Dynamic sink movement strategy for expedited query processing in Internet of things-based sensor networks

Abstract

Wireless sensor networks (WSNs) represent an essential infrastructure that supports the Internet of things (IoT) and enables intelligent data collection from various contexts. In IoT-driven systems, sensor nodes collect real-time data, initiate end-user or application requests, and forward the gathered data to a cloud server. Query processing in WSN aims to obtain accurate sensor data while conserving network resources. However, traditional static sink-based data collection and query processing methods often face challenges related to network lifetime and lengthy delays. To mitigate these drawbacks, this paper proposes a novel dynamic sink-based query processing strategy (DSQPS) for IoT-enabled WSNs. DSQPS first calculates the optimum number of rendezvous points on the network by solving a minimal set covering problem, followed by Aquila Optimizer (AO), which optimizes the number of mobile sinks. In addition, an optimized movement path for mobile sinks is determined, minimizing delays in data collection and query processing. DSQPS demonstrates superior performance over state-of-the-art approaches based on rigorous testing and mathematical analysis. Results indicate that DSQPS outperforms comparative methods regarding query processing delay, average energy consumption, network lifespan, and throughput, up to 38%, 30%, 150, and 60%, respectively.

Introduction

In the last decade, the Internet of things (IoT) has undergone phenomenal development in smart homes, personal monitoring, tracking applications, video surveillance, and intelligent products [1]. The IoT is a network that connects various sensors, data storage systems, and equipment, including GPS sensing and transmission devices, wireless communication technology, radio frequency identification (RFID) tags, laser scanners, and infrared detectors [2, 3]. These interconnected entities interact and share information via the Internet, functioning according to pre-established contractual agreements [4]. Enabled by intelligent management through a computer or mobile device, the IoT supports advanced capabilities such as sensing, recognition, placement, tracking, observing, and controlling [5].

Background

Technological advancements, including RFID, cost-effective wireless sensor devices, and network infrastructure, have facilitated IoT development. These developments have made it possible to link everyday things to the Internet [6]. This connectedness promotes smooth communication between machines and humans, as well as between machines themselves, in the actual world. Wireless sensor networks (WSNs) are vital parts of IoT ecosystems since they serve as a key technology that expands the Internet’s coverage and enhances computing capacities [7]. WSNs have gained considerable interest from academia and society, given their vast potential applications in national economies, social progress, and military systems [8]. Currently, WSNs are employed in several fields, including military applications, environmental monitoring, security surveillance, smart home design, and search and rescue operations [9]. These networks are especially beneficial in challenging or remote locations where they may replace manual techniques of gathering, transmitting, and processing information [10]. Over the past several years, there has been rising enthusiasm among academics in the study, advancement, and real-world use of WSNs, especially in areas connected to national security, economic advancement, and social networking [11, 12].

WSNs consist of separate sensor nodes that monitor different environmental conditions and communicate the collected observations to a central sink or base station [13]. Figure 1 depicts a general structure of WSNs. These networks are designed specifically for specific purposes, each with a distinct set of requirements and constraints. Replacing batteries in sensor nodes is a significant difficulty in time-critical WSN deployments for military operations, surveillance, security monitoring, landslide monitoring, forest fire monitoring, and volcanic eruption monitoring systems [14]. Furthermore, these nodes frequently encounter difficulties accessing external wired power sources conveniently. Therefore, the primary challenge is to reduce energy usage across all sensor nodes during communication. Extending the duration of network operation is vital, especially in unattended sensor network applications. In addition to the energy economy, providing rapid and dependable data transmission is crucial [15]. In catastrophe detection systems, the system may fail to achieve its goals if the collected data does not reach the central point within a predetermined period [16]. Hence, it is imperative to ensure optimal energy utilization while ensuring fast and reliable data transmission for time-critical WSN-enabled applications.

Fig. 1 [Images not available. See PDF.]

A general structure of WSN

The selection of a static or mobile sink in different sensor network applications depends on the unique demands of the given application. Mobile sinks may be necessary for time-sensitive applications that often handle crucial and secret data [17]. Conversely, applications such as landslide and volcanic eruption detection, which deal with essential but non-sensitive data, may use a stationary sink. When handling non-sensitive data, it may be preferable to use a static sink. However, a mobile sink is frequently preferred when the network manages sensitive data because of its security advantages. The mobile sink’s dynamic mobility increases the difficulty of tracking or pursuing it, boosting data transfer security [18].

Moreover, continual monitoring of various areas is typically required in time-sensitive applications. Heavy data traffic directed toward a static sink can lead to quicker depletion of nearby node batteries than other nodes, disrupting network connectivity and causing energy holes. In such cases, a mobile sink can prevent energy drainage near the sink, offering a better solution than a static sink. The mobile sink enhances security in time-critical applications and simultaneously prevents energy holes within the network [19].

Challenge

In mobile sink-based networks, timely dissemination of the sink’s updated position to source sensor nodes is crucial for effective data relay. Outdated sink positions can render the relayed data useless for achieving the network’s objectives [20]. While flooding is a simple method to propagate sink positions throughout a network quickly, it can lead to rapid energy consumption among nodes and introduce high traffic overhead, particularly in large-scale networks. Hierarchical routing schemes have been proposed to mitigate broadcasting costs associated with sink positions [21]. These protocols reduce traffic overhead and energy consumption by organizing sensor nodes into a virtual hierarchical architecture, such as grids, trees, clusters, and rings. Within this structure, sensor nodes are assigned multiple dynamic roles [22].

Hierarchical routing protocols efficiently handle sink mobility by ensuring that only specific higher-tier sensor nodes are informed about the new position of the sink instead of disseminating the information across the entire network. In this architecture, upper-level nodes store the latest mobile sink coordinates. Lower-level nodes can then issue queries to these upper-level nodes to obtain the sink’s positioning and forward their collected data toward the sink [23]. This hierarchical structure minimizes flooding and maximizes energy efficiency throughout the network. Dense deployment in time-sensitive applications with multiple or single mobile sinks presents challenges related to energy distribution and traffic management within the network [24]. While a hierarchy of roles helps reduce overall energy consumption, it often results in higher-tier nodes handling more traffic. This imbalance can lead to quicker battery depletion in higher-tier nodes, creating energy holes in the network. Routing protocols must ensure an even traffic load distribution between upper- and lower-tier nodes to prevent premature battery exhaustion in higher-tier nodes.

