An Adaptive Data Gathering Algorithm for Minimum Travel Route Planning in WSNs Based on Rendezvous Points

Abstract

A recent trend in wireless sensor network (WSN) research is the deployment of a mobile element (ME) for transporting data from sensor nodes to the base station (BS). This helps to achieve significant energy savings as it minimizes the communications required among nodes. However, a major problem is the large data gathering latency. To address this issue, the ME (i.e., vehicle) should visit certain rendezvous points (i.e., nodes) to collect data before it returns to the BS to minimize the data gathering latency. In view of this, we propose a rendezvous-based approach where some certain nodes serve as rendezvous points (RPs). The RPs gather data using data compression techniques from nearby sources (i.e., affiliated nodes) and transfer them to a mobile element when the ME traverses their paths. This minimizes the number of nodes to be visited, thereby reducing data gathering latency. Furthermore, we propose a minimal constrained rendezvous point (MCRP) algorithm, which ensures the aggregated data are relayed to the RPs based on three constraints: (i) bounded relay hop, (ii) the number of affiliation nodes, and (iii) location of the RP. The algorithm is designed to consider the ME’s tour length and the shortest path tree (SPT) jointly. The effectiveness of the algorithm is validated through extensive simulations against four existing algorithms. Results show that the MCRP algorithm outperforms the compared schemes in terms of the ME’s tour length, data gathering latency, and the number of rendezvous nodes. MCRP exhibits a relatively close performance to other algorithms with respect to power algorithms.

1. Introduction

In recent decades, the wireless sensor network (WSN) has positioned itself as one of the revolutionary network technologies that will positively impact the quality of human life. This is mainly due to the enormous benefits of WSN that span across many fields. WSN has become an integral part of human civilization. It has applications in disaster relief operations [1], biodiversity mapping [2], intelligent buildings or bridges [3], precision agriculture [4,5], earthquake early warning [6], medicine and health care [7], logistics [8], landscape services [9], route planing [10], and so on. To design and deploy WSNs effectively, it is important to address certain issues relating to a feasible node deployment, routing, energy consumption, and data gathering latency.

All the aforementioned issues arise because multi-hop (i.e., static) routing is required to relay data to the final destination. In such a static scheme, data packets are forwarded to the base station (BS) via multi-hop routing [11,12,13,14,15,16,17,18,19,20,21]. Strategies aimed at achieving energy balancing, load balancing, wake-up scheduling, and cluster-based routing have been studied to achieve an improved network performance. It is obvious that a substantial amount of energy is required to relay data in static data gathering schemes, which is a major drawback of these schemes.

Recent research has shown a rapid shift from the traditional static data gathering pattern to the introduction of mobile elements (MEs), which are capable of improving network connectivity and energy consumption. The introduction of MEs achieves significant energy saving in WSN as they minimize communications among nodes [22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44]. However, a typical ME has a velocity of 0.1–2 m/s [45], which might not be sufficient to achieve an effective network performance using this scheme. This makes it imperative that the ME should only visit certain nodes to overcome this limitation. This is premised on the fact that increasing the number of nodes the ME visits will increase the tour length, ultimately leading to a higher latency performance. Solving this problem is one of the key objectives of this paper. A typical illustration of common data gathering approaches is given in Figure 1.

In a nutshell, this paper contributes the following: (1) It presents a definition of the mobile data gathering problem with the consideration of rendezvous nodes. (2) It develops an efficient algorithm to solve the aforementioned mobile data gathering problem. (3) It presents a validation, testing, and comparison of the proposed algorithm with four existing algorithms through extensive simulations.

The rest of this paper is organized as follows: Related work is reviewed in Section 2. The basic preliminaries pertaining to the proposed scheme and the drawbacks of prior works are explained in Section 3. The proposed algorithm is presented in Section 4, while simulation results and discussions are detailed in Section 5. Section 6 concludes the paper and highlights future works.

2. Related Work

In this section, the recent works on mobile data gathering are extensively discussed and analyzed. Additionally, the proposed algorithm is positioned with respect to the state-of-the-art in this area.

