# What We Know So Far: Artificial Intelligence in African Healthcare

Naome Etori, Ebasa Temesgen, and Maria Gini

###### Abstract

Healthcare in Africa is a complex issue influenced by many factors including
poverty, lack of infrastructure, and inadequate funding. However, Artificial
intelligence (AI) applied to healthcare, has the potential to transform
healthcare in Africa by improving the accuracy and efficiency of diagnosis,
enabling earlier detection of diseases, and supporting the delivery of
personalized medicine. This paper reviews the current state of how AI
Algorithms can be used to improve diagnostics, treatment, and diseases
monitoring, as well as how AI can be used to improve access to healthcare in
Africa as a low-resource setting and discusses some of the critical challenges
and opportunities for its adoption. As such, there is a need for a well-
coordinated effort by the governments, private sector, healthcare providers,
and international organizations to create sustainable AI solutions that meet
the unique needs of the African healthcare system.

## Introduction

The application of AI in healthcare dates back to the 1950s. Researchers at
the Massachusetts Institute of Technology (MIT) developed “Project MAC” a
program to help analyze and interpret medical data, one of the first examples
of AI in healthcare. MAC stood for “machine-aided cognition” (Garfinkel 1999).

In the 1960s, AI was used to create knowledge-based expert systems, that mimic
the decision-making processes of human experts. The “MYCIN” system, developed
at Stanford University to aid in diagnosing and treating infectious diseases,
was an early example of an expert system in healthcare (Feigenbaum 1981).

During the 1980s and 1990s, AI-based Machine learning algorithms could learn
and adapt to new data without being explicitly programmed. This led to the
development of programs that could analyze medical images, such as X-rays, to
help diagnose diseases and AI algorithms used for diagnosing, identifying, and
analyzing public health threats (Kaul, Enslin, and Gross 2020).

More recently, the improvements in natural language processing (NLP) has been
used to understand and interpret human language. NLP techniques have been
applied in healthcare to extract and analyze data such as electronic health
records (EHRs),medical images and assist with tasks (such as appointment
scheduling and medication management). As a result of increases in computing
power, the availability of large amounts of data, and the rapid development of
big data analytics have enabled AI applications. Deep learning (DL) machine
learning technology, which involves training artificial neural networks (ANN)
on large datasets, has been a major driver of recent AI advances. This has
significantly impacted modernizing the global healthcare system to improve
diagnosis and clinical care accuracy and efficiency. A convolutional neural
network (CNN) is a type of DL algorithm that simulates the behavior of
interconnected neurons in the human brain (Kaul, Enslin, and Gross 2020).

The recent surge in AI healthcare research in Africa indicates the potential
of AI to improve patient outcomes and reduce the burden on the healthcare
system. This paper discusses AI algorithms (such as expert systems, machine
learning, deep learning, natural language processing, and image processing)
and how they are applied in the African healthcare systems, including
challenges in the application of AI systems in Africa as well as opportunities
for AI adoption.

## Problem Definition

There has been a lot of research on AI in healthcare, but there has been
minimal discussion about AI in African healthcare. AI researchers have also
found that there is a lack of diverse representation of AI models in
healthcare and particularly from low-resource languages. To fill this gap, we
address two main research questions:

RQ1: What role do AI algorithms play in African healthcare systems?

RQ2: How does a lack of resources impact AI implementation in Africa?

Our goal was to understand and explain the current integration and
implementation of AI in African healthcare systems to inspire future AI
research in African Healthcare.

## Related Work

Many researchers have shown that AI has the potential to improve patient care
and lower healthcare costs. Our review of the literature yielded the following
topics for discussion.

### Recent AI Advances in Healthcare in Developed Countries

AI has made significant advancements in the healthcare industry in developed
countries in recent years. This is because AI algorithms can handle and learn
from vast amount of healthcare data generated due to advancement of AI
technologies. Deep learning, in particular has impacted how we view AI tools
today and is the source of the recent advancement in AI applications (Bohr and
Memarzadeh 2020).