Related work

In WSN-driven systems, effectively processing queries is imperative for extracting valuable information while efficiently managing network resources. Over the last decade, various methodologies have been proposed to enhance query processing in WSNs, each aiming to overcome challenges such as extended delays and limited network lifetime commonly associated with traditional static sink-based approaches. This section delves into the existing body of literature, surveying prior works on query-processing strategies in WSNs. We investigate the strengths and limitations of these approaches, providing a comprehensive understanding of the evolving landscape. Table 1 summarizes the key contributions, challenges, and limitations of the discussed approaches.

Table 1. An overview of recent query processing approaches

References	Key contributions	Challenges and limitations
[25]	• Proposing an architecture employing multiple trees and heterogeneous nodes to enhance the energy efficiency of WSN queries • Introducing multiple-tree and multi-tree strategies for improving network performance • Handling scenarios with different energy consumption and latency requirements	Dissipation of energy by intermediate sensor nodes during query dissemination
[26]	• Proposing a query-driven virtual wheel-based routing scheme for limiting network-wide broadcasts of sink locations • Introducing angle-based forwarding to enhance data delivery rate • Mitigating the impact of mobile sinks on routing efficiency	Increased power consumption in wheel nodes while routing query and data packets
[27]	• Presenting a query-driven virtual grid-based strategy for effective data delivery to a mobile sink • Employing a virtual infrastructure to minimize network control overheads • Demonstrating improved latency, delivery ratio, energy consumption, and network traffic performance	Degradation of network performance due to the exchange of numerous messages
[28]	• Introducing the QoQ concept for adaptive query processing in WSNs • Defining four classes based on energy consumption and query result accuracy • Proposing the AdaQuali algorithm for dynamic control of sensor node activities	Limited to simulation-based validation, real-world deployment considerations need further exploration
[29]	• Suggesting an adaptive aggregation algorithm for adaptive in-network aggregation • Demonstrating adaptive behavior based on memory and energy consumption • Implementing accurate data aggregation in WSNs with packet replication	Evaluation is limited to experimental results without extensive real-world deployment scenarios
[30]	• Exploring curve query processing and introducing a sensed curve derivation method • Providing accurate and approximate aggregation procedures for energy-cost optimal results • Demonstrating effectiveness concerning energy efficiency and accuracy	Practical implementation considerations and scalability challenges need further investigation
[31]	• Introducing an in-network distributed query processor using a declarative query language • Incorporating freshness guarantees for cached sensor readings • Offering a resource-aware framework for dynamic adjustments to changing resource levels	Real-world deployment considerations and scalability challenges require further exploration
[32]	• Proposing greedy and boundary traversal for efficient and robust query processing • Achieving a 50% reduction in query responsiveness, energy consumption, and communication costs across large-scale networks • Providing a formal proof of correctness for termination and completeness	The serialized and localized nature may pose challenges in dynamic and diverse network environments
[33]	• Presenting a monitoring framework for streaming data analysis using deep learning • Introducing adaptive query refinement for timely analysis of data within specified deadlines • Handling scenarios with unsynchronized sensor data or pending data arrivals	The adaptability of the framework to varying network conditions and scalability concerns may require further exploration
[34]	• Proposing a dynamic query processing model to meet temporal deadlines • Incorporating real-time database management features	The practical implementation and adaptability in dynamic scenarios need further investigation
[35]	• Proposing a security scheme for query processing with a clustered structure • Focusing on maintaining confidentiality, integrity, and protection against replay attacks • Demonstrating superiority over competing schemes through qualitative and quantitative analyses	The scheme’s scalability and adaptability to evolving security threats may require continuous refinement

WSNs utilize a variety of network topologies to connect nodes. The topology affects the energy usage of any WSN. A well-designed topology can significantly reduce energy consumption by minimizing the number of packet transmissions. Snigdh et al. [25] proposed an innovative architecture for a sensor network, employing multiple trees and diverse nodes to create an energy-conscious query processing. They introduced multi-tree and multiple-tree approaches specifically tailored to enhance network performance in typical data collection scenarios within WSN applications. The concept of multi-tree involves organizing sensors with similar parameter types into a tree-based topology, aiming to decrease energy consumption and communication delays. On the other hand, the multiple-tree algorithm provides a superior approach to propagate query results in data-driven applications, particularly in scenarios without stringent delay constraints. The query reply follows the same path as the original query and is sent from the root node to the base station. Nevertheless, this method of query dissemination causes intermediate sensor nodes to dissipate more energy.

The sink injects queries regarding a region-of-interest (RoI) into the network in query-driven routing protocols. Upon receiving the query, sensor nodes within the RoIs forward their data to the sink. Mobile sinks make routing data challenging. As the sink moves over time, the location of the query injection and data collection may change, compromising performance. Typically, mobile sinks are located by broadcasting, which burdens resource-constrained sensor nodes. To address these issues, Jain et al. [26] proposed the “wheel,” a virtual infrastructure for limiting network-wide broadcasts of sink locations. They introduced QWRP, a query-driven virtual wheel-based routing protocol, for query-driven scenarios over the simulated wheel. A novel packet forwarding approach, angle-based forwarding, is also proposed as part of QWRP to enhance data delivery. Wheel nodes typically use this algorithm to effectively deliver query and data packets to RoIs and sinks. Data and queries are traversed through wheel nodes, increasing power consumption.

Khan et al. [27] proposed QDVGDD, a query-driven virtual grid-based data dissemination approach for improving data delivery efficiency. Using a virtual infrastructure, the proposed scheme causes minimum network control overheads while providing high-quality data to a mobile sink. They performed extensive simulations using NS-2.3 to assess QDVGDD’s efficiency at various sink speeds and network dimensions. Based on simulation outcomes, QDVGDD outperforms other state-of-the-art solutions regarding network traffic, energy consumption, data delivery ratio, and latency. However, the exchange of so many messages degraded the network’s performance.