Many research efforts have been made to explore ME-based data gathering approaches in WSNs [22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44]. Generally, these approaches can be grouped into two categories, namely uncontrollable and controllable [46]. In the former, sensor nodes are attached to an animal agent, as illustrated in [22]. This results in a higher latency without any guarantee of successful data delivery since there is a possibility of losing the mobile agent. The latter (controllable approach) is achieved by adding one or more mobile entities (i.e., mobile data collectors) to the network.

As noted earlier, an obvious bottleneck is the high latency incurred during data collection because the mobile elements travel with a significantly low velocity. There are three approaches by which this problem can be addressed. The first approach is deploying a single-hop scheme for data gathering. Using this stratagem, the ME visits the vicinity of each node or group of nodes and pulls their data from the respective sensors without involving a relay. In line with this, the authors in [22] proposed a three-tier architecture for data gathering. In the proposed architecture, an animal or vehicle is deployed as a mobile agent. The mobile agent retrieves data from the sensors by traversing the monitored area in a random fashion. However, this scheme is susceptible to higher data gathering latency and low data delivery. This is because such uncontrolled mobility increases the probability of losing the mobile agent and eventually leads to data loss.

The authors in [23] proposed a joint solution that consists of a mobile element at the routing layer and the space-division multiple access (SDMA) technique at the medium access control (MAC) layer. In this solution, the ME can upload data from two sensors simultaneously in a single hop using SDMA. This solution assumes that the ME is equipped with two antennas. However, the ME still visits each sensor node, which dramatically leads to increasing the tour length. Another approach was proposed in [24] where the authors applied multiple MEs to pull data from all sensors at every t seconds to avoid data overflow. Nonetheless, this approach requires utilizing several mobile nodes, which is not cost effective. The approach in [25] divides the deployment field into sub-regions and assigns an ME to each sub-region. Using this scheme, the length of the data gathering tour reduces, and data are uploaded via a single-hop only.

The authors in [35] proposed a mobile agent (MA)-based approach, which employs two algorithms: single-agent itinerary planning (SIP) and multi-ma itinerary planning (MIP). This approach is based on agent spawning. In other words, the main MA can spawn other MAs with different tasks. Another approach considered a multi-mobile element to reduce the data gathering latency, as proposed in [41]. The authors in [29] investigated the use of multiple mobile elements (called data mules). In particular, they proposed a load balancing algorithm that tries to balance the number of sensor nodes associated with each ME. Note that the approaches that pull data from sensors via a single-hop result in a higher data gathering latency, particularly in large-scale sensor networks.

To overcome this problem, the second class of mobile data gathering schemes aggregates the collected data and sends them via a multi-hop relay. These nodes represent a fraction of the total number of nodes and are responsible for aggregating data from respective sensors before delivering them to the ME. As such, the ME visits those nodes before it eventually returns to the BS. The authors in [30] presented a rendezvous-based data collection scheme. In this proposal, a restricted tour length was applied (i.e., the tour length should not be longer than L meters), and the mobile BS collected data from the rendezvous nodes in a single-hop fashion. These nodes act as a temporary BS. This approach minimizes the data gathering latency since it restricts the tour length to L.

Along the same line, the authors in [28] proposed a planned tour path for the ME. This was achieved by deploying the position of certain nodes as turning points. The turning points were selected adaptively while also avoiding obstacles. This adaptive selection highly depended on the sensor nodes’ distribution. The sensors sent their data packets via a multi-hop route in the course of the mobile element’s traversal. In order words, the data pass through multiple nodes before reaching the respective mobile element (i.e., without any constraints on the number of relays required).

Wu et al. [32] studied a scenario with poor network connectivity consisting of spatially-separated sub-networks. In this context, they proposed the use of a mobile mule, for visiting all the sub-networks. The mule collects data from specific nodes (also called landing nodes). This way, the tour path is minimized. Within each sub-network, data are aggregated through an unbounded multi-hop path. The authors in [43] proposed the use of a mobile sink for data collection. The mobile sink changes its position continuously, which eliminates the problem of unbalanced energy consumption due to energy holes. The change is triggered when the energy level of the nearby sensors becomes low. In addition, a new location is selected considering the position of candidate sensors in proximity.