Sophisticated AI algorithms have been applied in diagnosis and treatment
planning to analyze medical images, such as X-rays and CT scans, to help
doctors diagnose diseases (Liu et al. 2020; Vaishya et al. 2020; Lin et al.
2019; Hu et al. 2018) and decide plan treatment. For example, (Lakshmanaprabu
et al. 2019; Holbrook et al. 2021; Makaju et al. 2018; Ardila et al. 2019)
shows how an AI algorithm was able to detect lung cancer from CT scans with a
very high degree of accuracy, comparable to that of an experienced
radiologist.

Big data has created opportunities for AI-based Machine learning (ML)
algorithms, enabling them to learn from previous data to make accurate
predictions about new data. This can assist healthcare providers in
prioritizing their resources and intervening before a patient condition
deteriorates(Senders et al. 2018; Stafford et al. 2020; Lee et al. 2018; Choi
et al. 2016).

Pharmaceutical companies use AI algorithms to identify new candidates for drug
development and analyze the effects of different drugs (David et al. 2020;
Paul et al. 2021; Smith, Roitberg, and Isayev 2018; Smalley 2017; Fleming
2018; Chan et al. 2019; Lavecchia 2019).

AI-powered Virtual assistants help triage patients and provide them with
information about their condition and treatment options (Bharti et al. 2020;
Bates 2019; Fadhil 2018)

The use of clinical decision support (Loftus et al. 2020; Lysaght et al. 2019)
and medication management (Howe, Gardner, and Kadel 2006) have improved
patient care while reducing the workload for healthcare professionals in
hospitals.

### Recent AI Advances in African Healthcare

AI has enormous potential to help in the prediction and prevention of
outbreaks of infectious diseases. Data from the World Health Organization
(WHO) (Nkiruka, Prasad, and Clement 2021) shows the relationship between
malaria incidence and various climate variables, found that specific patterns
in the data were indicative of increased malaria risk, and used machine
learning algorithms to create a model for predicting malaria incidence based
on these patterns. Research conducted by (Colubri et al. 2016) used past Ebola
outbreak data to train the ML algorithm to accurately predict the outcomes of
Ebola patients with a high degree of accuracy which could be used in future
outbreaks to help guide clinical decision-making and improve patient outcomes.

AI can improve the accuracy of diagnoses and treatment recommendations in
Africa. Due to a lack of resources for optimal healthcare provision, trained
physicians, and underfunded public healthcare facilities, ML models can be
used to analyze medical images and provide diagnoses and chronic diseases such
as cancer. (Adeoye et al. 2022) shows the application and implementation
phases of oncological AI tools in Africa using patient cohorts in Africa.

### Status of AI in African Healthcare system

The application of AI in the African healthcare system is still in its early
stages. However, there is a growing interest and investment in the
implementation of AI to improve different aspects of healthcare delivery in
Africa. However, the implementation of AI in Africa confronts numerous
challenges(Owoyemi et al. 2020). Many African countries, for example, still
have limited access to reliable electricity and to high-speed internet, making
it challenging to implement and use AI systems. The successful implementation
of AI in health care depends on the availability and dependability of the
infrastructure(Mbunge, Muchemwa, and Batani 2022).

For many years, African healthcare systems have suffered from man-made issues
such as institutional, human resource, financial, technical, and political
developments (Oleribe et al. 2019). Hence, most African countries cannot meet
the fundamental requirements for effective healthcare systems. Ineffective
service integration is linked to poor governance, and human resource
challenges (Nutbeam 2000; Marais and Petersen 2015). The lack of basic access
to healthcare makes it even harder to implement AI solutions (Tran et al.
2019).

Additionally, the scarcity of trained professionals with expertise in AI in
Africa is a major concern; hence, many healthcare systems are struggling to
meet the rising demand for services while also facing significant shortages of
trained health workers and essential medicines (Naicker et al. 2009; Guo and
Li 2018). As a result, most African countries rely heavily on developed
nations for AI technologies to solve critical healthcare challenges due to
inadequate funding (Guo and Li 2018).

Ethical considerations around the use of AI in healthcare in Africa, including
issues related to data privacy and the potential for biased decision-making
could contribute to slow AI implementation in the African region (Hagerty and
Rubinov 2019).