Brayner et al. [28] introduced the quality of queries (QoQs) concept to optimize query processing in WSNs. QoQs focuses on intelligently managing the limited resources in WSNs while maintaining a satisfactory data quality level for client applications. The QoQ concept suggests that query results in the same WSN can be customized based on energy consumption and the accuracy of results. Four QoQ classes are defined to meet distinct requirements regarding these criteria. To implement these classes in a practical WSN context, a novel detection methodology named AdaQuali (ADAptive QUALIty control for query processing) is presented. AdaQuali dynamically adjusts sensor node activities, controlling data collection and transmission rates. Using actual temperature data, an experiment conducted with a prototype built in Sinalgo validates the proposed approach. The results demonstrate the effectiveness of AdaQuali, with energy consumption reductions of up to 66.76% for different scenarios.

Brayner et al. [29] suggested a flexible in-network aggregation process to handle WSN queries. This operator, termed ADaptive AGgregation Algorithm for sensor networks (ADAGA), demonstrates adaptive characteristics based on energy and memory consumption, adaptively tuning the periods for collecting and sending data. ADAGA was explicitly designed to perform accurate data aggregation employing packet replication. Additionally, ADAGA can predict values for non-performed detections based on collected data, producing results that closely approximate actual results without resource constraints. Experimental results validate the efficiency of ADAGA in practical scenarios.

Cheng et al. [30] conducted a study on curve query processing for WSNs, recognizing the efficacy of curves in representing continuous sensed data. The research aims to support curve query processing by introducing a sensed curve derivation procedure. Subsequently, the study offers accurate and approximate aggregation algorithms for aggregation operations. The proposed approximate aggregation algorithm is proven to be energy-cost optimal when meeting the specified precision requirements. Experiments confirm that the introduced algorithms excel in accuracy and energy efficiency.

Khoury et al. [31] introduced Corona, an in-network distributed query processor designed to facilitate the shared utilization of a sensor network among multiple users through a declarative query language. Corona incorporates an innovative strategy to minimize sensor triggering within shared WSNs. The concept of freshness is introduced to WSN, enabling users to request cached sensor readings with predefined freshness guarantees. Additionally, the system integrates a resource-aware framework, allowing the query processor to adapt dynamically as resource availability changes. The functionality of Corona is exemplified through various aggregation queries, catering to different users with diverse requirements for freshness and result precision.

Boukerche et al. [32] addressed the challenge of effective and reliable query processing by introducing a novel scheme known as greedy and boundary traversal (GBT). GBT is characterized by serialization and localization, with each node lacking knowledge of the network’s topology. Notably, GBT adopts a strategy where next-hop selection is entirely separate from preceding hops, eliminating the need for a predefined path. This unique feature contributes to the robustness of GBT, as evidenced by experiments reporting an approximate 50% decrease in communication, energy consumption, and query responsiveness at large scales. The study includes a comprehensive analysis of the query processing algorithm’s complexity, covering aspects such as time, space, and communication. A formal proof of correctness, encompassing termination and completeness, is also provided.

Lee et al. [33] presented a monitoring framework designed for analyzing streaming data in WSNs through deep learning. Ensuring deterministic results within a specified timeframe is essential when constraints are crucial. To address this, an adaptive query refinement was introduced into the predictor, allowing for timely analysis of data from the WSN. This approach enables the derivation of reasonably accurate query analysis results within the given deadline, even when dealing with unsynchronized sensor data or pending data arrivals.

Belfkih et al. [34] proposed RTQPS, a real-time query processing solution, to satisfy the time-sensitive requirements of WSNs. This system employs a query processing architecture, which includes an embedded real-time database management module. RTQPS facilitates the dissemination of queries and data collection. A deadline controller ensures real-time deadlines, and a real-time scheduler ensures queries are completed on time. The approach has been validated through simulations.

Ghosal and DasBit [35] proposed a security model for query processing in WSNs employing a clustered structure. Its primary purpose is maintaining fundamental security aspects like integrity and confidentiality and safeguarding against replay attacks. Specifically, the scheme emphasizes the higher probability of attacks on cluster heads and member nodes rather than the base station, considering the attacker as a mote class. Thus, the proposed approach ensures that keys are not sent or pre-deployed during cluster head-member communication. Qualitative and quantitative analyses have demonstrated the superiority of the scheme over competitors.

Contribution

A range of routing protocols have been proposed in the literature to manage sink mobility in time-sensitive applications in unattended networks [36]. However, in densely distributed networks, the mobility of sinks introduces several issues, such as increased traffic overhead, packet collisions, reduced data delivery rates, higher energy consumption, and longer end-to-end delays [37]. Thus, in such situations, efficient management of these issues becomes critical to ensuring efficient and dependable data delivery services and an extended network lifetime. Routing protocols should address these challenges to balance efficient data transmission and energy preservation, ensuring longevity and reliable data delivery in dense and highly mobile network environments.

Traditional static sink-based approaches in IoT-enabled WSNs suffer from several limitations, primarily energy inefficiency, high latency, and uneven network load distribution. In static sink architectures, sensor nodes near the sink deplete energy faster, creating energy holes and reducing network lifespan. Additionally, query processing delays increase due to congestion in hotspot areas, making them unsuitable for real-time applications. These challenges highlight the need for dynamic sink-based strategies, which optimize sink mobility, balance energy consumption, and minimize query response time. By intelligently repositioning sinks, dynamic strategies significantly enhance scalability, reliability, and energy efficiency in IoT-driven WSNs.

In WSNs, mobile sinks have proven to be an effective way to reduce energy consumption. There are two basic types of mobile sink-based query processing strategies: flat topology-based and rendezvous point-based, each using single or multiple mobile sinks [38]. In a flat topology-based design, mobile sinks interact with sensor nodes and gather their data directly through single-hop connectivity. While sensor nodes effectively save energy in communication and the impact of packet traffic is minimal, the length of the channel grows unreasonably long, leading to buffer overflow in the sensor nodes [39]. In the rendezvous point-based designs, the mobile sink travels to a predetermined set of resting sites called rendezvous points and gathers data from nearby sensor nodes. Utilizing this approach for data collecting results in equitable energy usage and lower delays in data collection. However, these strategies raise two significant issues: (1) How to determine the most efficient number of rendezvous points and their strategic placements? and (2) How to determine the appropriate set of mobile sinks needed to gather data from all sensor nodes while minimizing tour duration and latency? These matters are of paramount significance and necessary. To address these issues, this paper presents a novel query-processing strategy employing a mobile sink to improve IoT-enabled WSN efficiency. This study makes the following contributions:

• Development of an efficient selection mechanism for determining the number of rendezvous points aimed at minimizing sensor node energy consumption

• Presenting an optimal selection mechanism for minimizing the number of mobile sinks employing the Aquila Optimizer (AO), thereby enhancing network lifetime and throughput

• Developing a mobile sink-based query processing scheme to minimize query processing latency within the network

The remainder of the paper is laid out as follows. Methods section explains the network model and details the proposed query processing strategy. Results and discussion section compares the results of experiments with previous methods. Conclusions section concludes the paper and offers recommendations for upcoming research.