Vupputuri et al. [33] proposed a heterogeneous network consisting of high-density stationary sensor nodes, a few number data collectors (DCs), and a stationary BS. A uniform deployment of sensor nodes was considered, and the DCs were mobile. Note that in this case, their mobility was controlled. The DCs collect the data from nearby sensors in a multi-hop fashion and communicate with one another to send the data to the respective BS. Each DC changes its location in such a way that the load (i.e., forwarded data) is balanced and distributed among sensor nodes. The authors in [31,38,39,40] proposed a new model of mobile data collection that reduces data latency. This was achieved by combining the use of mobile data collectors and clustering.

Lai et al. [36] proposed an adaptive data-gathering technique in a mobile sensor network by using a speedy mobile element. The speedy mobile element collects the data from certain (proxy) nodes, which gather data temporarily from nearby movement nodes. Although these approaches effectively shorten the tour length of mobile elements, they are not constrained to a finite number of hops, which increases the amount of power consumed as a result of multiple packet forwarding.

The third category of mobile data gathering techniques aggregates data at selected nodes with a bounded number of relay hops. In this respect, the authors in [26] proposed a data-gathering scheme where data packets traverse a bounded multi-hop route to reach their respective polling points where the data from affiliated sensors are aggregated. The mobile data collector traverses these points to pull the aggregated data using short-range communication before it eventually returns to the BS. The k-hop relay scheme was proposed in [34]. In this scheme, the number of hops over which the data packet would be relayed is also bounded. The value of k maps to a trade-off between energy consumption and data gathering latency. Note that this is application dependent. A major drawback of this scheme is that it consumes a significant amount of energy as control messages are flooded to all nearby sensors and other sensors.

A tree-cluster-based data gathering algorithm (TCBDGA) was proposed by the authors in [42] for WSNs having a mobile sink. They deployed the root nodes of the trees as rendezvous points (RPs). Additionally, sub-rendezvous points (SRPs), which are special points, are selected based on their traffic load and the number of hops to root nodes. An efficient rendezvous-based mobile data gathering protocol was proposed in [27] for WSNs. In the proposed scheme, the aggregated data are relayed to the rendezvous node (RN) within a bounded number of hops, d. The protocol jointly considers MC tour and data routing routes in aggregation trees. Our proposed work falls into this category.

3. Preliminaries

This section presents an overview of the proposed algorithm. Furthermore, the mechanisms and assumptions used in this article are described. The assumptions used in this work are as follows:

• A total of Nsensor nodes is uniformly distributed over the specified area. Each node can be uniquely identified (i.e., it has a unique identity and location information). Furthermore, all the initial energy of sensor nodes is homogeneous. The sensor nodes are powered by a finite energy source.
• The BS is static, and it is located at the center of the deployment field.
• An ME collects data by visiting certain nodes before it eventually returns to the BS.

3.1. Network Model

Using the aforementioned assumptions, the shortest path tree is formed at the first stage based on hop count. An undirected graph $G(V,E)$ is used to represent the sensor network, where V = $\{v_1,v_2,v_3,v_4,\cdots ,v_n\}$ denotes the sensor nodes in the network. The bidirectional wireless links among nodes are represented as E$(i,j)$, and a link is denoted by $e(i,j)\in E$, where:

$$\begin{array}{ccc}\hfill e(i,j)& =\left\{\begin{array}{cc}d(v_i,v_j),\hfill & \mathrm{if}d(v_i,v_j)\le \mathrm{Tr}\hfill \\ Infinity,\hfill & \mathrm{Otherwise}\hfill \end{array}\right.\hfill & \hfill \end{array}$$

Before the ME embarks on data gathering, certain nodes are selected for local data aggregation. These nodes, called rendezvous points (RPs), gather the data from affiliated sensors. An ME moving through the deployment field stops at each RP to pull its data via a single hop. The ME collects the aggregated data when it arrives at a selected RP. Then, it moves straight to the next selected RP on the tour. Thus, the ME’s tour consists of a number of selected RPs and the straight line segments connecting them.

Now, let $R=\{r_1,r_2,r_3,\cdots ,r_n\}$ represent a set of RPs and BS represent the base station. Then, a typical ME’s tour can be represented as $(BS\to r_1\to r_2\to r_3\to BS)$. Therefore, the solution to the mobile data gathering problem can be achieved when the following sub-problems are jointly solved: (1) selection of the appropriate RPs and (2) determining the order for visiting them.