### AI Gaps in Africa: Key Challenges

African healthcare systems are lagging in implementing AI mainly due to lack
of resources. Implementing AI in healthcare can be expensive, and securing
funding for such initiatives can be challenging in most African countries.
Ensuring that AI models are sustainable in the long term is also an important
consideration (Wakunuma, Jiya, and Aliyu 2020).

  * •

There is often a lack of high-quality data available for training machine
learning models due to poor record-keeping and inadequate infrastructure for
data collection and storage. For example, doctors and nurses still use hand
written notes when seeing patients. This can make it difficult to develop
accurate and effective AI systems for the African region. Prior studies have
demonstrated disparate AI performance by race AI models, especially on African
datasets. The training datasets may not be representative of the African
population. If the datasets used to train the models are not diverse or
representative enough, the models may not be able to generalize well to new,
unseen data from Africa population (Banerjee et al. 2021; Kamulegeya et al.
2019; Harmon et al. 2020; Obermeyer et al. 2019).

  * •

Furthermore, the AI models may not have been specifically designed to handle
the unique challenges present in African datasets. For example, African
datasets may contain a greater variety of languages, dialects, and accents,
and the models may not have been trained on data that reflects this linguistic
diversity. In addition, there may be other cultural and societal factors that
are unique to Africa that the models have not been designed to handle.
According to estimates, 17% of the world’s languages, many of which are spoken
in Africa, are ”low-resource languages” in the digital realm (Gwagwa et al.
2020).

  * •

Despite these challenges, there have been some efforts to improve healthcare
in Africa. For example, some African governments have increased funding for
healthcare, and there have been efforts to train more healthcare professionals
and build new healthcare facilities, as many developing countries are
attempting to move more towards universal healthcare coverage (Lagomarsino et
al. 2012). In addition, some international organizations and charities have
provided assistance to boost the delivery of healthcare in Africa (Gibbs 2014;
Beigbeder 1991).

## Methodology

This paper reviews the current state of AI in healthcare in Africa, including
the challenges and opportunities for its adoption. A comprehensive search of
the literature was conducted using several databases. The survey reviewed 30
journal papers obtained electronically through four scientific databases
(Google Scholar, Scopus, IEEE, Pum Med, and Science Direct) searched using
three sets of keywords: (1) Artificial Intelligence in Africa (2) Artificial
Intelligence in Healthcare (3) African Healthcare Systems. We limited our
search to articles that made algorithmic contributions and addressed diseases
in their applications. We disqualified papers that only provided opinions,
theories, surveys, or datasets. This yielded a total of 12 papers.

## Findings

### RQ1: Role of AI Algorithms on African Healthcare

Based on our findings, different algorithms have been used to address
different healthcare, such as Expert systems, machine learning, and deep
learning. Although expert systems have been extensively researched globally,
little research has been conducted on its application in African healthcare
systems. Expert systems can be beneficial, especially where scarcity of
trained physicians and medical personnel exists, as is usually the case in
African countries. Expert systems can help African healthcare systems diagnose
patients and select treatment plans without extensively trained medical
personnel, where a decision must be made quickly to save lives (Wahl et al.
2018). An example is where an expert system has been incorporated with fuzzy
logic systems, to improve the diagnosis of chronic conditions like STDs,
HIV/AIDS, cholera, abdominal pain, and diabetes decision support application
in South Africa (Mburu, Lee, and Mbogho 2012; Thompson et al. 2017; Fathi-
Torbaghan and Meyer 1994; Fleming, Van der Merwe, and McFerren 2007; Lee and
Wang 2010).

Natural language processing (NLP) has been used in developing a Medical
Chatbot to diagnose patients in their early stages of the disease or to use
social media data for surveillance and monitoring of infectious disease
outbreaks (Gupta and Katarya 2020; Abdelwahap, Elfarash, and Eltanboly 2021).
The use of NLP in African healthcare is still at its infancy stage. (Li et al.
2020) conducted mental health condition research following the outbreak of
coronavirus(COVID-19), using Twitter data from Nigeria and South Africa.
(Oyebode and Orji 2018) demonstrated that Likita, a chatbot, could be used to
diagnose common ailments and improve healthcare delivery in Africa.