Methods

System model

In this section, we present the network and energy models, along with some underlying assumptions. This study considers the network structure as a graph, denoted by G(S, L), where $S=(s_1,s_2,s_3,\cdots ,s_n)$ represents the set of static sensor nodes and $L=(l_1,l_2,l_3,\cdots ,l_n)$ stands for the links or edges connecting any pair of sensor nodes (s_i, s_j). An edge is formed between two nodes only if s_i and s_j fall within each other’s communication range, mathematically expressed in Eq. 1.

1

$$L_{\mathit{ij}}=\left\{\begin{array}{c}1d_{i,j}\le R\hfill \\ 0otherwise\hfill \end{array}\right)$$where R represents the communication range of a sensor node and d_i,j denotes the Euclidean distance between two nodes, i and j.

The monitoring field is considered to be a square of dimensions $M\times M{m}^2$, hosting a deployment of n static and homogeneous sensor nodes distributed randomly across the area. Each sensor node is equipped with a geographical positioning system, enabling precise location awareness. Data collection is facilitated by a mobile sink moving at a constant speed of v m/sec. The base station is presumed to possess unlimited energy and computational power. These assumptions collectively define the operational environment for our proposed query processing strategy. Table 2 summarizes the terminologies used throughout the study.

Table 2. Abbreviation table

Abbreviation	Definition
kmax	Maximum number of iterations
TSP	Traveling salesperson problem
d0	Threshold distance
ed(i,j)	Euclidean distance between rendezvous points
d(i,j)	Euclidean distance between sensor nodes
c(j)	Cost associated with the jth set
$\xi mp$	Multi-path energy model
Rcomm	Communication range of sensor nodes and rendezvous points
MSstour	Set of all sub-tours
${\mathit{MS}}_{\mathit{stour}}^i$	Sub-tour of the ith mobile sink
MStour	Tour length of a mobile sink
$\iota$	The optimal number of mobile sinks
$\gamma$	Constant variable for estimation of max mobile sinks
Z	Set of subsets
r	Total number of rendezvous points
$T$	Total number of subsets
S	Set of sensor nodes
R	Set of rendezvous points
$R_{{\mathit{tour}}_i}$	Set of rendezvous points in the ith tour

The energy model calculates the energy sensor nodes consume when sending or receiving data. Figure 2 illustrates the radio energy dissipation model. The energy needed to transmit a k-bit message over a distance d, denoted as ETX(k, d), from a transmitter to a receiver ERX(k), is determined by Eq. 2.

2

$$E_{\mathit{Tx}}(k,d)=\left\{\begin{array}{c}k\times E_{\mathit{elec}}+k\times {\xi }_{\mathit{fs}}\times d^{2}ifd<d_0\\ k\times E_{\mathit{elec}}+k\times {\xi }_{\mathit{mp}}\times d^{4}ifd\ge d_0\end{array}\right)$$where d₀ represents the threshold transmission distance between the transmitter and receiver, given by $d_0=\sqrt{\frac{{\xi }_{\mathit{fs}}}{{\xi }_{\mathit{mp}}}}$. The term $E_{\mathit{elec}}$ denotes the energy consumption in electronics associated with sending or receiving a bit while ${\xi }_{\mathit{fs}}$ and ${\xi }_{\mathit{mp}}$ denote the amplifier parameters for the free space and multi-path models, respectively. The variables d² and d⁴ correspond to short- and long-distance transmissions, respectively. Based on the distance between the transmitter and receiver, the free space model is applied if the distance d is less than or equal to the threshold d₀; otherwise, the multi-path model is utilized. For the reception of a k-bit packet, the energy required by the receiver, denoted as ERX(k), is expressed by Eq. 3.

Fig. 2 [Images not available. See PDF.]

Energy consumption model

3

$$E_{\mathit{Rx}}(k)=k\times E_{\mathit{elec}}$$

Proposed approach

Our approach follows a structured process, as illustrated in Fig. 3, comprising three key phases: (1) selecting the optimal number of rendezvous points, (2) determining the optimal number of mobile sinks using the AO, and (3) implementing an intelligent mobile sink-based query processing strategy. Each phase is designed to enhance energy efficiency, reduce query processing delay, and improve network lifespan by dynamically adapting to network conditions. The iterative re-optimization step ensures continuous performance improvement until the stopping condition is met.

Fig. 3 [Images not available. See PDF.]

Flowchart of proposed approach

Optimal number of rendezvous points

The optimal number of rendezvous points is identified by a minimal set covering problem, reducing query processing delay and increasing network lifetime. Sensor nodes form sets based on their communication ranges and identify their neighbors. Further, these sets form supersets. When supersets are formed, already created regular sets are dropped. The first step involves selecting the minimal number of sets based on the super sets. Sensor nodes that belong to more than one super set are added to the super set with the smallest size if they belong to more than one super set. In the case of equal sizes, the common sensor node checks connectivity and joins the set with maximum connectivity. After optimal set formation, the center point of each super set serves as the optimal location for the rendezvous point, facilitating connection between isolated segments. Algorithm 1 provides the pseudocode for selecting the optimal number of rendezvous points, while Eqs. 4, 5, 6 and 7 define the mathematical formulation of the problem.