Applying the proposed minimal constrained rendezvous point (MCRP) algorithm for the data gathering technique in WSNs achieves the following: First, it minimizes the number of selected RPs. Second, it shortens the tour length of the ME since a limited number of nodes are visited. This reduces data gathering latency. Below, we formulate the mobile data gathering problem in WSNs.

Given a set of sensors S, relay hop bound d, and threshold $th$, the sub-problems are as follows:

• A subset of S, denoted by $R(R\subseteq S)$, represents the rendezvous nodes.
• A set of geometric trees is rooted in each rendezvous node $\left\{T_i(V_i,E_i)\right\}$. The maximum depth of each geometric tree is constrained by d and $th$.
• The ME tour path U visits each rendezvous node and the BS. The tour path should be shortened to minimize the data gathering latency.

From the above discussion and sub-problems, the RPs, hop constraints, threshold, and the position of the RP should be jointly considered to determine the optimal solution. Therefore, the mobile data gathering problem is formulated as follows:

$$\begin{array}{cc}\hfill \mathit{Minimize}\sum _{u,v\in U,u\ne v}{d}_{uv}& \hfill \end{array}$$

(1)

Subject to:

$$\begin{array}{ccc}\hfill C_{s_i,r_i}=1& ,\forall s_i\in S,\forall r_i\in R\hfill & \hfill \end{array}$$

(2)

$$\begin{array}{ccc}\hfill \sum _{r_i\in R}{C}_{s_i,r_i}& =1,\forall s_i\in S,0\le h\le d\hfill & \hfill \end{array}$$

(3)

$$\begin{array}{ccc}\hfill s_i,r_i\le s_i& ,r_j,\forall s_i\in S,\forall r_i\in R,r_i\ne r_j\hfill & \hfill \end{array}$$

(4)

For nodes $r,v\in V$ in G, if there exists a path from v to r, r covers v. A node v is $d-hop$ covered by r if the length of this path is shorter than d, written as $c_{v,r}^d$. A set of sensors covered by r indicates that an aggregation tree is produced, which is rooted at r. The $d-hop$ cover assures that the rendezvous node r can receive any packet from the source within d hops.

Theorem 1.

The MCRP problem is an NP-hard problem.

Proof. 

This problem can be proven to be NP-hard by looking into the polynomial-time reduction from the Euclidean traveling salesman problem (TSP). A special case of MCRP is when the transmission range is set to a minimum level. Thus, each node in the deployment field cannot communicate with other nodes that are too far away and beyond its reach. In such a case, there is no relay hop d (i.e., $d=0$). In order words, the mobile element should visit each sensor node (i.e., rendezvous point) to gather data individually. This clearly shows that the MCRP problem is an NP-hard problem. □

3.2. Limitations of Previous Work

In this section, the limitations of the previous works are presented. As discussed earlier, the number of polling nodes has a direct impact on the final tour path of the ME. Thus, minimizing the number of polling nodes minimizes the total tour length. In shortest path tree (SPT)-DGA, MDG-NL, ZDG-MME, and the load priority-based RN determination algorithm (LP-RDA), the polling nodes are selected based on a bounded number of relay hops, which leads to the following problems:

• Some polling nodes may reach only a few sensors since the sensor nodes are randomly deployed.
• The affiliation nodes may be closer to the BS than the polling nodes.

To clearly illustrate these problems, Figure 2 depicts fifty sensor nodes randomly distributed within a specified area with the BS located at the center. Nine nodes were selected as polling nodes. Node Number 2 was selected as a polling node, even though it only had two affiliation nodes; whereas, the location of Node 49 was closer to the BS as compared to that of Node 2. This occurred because the number of relay hops played a significant role in determining the polling node. Consequently, the ME visited Node Number 2, which pulled its aggregated data from two sensors only, and it was the farthest within the group. This scenario lengthened the ME’s tour path and lead to a corresponding increase in data gathering latency. In the same vein, Node Number 29 was closer to the BS in comparison to the polling Node Number 14.

4. The Proposed MCRP Algorithm

The MCRP algorithm in this paper was designed to overcome the limitations stated in the previous section. The proposed algorithm was thus designed to achieve a lower data gathering latency. The algorithm minimized the number of rendezvous nodes (i.e., polling nodes) selected as pause locations for the mobile data collector and ensured their locations were the closest to the BS.

