clustering is used for clustering the sensor network with threshold (T) selection for sensor nodes based on desired percentage of cluster heads, node density and residual energy ratio. It is calculated as w 1 , w 2 , w 3 are the weights of importance given to desired percentage of cluster heads, node density and residual energy ratio. The values are allocated in such a way that The desired percentage of cluster heads ( P CH ) is calculated as where N CH is the number of cluster head desired out of total M sensor nodes.
The node density ( N d ) is calculated as where N num is the number of one hop neighbors of the node. The residual energy ratio ( E RR ) is calculated as

Fig. 2 Steiner point selection
where E R is the current residual energy at node and E T is the initial energy available at the node. The T value is calculated at every round for all the nodes. For a node which is not selected as cluster head in previous round, if its random variable R is above T , the node is selected as cluster head. The other nodes associate to the cluster head which is geographically closer to it.

Selecting the Steiner Points
The location which is close to all the nodes is the cluster is selected as the strategic points. Each node in the cluster advertises its location (x, y) to all other nodes. From it the extreme west (A.x, A.y) , east (B.x, B.y) , north (C.x, C.y) and south (D.x, D.y) are known. The cluster head calculates the strategic point (X s , Y s ) by calculating the intersection of line connecting AB and CD . It is calculated as Once all the strategic points are found, the Steiner minimal tree is constructed with Graph Iterated 1-Steiner (GI1S) algorithm with KMP heuristics [25]. Given a set P on n strategic points, Steiner minimal tree is constructed with S Steiner points in a way that minimum spanning tree (MST) cost over P ∪ S is minimized. A weighted graph is constructed with P strategic points as vertices and the Euclidean distance between the points as edge weight.
The output of GI1S algorithm is the Steiner points connecting all the N strategic points with minimal path length. An example of Steiner points and path through Steiner points for a sample network deployment returned by GI1S algorithm is given below.
The S Steiner points are selected by the GI1S algorithm in such a way that

Grouping the Steiner Points
The strategic points must be grouped into K groups where K is the number of mobile sinks. The strategic points must be grouped in such a way, that delay is minimized and coverage of points must be increased. When coverage increased delay increases. So an optimum coverage bound by delay must be selected. Since this is a combinational explosion problem which increases with size of the network, heuristics search is needed. This work uses PSO to find the optimum groups of strategic points.
PSO is a swarm intelligence algorithm simulating the social behavior of swarm of organisms. This method is popular for solving optimization problems due it its simplicity, flexibility and versatility. Organisms move randomly with different velocities and use these velocities to update their individual position. Each candidate solution is a 'particle'. Each particle tries to attain its best velocity based on its own local best ( p best ) value and its neighbor's global best ( g best ). Each particle's next position depends on the current position, current velocity, distance from current position to p best , distance from current position to g best . The movement of particle in its search space depends on its velocity. For a particle X, it current position X i and current velocity V i is updated as In the above equations, t is the iterative value. c 1 and c 2 are acceleration coefficients,. r 1 and r 2 are random numbers, w is the inertia weight. The iteration is repeated till termination condition is met.
In this work, each particle is K (number of mobile sink) S bit binary string with each position representing a Steiner point. The value is 1 when Steiner point is part of the group and 0 when Steiner point is not part of the group. The fitness function is calculated as minimization of delay traversing the points in the group and the maximization of coverage (number of Steiner point in the group). The fitness function is given as where | | G i | | is the number of Steiner points marked as 1 in the group G i and SP(G i ) is the length of the shortest path connecting all Steiner points marked as present in the group G i .
The pseudo code of the algorithm for selection of optimum groups is given below.
Once the Steiner points are grouped to K groups, one mobile sink is allocated to each group for data collection in that group.

Mobile Sink Data Collection
The mobile sink allocated to group visits each of Steiner points in the group. The path for visiting the Steiner points is found by calculating a shortest path using Dijikstra shortest path algorithm. The mobile sink each Steiner point in the shortest path order. At every point, it stops temporarily and sends a hello broadcast. On receiving the hello message, Cluster head sends the cached packets to mobile sink.
The sensor nodes send the data to the cluster head. The cluster head decides to forward the packet immediately or cache it till sink arrival based on delivery deadline of the packet. Packets without delivery deadline are cached and sent to sink on receiving hello broadcast. When packets are marked for deadline delivery they are broadcasted in the network. Any node near the Steiner point rebroadcasts the packet. Once the node broadcasts the packet, it never rebroadcasts the same packet. Through broadcasting, the sink receives the deadline marked packet.

Results
The proposed solution was simulated in NS2 with following simulation configuration parameters.
The performance of the proposed solution was compared against mobile sink based data collection. approach proposed by Chen et al. [2], clustering based data collection with mobile sink proposed by Wei et al. [5] and ant colony optimized data gathering proposed by Raj et al. [18].
The average energy at nodes is measured at end of simulation and the result is given in Fig. 3 The average packet delay is measured for different number of nodes and the result is given in Fig. 5 (Table 1). This is done by grouping Steiner points and allocating mobile sink for each group. While existing solutions have longer path for sink traversal due to which delay for packet delivery in higher in those solutions.
Life time is varied by changing the number of sinks and the result in given in Table 2. The average value calculated from Table 2 is plotted in Fig. 6. From the results, it can be seen the proposed solution is able to increase the life time faster for increase in number of mobile sink compared to existing works. This is because, as mobile sink increases more small groups can be created in proposed solution. This reduces the packet traversal length for sink, so life time is increases.

Conclusion
In this work, a hybrid rendezvous clustering model is proposed for efficient data collection using mobile sinks. The method proposed in this work is able to reduce the energy consumption at same time reduce the delay for deadline marked packets. Path for data  collection for each mobile sink is decided based on the locating strategic points for data collection and establishing a efficient path covering the strategic points using graph theory concepts. The proposed solution is able to increase the life time of network by atleast 26.47% and reduce the average latency for packet delivery by atleast 6% compared to existing works.  Funding The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

Data Availability
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Code Availability
The code is available with corresponding Author.