4

$$x\left(i,,,j\right)=\left\{\begin{array}{cc}1\hfill & ifthesensornodeiisincludedintheset{\varphi }_j\hfill \\ 0\hfill & \mathit{otherwise}\hfill \end{array}\right)$$

5

$$\upsilon \left(i\right)=\left\{\begin{array}{cc}1\hfill & iftheset{\varphi }_{i}isincludedinthemincov\hfill \\ 0\hfill & \mathit{otherwise}\hfill \end{array}\right)$$

6

$$l\left(i,,,j\right)=\left\{\begin{array}{cc}1\hfill & ifthesensornodeiisinthecommunicationrangeof{R}_j\hfill \\ 0\hfill & \mathit{otherwise}\hfill \end{array}\right)$$

7

$$\delta \left(i,,,j\right)=\left\{\begin{array}{cc}1\hfill & if{R}_{j}and{R}_i\in {\mathit{MS}}_{\mathit{tour}}\hfill \\ 0\hfill & \mathit{otherwise}\hfill \end{array}\right)$$

According to Eq. 4, every sensor node is included in at least one set. Using Eq. 5, all sets must be considered in determining the optimal number of sets. A rendezvous point assigned to each sensor node is ensured by Eq. 6. Equation 7 determines whether two rendezvous points are part of the mobile sink tour. Equation 8 is used to formulate integer linear programming based on these equations.

8

$$\text{min}\left(F_1\right)=a_1\times mincov+a_2\times {\mathit{Ms}}_{\mathit{tour}}$$

F₁ is minimized by optimizing both mincov and mobile sink tours simultaneously as follows.

9

$$mincov={\sum }_{j=1}^{r}c\left(j\right)v(j)$$

10

$${\mathit{MS}}_{\mathit{tour}}=\sum _{1\le i,j\le r,i\ne j}ed(i,j)\delta (i,j)$$

11

$${\sum }_{j=1}^{k}x\left(i,,,j\right)v\left(j\right)\ge 1,i=\text{1,2},3,\cdots ,n$$

12

$$\prod _{1\le i\le n,1j\le m}l\left(i,,,j\right)=1$$

13

$$a_1+a_2=1$$

Equation 11 guarantees that each sensor node is encompassed in at least one set, while Eq. 12 ensures that each rendezvous point is precisely included once in the mobile sink tour.

Consider the example illustrated in Fig. 4 and the set formation process presented in Table 3. The scenario involves 14 sensor nodes with gray circular highlights indicating their communication range and five rendezvous points represented by green dotted circles indicating their communication range. It is clear that S5 is covered by two rendezvous points, namely R1 and R2, and similarly, S10 is covered by two rendezvous points, namely R3 and R4. The node degrees of R3 and R4 are evaluated in the first case, while the node degrees of R1 and R2 are assessed in the second case. In the first case, the inclusion of S10 in either set results in a node degree of 3, making it eligible for addition to either set. Conversely, in the second case, adding S5 to R2 increases its node degree to 2, and adding it to R1 increases R1’s node degree to 4. However, placing S5 in R2 balances the node degrees of both R1 and R2 at 3. This equitable distribution contributes to normalizing average energy consumption among the sensor nodes.

Fig. 4 [Images not available. See PDF.]

Rendezvous point-based data collection strategy

Table 3. Set formation process

Sensor nodes	Sensor nodes in the communication range	Set number
1	2, 3
2	1
3	1, 5	${\varphi }_1$
4	2, 5, 6
5	2, 3, 4	${\varphi }_2$
6	4
7	8, 10	${\varphi }_3$
8	7	${\varphi }_4$
9	11	${\varphi }_5$
10	7
11	9
12	13	${\varphi }_6$
13	12
14	–	${\varphi }_7$

Optimal number of mobile sinks

The AO is adapted and utilized in this study to solve the critical optimization problem of determining the optimal number of mobile sinks in WSNs. The issue demands minimizing energy consumption, reducing latency, and ensuring efficient query processing while maintaining the network’s lifespan. AO, inspired by the strategic hunting behaviors of the Aquila bird, is well-suited for addressing the dynamic and complex optimization challenges inherent to WSNs. AO employs four distinct strategies for exploration and exploitation to identify the best solution. These strategies are advantageous for problems that balance global search (exploration) and local refinement (exploitation).

In WSNs, mobile sinks reduce energy dissipation and extend network lifetime by alleviating the “hotspot problem” (excessive energy usage around static sinks). The optimization goal is to determine the optimal number of mobile sinks to cover all rendezvous points and the strategic placement and movement paths of mobile sinks to minimize query processing latency and energy consumption. The fitness function for AO in this context is formulated as:

14

$$Fitness(X)={\omega }_1\times EnergyConsumption(X)+{\omega }_2\times Latency(X)+{\omega }_3\times NetworkLifespan(X)$$where ω₁, ω₂, and ω₃ are weights assigned to reflect the importance of each objective. The fitness function evaluates candidate solutions (positions and numbers of mobile sinks) generated by AO to identify the optimal configuration.

• Strategy 1: expanded exploration (high-altitude search)

The algorithm begins by extensively exploring the search space to locate potential solutions. This phase simulates Aquila flying at high altitudes and is particularly useful for initializing a diverse population of candidate solutions, avoiding premature convergence. The position update is performed as follows:

15

$$X(t+1)=X_{\mathit{best}}\left(t\right)\left(1,-,\frac{t}{T}\right)+\left(X_M,\left(t\right),-,X_{\mathit{best}},\left(t\right)\right)\times rand$$

16

$$X_M\left(t\right)=\frac{1}{N}\sum _{i=1}^N{X}_i\left(t\right)$$where $X_{\mathit{best}}\left(t\right)$ stands for the current best solution, representing an optimal number and placement of mobile sinks, $X_M\left(t\right)$ refers to the mean position of all candidate solutions at iteration t, helping the algorithm maintain diversity, T specifies the total iterations, and rand is a random number in [0, 1]. This phase ensures the algorithm explores various configurations of mobile sinks to identify areas in the solution space with the highest potential.

• Strategy 2: narrowed exploration (contour flight)

After broad exploration, the algorithm transitions to a more refined search, simulating the Aquila’s contour flight near prey. This phase reduces the search space, allowing the algorithm to focus on promising configurations with fewer mobile sinks and better energy efficiency. This behavior is mathematically presented as in Eq. 17.

17

$$X\left(t,+,1\right)=X_{\mathit{best}}\left(t\right)\times LF\left(D\right)+X_R\left(t\right)+\left(y,-,x\right)\times rand$$where LF(D) is the Levy flight function, facilitating local exploitation, calculated as follows:

18

$$LF(D)=s\times \frac{u\sigma }{{\left|\upsilon \right|}^{1/\beta }}$$with constants β = 1.5, s = 0.01, and random variables u, v. Polar coordinates define the local search radius as follows:

19

$$x=r\times sin(\theta )$$

20

$$y=r\times cos(\theta )$$

21

$$r=r_1+0.00565\times D_1$$

22

$$\theta =-\omega \times D_1+\frac{3\pi }{2}$$

This phase identifies potential mobile sink configurations that minimize query processing latency by focusing on regions with high data density and low communication cost.