The proposed algorithm effectively shortened the tour length of the ME by considering two factors during the selection of rendezvous nodes. The first was the proximity to the BS, and the other was the number of rendezvous nodes. In this case, the number of rendezvous nodes would be minimized. The pseudocode of the proposed MCRP algorithm is given in Algorithm 1. MCRP considered two constraints for selecting a sensor node as a pause location for the ME. First, the number of sensors affiliated with the ME should be greater than a threshold. This constraint would ensure that the ME visited an area having a reasonably large group of nodes. Second, since the location of the rendezvous node had a direct impact on the tour length of ME, the algorithm ensured that the selected node was closest to the BS as compared to other nodes that belonged to the same group (i.e., geometric tree). Both constraints are clearly depicted in the algorithm (Lines 6–27). The threshold was selected based on Equation (5), and it changed depending on the relay hop bound to ensure a sufficient number of affiliation sensors.

$$\mathit{Threshold}=(2\times hopBound)+1$$

(5)

Algorithm 1: Minimal constraint rendezvous node (MCRP) algorithm.

Figure 3a,b and Figure 4a,b illustrate the process of building the SPT until the sensed data are gathered by the ME. Thirty-three sensor nodes were uniformly distributed over the specified area, while the BS was located at the center of the deployment field.

Figure 3a illustrates the process of building SPT based on the minimum hop count to the BS (i.e., the tree root). Figure 3b illustrates two types of polling nodes: the RP and the potential RP. A potential RP is selected using the bounded relay hop strategy [26,44]. In this example, the relay hop is bounded to two hops, while the RP is selected based on the proposed algorithm. The MCRP algorithm selects the RPs, while considering three constraints, i.e., bounded relay hop, number of affiliation sensors, and the distance between RP and the BS. The farthest leaf is searched using the proposed algorithm. In this case, the farthest leaf is Node 32, which is five hops away from the BS. Then, the algorithm moves two-hops upwards to Node 29. At this stage, Node 29 will be selected as the potential RP. Afterward, the algorithm calculates the number of affiliation sensors before the final decision is made. Now, if the number of affiliation sensors is greater than a threshold, the algorithm marks this node as the RP. In contrast, if the number of affiliation sensors is less than or equal to the threshold, the algorithm moves up the tree one hop to Node 18, which it considers as the RP. Along with the RP, all the nodes affiliated with Node 18 are removed from the main tree. The process is repeated until it removes all nodes from the main tree and affiliates them with one of the RPs or the BS (the BS is considered a special RP).

Figure 4a illustrates the tour path of the ME that visits the locations of the RP and the potential RP selected based on the criteria given in the base work. Including the BS, nine nodes are selected as pausing locations (i.e., stopover points) for the ME. Figure 4b illustrates the tour path of ME based on the proposed algorithm. Five nodes (including the BS) are selected as RPs. A fewer number of pausing locations has a direct impact on the total tour length, which consequently affects data gathering latency.

5. Performance Evaluation

The performance analysis of the MCRP algorithm is examined in this section. To evaluate the performance of the proposed MCRP algorithm, we conducted extensive simulation experiments in a dense network while considering different network scenarios using the simulation proposed in [47]. The MCRP was compared against four algorithms (SPT-DGA [26], MDG-NL [44], ZDG-MME [48], and the load priority-based RN determination algorithm (LP-RDA) [27]) in terms of average RP, mobile tour length, and total energy consumption. These algorithms were selected because they fall into the same class as the proposed MCRP algorithm. In particular, in these algorithms, the aggregated data are relayed to the RP via a bounded number of relay hops. LP-RDA always selects the node with the maximum load from the d-hopneighbors of the farthest node from the BS. Furthermore, these algorithms can minimize tour length/power consumption depending on the studied scenario. The comparison of these algorithms is illustrated in

Table 1. Comparison among the respective algorithms. DGA, data gathering algorithm; LP-RDA, load priority-based RN determination algorithm.