Deep learning (DL) can process large amounts of data, such as images, and
could potentially aid medical workers in decision-making, using an X-ray image
to analyze multiple diseases. For instance, (Stephen et al. 2019) used X-ray
images to classify Pneumonia with a validation accuracy of 93.73%. (Simi
Margarat et al. 2022) also used X-ray data to diagnose early stage
Tuberculosis using a DL algorithm and achieved 99% accuracy. (Holbrook et al.
2021) used three pre-trained DL models (faster R-CNN, single-shot multi-box
detector (SSD), and RetinaNet) for the microscopic diagnosis of malaria
parasites, malaria is one of the deadliest diseases in Sub-Sahara Africa in
thick blood smears. The result found that a faster R-CNN has a higher accuracy
than the other two models used in the study with an average precision of over
0.94. Hence this approach can improve the accuracy and efficiency of malaria
diagnosis compared to traditional methods.

ML models are used to predict and classify chronic diseases in Africa. They
are gaining popularity for their simplicity and the availability of data in a
few African countries. Table 1 has summarized some of the research on applying
AI to address different diseases in African countries.

### RQ2: How does the lack of resources impact AI implementation in Africa?

African healthcare systems suffer from the lack of data access due to
inadequate resources, which is often a key ingredient in the development and
training of AI systems. Lack of infrastructure and investment in data
collection and storage has made it difficult for organizations to obtain the
data they need to develop and train AI systems (Banerjee et al. 2021;
Kamulegeya et al. 2019; Harmon et al. 2020; Obermeyer et al. 2019)

Table 1: Application of AI and Machine Learning in Africa healthcare System Disease |  Country |  Algorithm |  Dataset |  Accuracy |  Reference
---|---|---|---|---|---
HIV/AIDS |  S.Saharan.A |  XGBoost |  PHIA |  90% males, 92% female |  (Mutai et al. 2021)
HIV/AIDS |  Kenya, Uganda |  - |  Data from 16 communities |  78% |  (Balzer et al. 2020)
Malaria |  Burkina Faso |  Random forest |  georeferenced raster(SPOT) |  84% |  (Taconet et al. 2021)
Ebola |  W.Africa |  Central Bayesian |  842 molecules |  83% |  (Anantpadma et al. 2019)
Colorectal Cancer |  S.Africa |  Artificial NN |  WDGMC CRC |  87.0% |  (Achilonu et al. 2021)
Breast cancer |  Nigeria |  Random Forest |  Surgical data(LASUTH) |  96.67% |  (Macaulay et al. 2021)
Cervical cancer |  African countries |  Ensemble learning |  SMOTE |  87.21% |  (Ahishakiye et al. 2020)
COVID-19 |  African Countries |  Ensemble |  (WHO) database |  MAD = 0.0073, MSE = 0.0002, R2 = 0.9616 |  (Ibrahim et al. 2023)
Diabetes |  Nigeria |  Binarized Naïve Bayes (BNB) |  Collected(nairaland) |  87.08% |  (Oyebode and Orji 2019)
Coronary Heart D |  South Africa |  Naïve Bayes,SVM and Decision Tree |  S.Africa-KEEL |  higher than 70% |  (Gonsalves et al. 2019)
Obstetric Fistula |  Tanzania |  Logistic Regression |  Collected from CCBRT,Dar-es-Salaam |  86% |  (Fihavango et al. 2021)
Malaria |  Sub-Saharan |  Decision Tree |  (WHO) datasets |  75.10% |  (Masinde 2020)

AI in African healthcare has generally been used in diseases mapping such as
HIV. ML techniques identify HIV predictors for screening in sub-Saharan Africa
(Mutai et al. 2021), malaria predictions (Nkiruka, Prasad, and Clement 2021).
Even though African healthcare systems strive to implement AI to assist with
healthcare operations, it is still difficult to respond to public health
emergencies such as disease outbreaks, resulting in increased mortality and
morbidity.