• Strategy 3: expanded exploitation (low-altitude descent)

Once the prey (optimal solution) is approximately located, the algorithm intensifies its focus, simulating a low-altitude descent for a precise search. In this stage, AO adjusts the number and placement of mobile sinks to balance network coverage and energy efficiency. This behavior is mathematically presented as in Eq. 23.

23

$$X\left(t,+,1\right)=\left(X_{\mathit{best}},\left(t\right),-,X_M,\left(t\right)\right)\times \alpha \times rand+\left(\left(U,B,-,L,B\right),\times ,r,a,n,d,+,L,B\right)\times \delta$$where α and δ are tuning parameters controlling exploration and exploitation balance. LB and UB are the lower and upper bounds of the search space, representing constraints on the number of mobile sinks. This strategy ensures the solution evolves toward configurations that provide comprehensive coverage with minimal redundancy in mobile sink deployment.

• Strategy 4: narrowed exploitation (ground attack)

In the final phase, AO performs a highly localized search to refine the optimal solution. This phase simulates the Aquila following and attacking prey on the ground, representing fine-tuning of the mobile sink configuration. This behavior is mathematically presented as in Eq. 24.

24

$$X\left(t,+,1\right)=2F\left(t\right)\times X_{\mathit{best}}\left(t\right)-\left(G_1,\times ,X,\left(t\right),\times ,r,a,n,d,-,G_2,\times ,L,F,\left(D\right)\right)+rand\times G_1$$

25

$$2F\left(t\right)=\frac{2\times rand-1}{{\left(1,-,t,/,T\right)}^2}$$

26

$$G_1=2\times rand-1$$

27

$$G_2=2\times \left(1,-,\frac{t}{T}\right)$$

This stage finalizes the solution by eliminating unnecessary mobile sinks and ensuring that the chosen sinks are optimally placed to reduce communication delay and energy usage.

The AO iteratively determines the optimal number of mobile sinks and their corresponding sub-tours to achieve an efficient network configuration. The sub-tour lengths are minimized by reducing query processing latencies during optimization. The pseudocode of the AO is presented in Algorithm 2. This approach leverages the ideal number of rendezvous points and the tour lengths of mobile sinks as input parameters. The mobile sink sub-tours are derived by evaluating the global fitness value, which identifies mobile sinks’ optimal count and placement. Finally, the traveling salesperson problem (TSP) is solved for each sub-tour using Christofides heuristics, resulting in efficient paths for the mobile sinks. The primary advantage of employing AO lies in its adaptive balance between exploration and exploitation, ensuring global search efficiency and precise local optimization. This balance allows AO to converge effectively to optimal solutions.

Mobile sink-based query processing strategy

The query processing step commences after identifying the ideal number of rendezvous points, mobile sinks, and sub-tours of each sink. When the base station receives queries from the end-user regarding different ROIs, it transfers them to the corresponding mobile sink associated with the specified ROI. Upon receiving the information from the base station, each sink assesses its coverage area and number of rendezvous points and determines if the specific ROI fits within its coverage area. If the ROI is within the range covered by a designated mobile sink, it promptly relocates towards the ROI and visits the rendezvous point of that area. Upon reaching the designated rendezvous point, the sink transmits a dataupload message, including the sink ID and queryreq to all the sinks in that area.

Upon receiving the dataupload message, the sensor nodes respond to the mobile sink by sending an acknowledgment message (ACK), including their sensor node ID, remaining energy, and data size. The mobile sink assigns a specific time interval to each sensor node and retrieves the data from the ROI. Ultimately, the collected data is transmitted to the base station, and the sink proceeds to the subsequent ROI by examining its buffer for any outstanding requests. Additionally, each sink gathers data from its designated ROIs and transmits it to the base station. The base station receives and analyzes the data collected from all the mobile sinks and then sends it to the cloud server. The cloud server handles every query according to the specific needs of the end-users.

Complexity analysis

Identifying the ideal number of rendezvous points involves forming sets based on the coverage range of sensor nodes, which has a worst-case time complexity of O(n²). Once the number of potential sets is determined, disjoint sets are recognized according to the node degree. The complexity of time is O(logx) since the number of sets with a dual entry for a sensor node determines it. Consequently, the ultimate temporal complexity of this stage is about O(n²logx). In the AO, steps 1 to 3 have a time complexity of O(1), including the initialization of variables. Moreover, a for loop is iterated k times, calculating the ideal quantity of mobile sinks.

Additionally, the outcome is influenced by the ideal quantity of rendezvous points and sub-tours for each mobile sink, assessed over a series of k steps. Hence, the overall time complexity is determined by the number of mobile sinks detected in k stages, approximately O(mk). The mobile sink-based query processing strategy assumes that the base station creates q queries for m mobile sinks. Consequently, every sink must respond to q/m queries. The duration needed to gather the data from each ROI is denoted as T_qt. The total time required by all the sinks to process q/m number of ROIs’ queries can be approximated as $O(\frac{q}{m})T_{\mathit{qt}}$.

The computational efficiency of DSQPS lies in its lightweight optimization approach that ensures adaptability in dynamic WSN scenarios. By employing the AO for mobile sink selection and a minimal set-covering strategy for rendezvous point determination, DSQPS efficiently minimizes computational overhead while maintaining high performance. The algorithm dynamically adjusts to varying query loads and sink speeds, optimizing data collection without excessive processing delays. This adaptability allows DSQPS to function effectively in real-time applications, ensuring low-latency query processing, reduced energy consumption, and prolonged network lifespan, even under rapidly changing network conditions.