	MDG-NL	ZDG-MME	SPT-DGA	LP-RDA	MCRP
Main Objective	To minimize the tour length	To minimize the tour length	To minimize the tour length	To minimize the tour length	tour length tour length
Technique	Minimize common turning points	Field Segmentation (Inner, Outer)	Minimize polling nodes	Minimize rendezvous nodes	Minimize rendezvous points
Applications	Delay tolerant	Delay intolerant	Delay tolerant	Delay tolerant	Delay tolerant
Segmentation Field	No	Yes	No	No	No
Data Delivery to the BS	Via mobile element	Via mobile and multi-hop	Via mobile element	Via mobile element	Via mobile element
No. of ME	One	One	One	One	One

. In each duty cycle, every sensor node sends a fixed packet size, which it generates for its parent. Size reduction (data compression) is used for in-network aggregation. This is achieved by merging the data packets received from all the children of the current node. This merger produces one data packet sent to the upper level. The parameters used in the simulations are presented in

Table 2. Simulation parameters.

Simulation Parameters	Values
Initial Energy (J)	0.25
Number of Sensor Nodes (N)	100, 150, 200, 250, 300, 350, 400
Transmission Range Tr (m)	20, 25, 30, 35, 40, 45, 50
Relay Hop Count d	0, 1, 2, 3, 4, 5
Mobile Velocity (m/s)	1
Packet Length K (bits)	640
Deployment Area Size L (m)	150, 200
Duty Cycle	200

.

5.1. Energy Model

To evaluate the dissipated energy, we used a first-order radio model [49]. In this simple model, the radio dissipates $E_{elec}=50$ nJ/bit to run the transmitter or receiver circuitry and ${\epsilon }_{amp}=100$ pJ/bit/m${}^2$ for the transmit amplifier. Thus, transmitting or receiving a K-bit message, a distance $\left(d\right)$, uses up energy based on the following model:

$$\begin{array}{cc}\hfill E_{Tx}& (K,d)=E_{elec}\ast K+{\epsilon }_{amp}\ast K\ast d^2\hfill \end{array}$$

(6)

$$\begin{array}{cc}\hfill E_{Rx}& \left(K\right)=E_{elec}\ast K\hfill \end{array}$$

(7)

The energy dissipated to transmit a message of size K-bits is more than the energy required to receive a message of the same size. In addition, transmitting a K-bit message from node A to node B is the same as transmitting a message of K-bits from node B to node A. Figure 5 illustrates the radio model used in this simulation.

5.2. Simulation Architecture and Assumptions

In this subsection, a detailed exposition is given of the consolidated and unified architecture developed. Aside from the assumptions highlighted in Section 3, other relevant assumptions were as follows:

• The transmission range, deployment field, and the number of sensor nodes are adjustable.
• Each sensor node continually generates a fixed data packet size and sends it to the parent node.
• Communication is symmetric (among nodes), and the power consumption studied is only for the packet transmission and reception. Furthermore, sensing and computation costs for data aggregation are very low, which are considered negligible.
• The ME collects data from a certain number of selected nodes. In addition, ME traverses the deployment field in a linear fashion. It is also assumes that there are no obstacles on the ME’s path. In addition, the ME (i.e., vehicle) can be recharge when it arrives back at the BS or using some sort of solar power. Thus, the power of the ME is not an issue in this paper.

5.3. Rendezvous Node Analysis

Figure 6 presents the average number of rendezvous nodes under varying network sizes. In this simulation scenario, $Tr$, hop number, and field size were set to 30 m, 2, (200 m × 200 m), respectively. The result showed that the average RP increased as the network size increased. Note that the proposed algorithm outperformed SPT-DGA, LP-RDA, and ZDG-MME. This was because the number of RPs selected by the proposed algorithm was reduced and the selected RPs were closer to the BS. However, the pause locations for the ME were minimal in the MDG-NL algorithm as it pulled data from two overlapped sub-polling points (SPPs) in one pause.

Figure 7 presents the average number of rendezvous nodes under varying transmission ranges $Tr$. L, d, and N were set to (150 m × 150 m), 2, and 150 nodes, respectively. It was obvious that when the transmission range increased, the average number of rendezvous noded decreased. This shows that a lower number of RPs can provide sufficient coverage in the network. This was because more sensors were affiliated with the same RP. The proposed algorithm outperformed the SPT-DGA and LP-RDA algorithms in all cases. However, increasing the transmission range beyond a certain threshold limited the proposed algorithm’s performance as the number of nodes affiliated with each RP increased. ZDG-MME decreased the number of pause locations dramatically because it divided the deployment field into two zones. Moreover, most of the pause locations were in the inner zone as a result of the increase in the transmission range. This problem should be avoided and consequently eliminated. Note that MDG-NL outperformed the compared algorithms because it minimized the number of common turning points (CTPs) as compared to the number of SPPs.