## Discussion

AI has been applied in various healthcare settings in Africa, as shown in
Table 1. Hence has the potential to significantly improve Human
Immunodeficiency Virus (HIV) care in Africa by providing more accurate
diagnoses, predicting patient outcomes, and optimizing treatment programs. For
example, (Bauer and Schedl 2019) used DL to improve the accuracy of HIV
diagnoses in sub-Saharan Africa, (Mutai et al. 2021) applied ML approaches for
building models in identifying HIV predictors as well as predicting persons at
high risk of infection, the XGBoost algorithm significantly improved the
identification of HIV positivity by f1 scoring mean of 90 and 92% for males
and females. respectively. Also, (Balzer et al. 2020) used ML to Identify
Persons at High-Risk of HIV Acquisition in rural Kenya and Uganda, and the
result shows that ML improved efficiency by 78%.

Malaria has been (and still is) a major public health crisis in Africa, with
an estimated 435 million cases and 1.3 million deaths yearly (WHO, 2021).
Experts say malaria slows economic growth in Africa by up to 1.3 percent per
year. AI can be used in the fight against malaria in Africa; for example,
(Taconet et al. 2021) used data-driven and interpretable ML modeling Algorithm
(Random Forest) to explore malaria vector biting rates in rural Burkina Faso.
The results identified several aspects of the bio-ecology of the main malaria
vectors (Masinde 2020) Decision trees algorithm and climate data produced
accuracy results of 99%.

Furthermore, AI has the potential to significantly improve the response to
Ebola outbreaks in Africa by providing more accurate and timely predictions,
faster diagnoses, and more efficient use of resources; for example, Bayesian
(ML) Models were used to enable new in Vitro Leads(Anantpadma et al. 2019;
Lane et al. 2019).

Research has highlighted the potential benefits of using AI to improve cancer
diagnosis and treatment in Africa. For example, in predicting colorectal
cancer recurrence and patient survival using Artificial neural network(ANN), a
supervised ML approach where scored the highest AUC-ROC for recurrence (87%)
and survival (82%) in South Africa (Achilonu et al. 2021). Random forest (ML)
models have been used in Breast cancer risk prediction among African women in
Nigeria by (Macaulay et al. 2021); the Chi-Square selected features gave the
best performance with 98.33% accuracy, 100% sensitivity, 96.55% specificity,
and 98% AUC. Also,(Ahishakiye et al. 2020) predicted Cervical Cancer Based on
risk factors using the Ensemble Learning model with an accuracy of 87.21%.

Since the COVID-19 pandemic, the demand for use of AI in the African
healthcare sector to aid in the pandemic response has increased. Many African
countries have been conducting studies on this area; for example, (Ibrahim,
Tulay, and Abdullahi 2022) conducted a study to predict daily COVID-19 cases
spreading across the north, south, east, west, and central Africa regions and
countries using ML, including Artificial neural network(ANN), adaptive neuro-
fuzzy inference system (ANFIS), support vector machine (SVM) and convent and
the result shows high accuracy performance.

According to the International Diabetes Federation (IDF), 24 million adults
(ages 20-79) have diabetes, which accounts for 416,000 deaths in the IDF
Africa Region in 2021. AI can potentially improve diabetes care in Africa by
improving access to care and providing more personalized treatment options.
For example, using social media and ML (Oyebode and Orji 2019) detected
factors responsible for Diabetes prevalence in Nigeria.

Management and treatment of coronary heart disease (CHD) in African healthcare
systems have been a huge challenge. Recently, there has been a growing
recognition of the potential for AI to improve CHD disease treatment and care.
For example, by using historical medical and ML models such as Naïve Bayes,
SVM, and Decision Tree (DT) data to predict CHD (Gonsalves et al. 2019).

WHO estimated more than 2 million young women live with untreated obstetric
fistula (OF) in Asia and sub-Saharan Africa. Limited research on the use of AI
in obstetric fistula disease management and treatment in Africa has been seen.
For example, (Fihavango, Mohsini, and Mselle 2021) used Data Mining techniques
to Predict Obstetric Fistula in Tanzania.

This survey did not cover the entire African continent. The results are
promising, and the future of AI tools and algorithms to improve healthcare in
the African continent look promising.