Results and discussion

We conducted thorough simulations of our suggested approach, DSQPS, using the network simulator-3 on a Windows 10 operating system (64-bit) running on an Intel(R) Core (TM) i7-8550U CPU 1.80 GHz × 8 processor with 8 GB of RAM. The simulation features a monitoring area of 500 × 500 m², with a variable number of sensor nodes ranging from 100 to 500 and two distinct communication ranges of 20 and 40 m. We considered three related algorithms, i.e., QDWSN, QWRP, and QDVGDD, and compared them with DSQPS. Each algorithm attempts to find the optimal number of sinks for data collection. We have employed a parameter configuration similar to those specified in these studies. For a thorough performance assessment, we varied the sink speeds at 2, 4, 6, 8, and 10 km/h and tested the system under query loads ranging from 10 to 50 queries. The evaluation criteria included throughput, network lifespan, query processing delay, and energy consumption, considering the impact of sensor node distributions, query rates, and sink mobility patterns. To ensure a fair comparison, we have obtained an average of 15 outcomes for each algorithm by considering various parameters. This is necessary since the network topology may alter in each simulation run.

Throughput analysis

Throughput measures the quantity of data sent between two locations within a specific time frame. It quantifies the speed at which data may be sent across a network. The objective of WSN is to enhance the longevity and dependability of the network by increasing the data transfer rate. The limited supply of energy resources is the primary cause of the growing throughput. Enhancing energy levels results in a notable enhancement in throughput. In this work, we employed Eq. 28 to calculate the mean throughput. Here, $D_{\mathit{SN}}$ represents the data packet generation rate of sensor nodes, whereas $D_{\mathit{BS}}$ signifies the data packet arrival rate.

28

$$T=\frac{D_{\mathit{BS}}}{D_{\mathit{SN}}}$$

Figures 5 and 6 illustrate the comparison of throughput while using different communication ranges for the sensor nodes, with the sink speed fixed at 8 km/h. The evaluation considers how varying communication ranges impact data transmission efficiency and overall network performance under consistent sink mobility. Within a communication range of 20 m, Fig. 5 shows that DSQPS significantly outperforms QDWSN by 30.1%, QWRP by 50.8%, and QDVGDD by 60.1% in terms of throughput. Figure 6 illustrates the improvement in throughput achieved by DSQPS when communicating over a distance of 40 m. The prompt collection of data from the sensor nodes increases throughput. Employing numerous mobile sinks minimizes packet losses to the greatest feasible degree.

Fig. 5 [Images not available. See PDF.]

Throughput comparison for a communication range of 20 m

Fig. 6 [Images not available. See PDF.]

Throughput comparison for a communication range of 40 m

Figure 7 presents the throughput comparison for different numbers of queries while keeping the network size fixed at 300 nodes and the sink speed at 8 km/h. The results demonstrate that DSQPS consistently outperforms QDWSN, QWRP, and QDVGDD, maintaining significantly higher throughput across all query levels. As the number of queries increases, throughput slightly declines due to the increased communication load, but DSQPS remains superior in handling multiple queries efficiently.

Fig. 7 [Images not available. See PDF.]

Throughput comparison for different numbers of queries

Figure 8 illustrates the impact of sink speed on throughput, with the network size fixed at 300 nodes. The results indicate that higher sink speeds generally lead to lower throughput for all approaches due to reduced data collection efficiency. However, DSQPS shows greater resilience to increasing sink speed compared to other algorithms, maintaining a higher throughput even at the maximum tested speed of 10 km/h. This highlights the effectiveness of DSQPS in adapting to varying sink mobility conditions.

Fig. 8 [Images not available. See PDF.]

Throughput comparison for different sink speeds

Network lifespan analysis

Network lifespan refers to the period starting from the deployment of the network until the last sensor node ceases to function, which may result in network partitioning or loss of coverage. This parameter explicitly denotes the duration until the final node in the network depletes its energy. It is computed using Eq. 29, where the value of i falls between the range of 1 to r.

29

$$N=\left\{\begin{array}{c}i\forall {\mathit{SN}}_{\mathit{re}}=0\\ otherwise\end{array}\right)$$

Figures 9 and 10 depict the outcomes of the network’s lifespan as the communication range of sensor nodes varies. Figure 9 shows that our strategy increases network longevity by 65.2% over QDWSN, 77.9% over QWRP, and 139.3% over QDVGDD. As shown in Fig. 10, our strategy improves network longevity by 69.2% compared to QDWSN, 113.1% compared to QWRP, and 150.9% compared to QDVGDD, over a communications range of 40 m. The enhanced network lifespan is attributed to carefully selecting optimum rendezvous points and efficiently utilizing the mobile sink-based query processing mechanism.

Fig. 9 [Images not available. See PDF.]

Network lifespan comparison for a communication range of 20 m

Fig. 10 [Images not available. See PDF.]

Network lifespan comparison for a communication range of 40 m

Figure 11 illustrates the network lifespan comparison for different numbers of queries, keeping the network size fixed at 300 nodes and the sink speed at 8 km/h. The results indicate that DSQPS significantly outperforms QDWSN, QWRP, and QDVGDD in terms of network lifespan across all query levels. As the number of queries increases, network lifespan decreases for all approaches due to the increased energy consumption. However, DSQPS demonstrates superior energy efficiency, maintaining a prolonged network lifespan even at higher query loads.

Fig. 11 [Images not available. See PDF.]

Network lifespan comparison for different numbers of queries

Figure 12 presents the network lifespan comparison for different sink speeds, with the network size fixed at 300 nodes. The results show that network lifespan generally decreases as sink speed increases due to higher energy consumption in frequent communication updates. Despite this trend, DSQPS consistently maintains a longer network lifespan compared to the other approaches, proving its efficiency in energy management and mobility-aware data collection strategies.

Fig. 12 [Images not available. See PDF.]

Network lifespan comparison for different sink speeds

Query processing delay analysis

This parameter represents the temporal interval between the query launched by the base station ($Q_{\mathit{BS}}^L$) and the response received by the base station ($Q_{\mathit{BS}}^R$), as determined by Eq. 30.

30

$$D={\sum }_{i=1}^r{Q}_{\mathit{BS}}^R-Q_{\mathit{BS}}^L$$

Figures 13 and 14 illustrate the comparison of query processing latency while using different communication ranges for sensor nodes. As shown in Fig. 13, DSQPS reduces query processing latency by 16.9% compared to QDWSN, 24.4% to QWRP, and 32.5% to QDVGDD, within a 20 m range. As shown in Fig. 14, DSQPS reduces query processing latency by 22% over QDWSN, 29.4% over QWRP, and 38.2% over QDVGDD within a 40 m communication range. The decrease in query processing duration is attributed to identifying the ideal number of mobile sinks using the AO algorithm, effectively reducing query injection and data collecting delay.