Figure 8 presents the average rendezvous node under varying hop counts. Simulation parameters $Tr$, network size N, and field size L were set to 30 m, 200, and (200 m × 200 m), respectively. The result showed that the average RP decreased as the hop count increased. This was because a few nodes were selected as rendezvous nodes in all the considered algorithms. The proposed algorithm outperformed the SPT-DGA, LP-RDA, and ZDG-MME algorithms, especially at lower hop counts. This was because the technique used in the proposed algorithm selected the RP based on the hop count and the number of affiliated sensors within each group.

5.4. Power Consumption Analysis

Considering the total energy consumption with respect to the number of nodes, N, Figure 9 illustrates the performance of MCRP as compared to SPT-DGA, MDG-NL, and ZDG-MME. It can be observed that when N had the smallest value, the total number of sensor nodes that were affiliated with each rendezvous point was less. Thus, the level of communication required to transmit data to the nearest RP and receive the data reduced, which drained less energy. However, the total energy consumed by each algorithm was closer to the others. In this context, the proposed algorithm slightly improved compared to the other schemes.

Figure 10 illustrates the transmission range ($Tr$) of MCRP against SPT-DGA, MDG-NL, and ZDG-MME with respect to the total energy consumption. It is visible that when the transmission range Tr had the smallest value, the total energy consumption was reduced. This was because a shorter communication distance required less energy and vice versa. Furthermore, when the transmission range was increased, the sensor nodes were left with no choice, but to send their data to the farthest neighbor towards the direction of the BS. The total energy consumed by all algorithms was relatively similar with a slight improvement in the proposed algorithm.

5.5. Tour Length Analysis

To reveal how the number of RPs and their positions impacted the mobile tour length, Figure 11 presents the mobile tour length under varying network sizes. In this simulation scenario, $Tr$, hop count, and field size were set to 30 m, 2, and (200 m × 200 m), respectively. The result showed that the tour length increased as the network size increased. We note that the proposed algorithm outperformed the SPT-DGA, ZDGMME, MDG-NL, and LP-RDA algorithms because it selected RPs that were close to the BS. In other words, the RP selection design in the proposed algorithm mainly considered two factors, which related to the number of RPs and their location with respect to the BS. However, a further increase in the number of deployed nodes limited the proposed algorithm’s performance due to the larger network density. Deductively, the proposed algorithm was more efficient in scenarios with a low network density.

Figure 12 illustrates the mobile tour length under a varying transmission range. In this simulation scenario, the number of nodes N, hop count d, and field size L were set to 200, 2, and (200 m × 200 m), respectively. Whenever the transmission range of each sensor node was increased, each sensor would have more neighbors for itself. In addition, the tour length of the mobile element reduced when the number of RPs were reduced since more sensors were affiliated with the same RP. In all cases, due to the nature of selecting RP, the MCRP algorithm outperformed the SPT-DGA, ZDGMME, MDG-NL, and LP-RDA algorithms.

6. Conclusions

This paper presented a detailed description of a new approach for selecting rendezvous nodes during MEs’ data collection. On this subject, an efficient algorithm, the minimal constrained rendezvous point (MCRP) algorithm, was developed to enhance data gathering latency, power consumption, and reduce the number of rendezvous nodes (RP). The selection of an RP was dependent on the number of affiliation nodes, the location of the RP, and the bounded relay hop. As such, it ensured the RPs were close to the BS. The enhanced method minimized the number of pause locations for MEs and guaranteed that their locations were the closest to the BS. Simulation results showed significant improvement in the tour lengths of MEs, which in turn minimized the data gathering latency while maintaining a power consumption close to the compared algorithms. The MCRP algorithm outperformed other state-of-the-art algorithms. As future work, we will examine the algorithm with different locations of the BS (i.e., center, corner) and more than one mobile element (i.e., vehicle). In addition, we will enhance the power consumption in our proposed algorithm. Different data compression techniques will be considered in future work. We will also examine our algorithm in a scenario similar to a real urban area.