## Conclusions

AI has the potential to predict and control diseases, expand and augment
service delivery, and address several lingering social inequities by improving
the accuracy and efficiency of diagnosis, enabling earlier detection of
diseases, and supporting the delivery of personalized medicine. However,
several challenges must be addressed to realize its full potential, including
the lack of infrastructure, limited access to data, and the need for
regulatory frameworks. African countries must build the necessary
infrastructure to support technological advancements. This can include
investing in high-speed internet, data centers, and cyber security systems.
Governments can help promote the development and adoption of AI by
establishing clear AI regulatory standards. Private sector, healthcare
providers, partnership with international stakeholders can design a
sustainable AI solutions that meet the unique needs of the African healthcare
system

## Future Work

AI and machine learning are critical to addressing health care inadequacies in
African countries. AI models may perform poorly on African datasets, However,
to improve the performance of AI models on African datasets, it will be
necessary to create a more diverse and representative datasets as well as
design models that are specifically tailored to deal with the unique
challenges presented in African data.

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# Probabilistic On-Demand Charging Scheduling for ISAC-Assisted WRSNs with
Multiple Mobile Charging Vehicles

Muhammad Umar Farooq Qaisar11, Weijie Yuan11, Paolo Bellavista2,
Guangjie Han3, Rabiu Sale Zakariyya1, and
Adeel Ahmed4 1 Department of Electronic and Electrical Engineering, Southern
University of Science and Technology, Shenzhen, China
2 Department of Computer Science and Engineering, University of Bologna,
Bologna, Italy
3 Department of Internet of Things Engineering, Hohai University, Changzhou,
China
4 School of Computer Science and Technology, University of Science and
Technology of China, Hefei, China
1Corresponding authors: Weijie Yuan and Muhammad Umar Farooq Qaisar,
Email:{yuanwj<EMAIL_ADDRESS>
###### Abstract

The internet of things (IoT) based wireless sensor networks (WSNs) face an
energy shortage challenge that could be overcome by the novel wireless power
transfer (WPT) technology. The combination of WSNs and WPT is known as
wireless rechargeable sensor networks (WRSNs), with the charging efficiency
and charging scheduling being the primary concerns. Therefore, this paper
proposes a probabilistic on-demand charging scheduling for integrated sensing
and communication (ISAC)-assisted WRSNs with multiple mobile charging vehicles
(MCVs) that addresses three parts. First, it considers the four attributes
with their probability distributions to balance the charging load on each MCV.
The distributions are residual energy of charging node, distance from MCV to
charging node, degree of charging node, and charging node betweenness
centrality. Second, it considers the efficient charging factor strategy to
partially charge network nodes. Finally, it employs the ISAC concept to
efficiently utilize the wireless resources to reduce the traveling cost of
each MCV and to avoid the charging conflicts between them. The simulation
results show that the proposed protocol outperforms cutting-edge protocols in
terms of energy usage efficiency, charging delay, survival rate, and travel
distance.

###### Index Terms:

Wireless rechargeable sensor networks, on-demand, partial charging, ISAC,
mobile charging vehicles.

††publicationid: pubid:  979-8-3503-1090-0/23/$31.00 © 2023 IEEE

##  I Introduction

The internet of things (IoT) based wireless sensor networks (WSNs) have seen
significant growth in a broad range of applications over the last decades,
including industrial automation, military applications, smart cities,
environmental monitoring, and healthcare. A WSN is composed of numerous
battery-operated sensor nodes that continuously monitor the state of the
environment and send the sensed data to a sink through single or multi-hop
communication. A low battery level in sensor nodes can reduce the lifetime of
WSNs [1, 2]. Due to the small batteries that power the sensor nodes, energy
consumption becomes a significant challenge for WSN applications. In recent
years, numerous research studies have been conducted to extend network
lifetime. These studies are classified into two categories: energy
replenishment [3] and energy conservation [4].

Wireless Power Transfer (WPT) technology has made it possible to effectively
replenish the energy in wireless rechargeable sensor networks (WRSNs). A WRSN
generally consists of three components: a sink that also serves as a depot for
mobile charging vehicles (MCVs), single or multiple MCVs, and sensor nodes
with rechargeable batteries that allow MCVs to recharge them by transmitting
wireless signals [5]. The way the sensor nodes are recharged allows the WRSNs
to operate continuously in an efficient manner [6].