Fig. 13 [Images not available. See PDF.]

Query processing delay comparison for a communication range of 20 m

Fig. 14 [Images not available. See PDF.]

Query processing delay comparison for a communication range of 40 m

Figure 15 presents the query processing delay comparison for different numbers of queries, keeping the network size fixed at 300 nodes and the sink speed at 8 km/h. The results show that as the number of queries increases, the query processing delay rises across all algorithms due to higher data traffic and processing demands. However, DSQPS exhibits significantly lower delay compared to QDWSN, QWRP, and QDVGDD, demonstrating its superior efficiency in handling multiple queries by optimizing sink mobility and data retrieval processes.

Fig. 15 [Images not available. See PDF.]

Query processing delay comparison for different numbers of queries

Figure 16 illustrates the query processing delay comparison for different sink speeds, with the network size fixed at 300 nodes. The results indicate that higher sink speeds lead to increased query processing delays in all algorithms due to frequent location updates and increased data transmission complexity. Despite this trend, DSQPS consistently maintains the lowest delay, proving its effectiveness in optimizing query execution and reducing response times even under high-mobility conditions.

Fig. 16 [Images not available. See PDF.]

Query processing delay comparison for different sink speeds

Energy consumption analysis

Average energy consumption is the total energy consumed by all sensor nodes during data sensing, communication, and aggregation. The average energy consumption of a sensor node is determined by Eq. 31, where $E_i$ and $E_f$ denote the initial and final energy of the sensor nodes, respectively.

31

$$E=\frac{{\sum }_{i=1}^r{E}_f-E_i}{n}$$

An average energy consumption comparison between sensor nodes with a different communication range is shown in Figs. 17 and 18. Figure 17 shows that our strategy reduces average energy consumption by 14.6% compared to QDWSN, 21.1% compared to QWRP, and 30.7% compared to QDVGDD over a 20 m communication distance. With a 40 m communication range, Fig. 18 shows a reduction of 12.2% in energy consumption compared to QDWSN, 17.3% compared to QWRP, and 25.5% compared to QDVGDD using the proposed method.

Fig. 17 [Images not available. See PDF.]

Energy consumption comparison for a communication range of 20 m

Fig. 18 [Images not available. See PDF.]

Energy consumption comparison for a communication range of 40 m

Figure 19 illustrates the energy consumption trends as the number of queries increases, with a fixed network size of 300 nodes and a sink speed of 8 km/h. The results show that as more queries are processed, overall energy consumption rises due to the increased demand for data transmission and processing. However, DSQPS demonstrates superior energy efficiency, consistently consuming less energy compared to QDWSN, QWRP, and QDVGDD. This highlights its ability to optimize data collection and minimize unnecessary energy expenditure.

Fig. 19 [Images not available. See PDF.]

Energy consumption comparison for different numbers of queries

Figure 20 compares energy consumption at different sink speeds, keeping the network size constant at 300 nodes. The findings indicate that as the sink speed increases, energy usage also rises due to frequent location updates and additional communication overhead. Among all evaluated methods, DSQPS proves to be the most energy-efficient, effectively reducing power consumption by optimizing sink mobility and minimizing redundant data transmissions.

Fig. 20 [Images not available. See PDF.]

Energy consumption comparison for different sink speeds

Conclusions

This paper introduced DSQPS, a dynamic sink-based query processing strategy for IoT-enabled WSNs. DSQPS addressed the inherent challenges of traditional static sink-based data collection and query processing methods by incorporating a multi-faceted approach. The optimization of rendezvous points through a minimal set covering problem, coupled with applying the AO algorithm to optimize the number of mobile sinks, reflects the innovativeness of DSQPS. Furthermore, the computation of an optimized movement path for mobile sinks significantly reduced data collection and query processing delays. Extensive simulations are conducted to confirm the superiority of DSQPS compared to state-of-the-art methods. Obtained results suggested that DSQPS excels in minimizing query processing delays, reducing average energy consumption, and enhancing network longevity and throughput. DSQPS offers significant advantages for various real-world applications dependent on WSNs for efficient data collection. In environmental monitoring, DSQPS can enhance real-time data retrieval for tracking climate changes and pollution levels. Smart city solutions benefit from improved traffic and infrastructure monitoring. In disaster management, DSQPS can enable rapid data transmission for early warnings of earthquakes or floods. Healthcare monitoring systems can utilize DSQPS for patient tracking and vital signs monitoring. Furthermore, industrial IoT applications can leverage DSQPS for predictive maintenance and energy-efficient sensor data aggregation, enhancing overall system reliability and performance.

Subsequent research efforts should prioritize the efficiency of query processing techniques by tackling several crucial areas. Firstly, developing methods to adjust to fluctuating network circumstances and dynamic application needs will guarantee their ongoing optimization in dynamic IoT contexts. In addition, investigating sophisticated algorithms or heuristics for the energy-efficient routing of mobile sinks might enhance the system’s overall energy efficiency. It is essential to conduct real-world deployment tests, integrate with edge computing, and incorporate strong security mechanisms to prove the practical applicability and security resilience of methods in various circumstances. Furthermore, scalability analysis, cross-layer optimization, and user-centric customization capabilities will enhance the ability of the technique to accommodate large-scale deployments of IoT-enabled WSNs and meet the particular requirements of individual users.

Acknowledgements

Not applicable.

Authors’ contributions

DX contributed to writing the draft, editing the manuscript, and conceptualizing the research.

Funding

This work was supported by project of research on the Digital Twin Design and Application of Intelligent Agricultural Production Monitoring Systems in the Context of Rural Revitalization (No. KJQN202204009).

Data availability

The data that support the findings of this study are available on request from the corresponding author.

Declarations

Competing interests

There are no competing interests to declare.

Abbreviations

WSN

Wireless sensor network

IoT

Internet of things

DSQPS

Dynamic sink-based query processing strategy

AO

Aquila Optimizer

RFID

Radio frequency identification

RoI

Region-of-interest

QoQs

Quality of queries

ADAGA

Adaptive aggregation algorithm for sensor networks

GBT

Greedy and boundary traversal

TSP

Traveling salesperson problem

QWRP

Query-driven virtual wheel-based routing protocol

QDVGDD

Query-driven virtual grid-based data dissemination

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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