The MCVs generally use one of two fundamental charging scheduling strategies:
on-demand charging [7] and periodic charging [8]. In periodic charging, an MCV
travels the network according to a predetermined and known schedule.
Unfortunately, due to the dynamic energy depletion rate of the nodes, this
charging schedule is not ideal. On the contrary, on-demand charging appears to
be more realistic because it makes real-time decisions based on the energy
requirements of the sensor nodes. Therefore, it can handle situations where
the node's energy depletion rate is highly unpredictable. Moreover, charging
strategies generally follow either full charging or partial charging models.
In a full-charging model, the sensor nodes receive a full recharge to their
battery capacity, resulting in significant charging delays. In contrast, the
partial charging model allows for more sensor nodes to be recharged. However,
in a charging process, the traveling time and conflicting between multiple
MCVs must also be addressed properly.

To address the aforesaid issue, we intend to employ the Integrated Sensing and
Communication (ISAC) technique [9], which combines sensing and communication
functionality to efficiently use wireless resources, realize wide area
environment sensing, and even to pursue mutual benefits. Therefore, ISAC can
improve charging efficiency and reduce travel time of MCVs by leveraging the
benefits of wireless signal [10]. A charging node can be in a priority queue
of multiple MCVs but with different priorities. Thus, whenever an MCV enters
the sensing range of a prioritized charging node, the node will send the ISAC
signal to the MCV, receive the echo from the MCV via wireless transmission,
analyze it, and then communicate with the sink node to update the priority
queues of other MCVs. This mechanism significantly reduces travel time and
avoids conflicts when multiple MCVs attempt to overcharge a node in a single
request.

The aforementioned studies have provided convincing motivations to address the
issues of deploying multiple MCVs and developing an effective on-demand
charging strategy for sensor nodes, as well as integrating the ISAC concept
with WRSNs to optimize network stability. Therefore, this paper proposes a
probabilistic on-demand charging scheduling for ISAC-assisted WRSNs with
multiple mobile charging vehicles (Poised). The contribution of our paper lies
in several unique aspects. Firstly, it offers a balanced charging load
strategy on each MCV priority queue by utilizing four attributes with their
probability distributions, namely the residual energy of the charging node,
the distance from the MCV to the charging node, the degree of a charging node,
and the charging node betweenness centrality. These attributes help achieve
charging efficiency and network lifetime. Secondly, it employs a charging
factor strategy for each MCV queue, which partially charges all nodes while
further improving charging efficiency and coverage. Lastly, the integration of
the ISAC concept with WRSNs efficiently utilizes wireless resources to reduce
travel time and avoid conflicts between multiple MCVs overcharging the same
node. The primary goal of our paper is to provide a well-balanced charging
strategy for multiple MCVs with an efficient on-demand charging strategy to
optimize charging efficiency. Additionally, we integrate sensing and
communication techniques to reduce MCV travel time within the network, thereby
improving network stability. The unique aspects and contributions of our
approach make our proposal an innovative and effective solution to the
identified issues.

##  II Related Work

This section provides a brief overview of several studies on WRSNs energy
replenishment that are relevant to our work.

The authors of [11] developed a charging method that clusters the energy
requirements of nodes in order to equally distribute the charging load across
the MCVs. It reduces the charging delay to some extent by increasing the
number of recharged nodes. In [12] and [13], the authors introduced charging
scheduling approaches for the problem of minimizing the longest delay. To
prevent a sensor node from being charged by two or more MCVs at once, they
sought to identify a closed charging tour for each MCV. However, the charging
load across the MCVs were unbalanced due to their methodology. The authors of
[7] introduced a distributed mobile charging protocol to schedule multiple
MCVs in dense WRSNs. They focused on an on-demand partial charging strategy
and applied a game theory technique to address the multiple charging problem,
which resulted in repetitive games played by the MCVs. Their approach reduced
charging delay to some extent by improving charging coverage. The authors of
[14] addressed the problem of multiple MCVs coordination, which consists of
scheduling multiple chargers and optimizing travel time with the goal of
reducing the overall energy usage of MCVs by modifying their mobility speed
and charging time. The authors of [15] introduced an uneven cluster-based
mobile charging approach that allocates nodes into clusters and then focuses
on the charging schedule for each MCV while taking remaining energy and sensor
node distance into account. Despite this, their approach has a lower charging
efficiency. The authors of [6] introduced a charging scheduling approach based
on fuzzy logic with multiple MCVs. Their approach divides the network to
evenly distribute the charging load of sensor nodes on each MCV, and it also
determines a dynamic charging threshold for each node depending on their
respective energy usage rates. Furthermore, for each MCV, the next node to be
charged is determined by combining fuzzy logic and multi-metric inputs.
However, due to an inefficient multi-metric strategy, their approach falls
short in the efficient selection of the next node to be charged. The authors
of [16] introduced an approach for reducing charging delays by charging sensor
nodes with multiple MCVs. Unlike prior studies, the travel trajectories of
MCVs were predetermined, and their speed was varied.

The aforementioned approaches demonstrated the feasibility and acceptability
of charging scheduling strategies in WRSNs. However, these approaches lacked a
combined focus on an effective multi-metric strategy for balancing the
charging load on the MCVs and an efficient charging factor strategy for each
MCV to partially charge the network nodes. Additionally, they did not
effectively address the issue of reducing travel time for multiple MCVs and
their charging conflicts in the network. Therefore, this paper attempts to
address the aforesaid issues by employing an effective multi-metric and
efficient charging factor strategy. It also applies ISAC in WRSNs to reduce
travel time and avoid charging conflicts through sensing and communication
tasks between charging nodes and MCVs.

##  III The Proposed Protocol

This paper proposes probabilistic on-demand charging for ISAC-assisted WRSNs
with multiple mobile charging vehicles (Poised), and it goes into detail about
effective strategies for balancing the charging load on each MCV. It also
partially charges all of the nodes in their queues in an efficient manner to
improve charging coverage and efficiency. Furthermore, it integrates the ISAC
concept by utilizing wireless resources to reduce the traveling time of each
MCV in the network.

###  III-A Network Model and Initialization

A standard wireless rechargeable sensor network is assumed to consist of a set
of randomly deployed sensor nodes,
$\mathcal{N}=\\{{Sn_{0},Sn_{1},Sn_{2},...,Sn_{r}}\\}$ and a set of mobile
charging vehicles (MCVs),
$\mathcal{V}=\\{{Cv_{1},Cv_{2},Cv_{3},...,Cv_{m}}\\}$, with $m=|\mathcal{V}|$
in a two-dimensional region. When the energy level of the sensor nodes
($Sn_{i}$) falls below a certain level called threshold ($\mathcal{E}_{th}$),
charging requests are sent to the sink node ($Sn_{b}$). The sink is positioned
in the center of the region and also serves as a depot for the MCVs. In this
work, the initial position of the MCVs is adapted from [7]. The Eq. (1) is
employed in particular to determine the coordinates $(x_{i},y_{i})$ of MCVs
initial position in $k$ different regions.

$\small(x_{i},y_{i})=\left(\frac{\mathcal{C}_{c}}{2}\cos{\left(\frac{\pi}{m}(2j-1)\right)},\frac{\mathcal{C}_{c}}{2}\sin{\left(\frac{\pi}{m}(2j-1)\right)}\right)$
(1)

Here, $\mathcal{C}_{c}$ is the radius of circumscribed circle of a two-
dimensional region. The MCV recharges one sensor node ($Sn_{i}$) at a time. It
should be noted that an MCV has a substantially higher energy capacity than a
sensor node ($Sn_{i}$). Table I provides a summary of the notations used in
this work.

TABLE I: Notations Notation |  Definition
---|---
$\mathcal{N}$ |  $\mathcal{N}=\\{{Sn_{0},Sn_{1},Sn_{2},...,Sn_{r}}\\};Sn_{i}\in\mathcal{N}$ is a sensor node$;r$ is the size of $\mathcal{N}$.
$\mathcal{N}_{i}$ |  The neighboring nodes of $Sn_{i}$; $r_{i}$ is the size of $\mathcal{N}_{i}$.
$\mathcal{V}$ |  $\mathcal{V}=\\{{Cv_{1},Cv_{2},Cv_{3},...,Cv_{m}}\\};Cv_{j}\in\mathcal{V}$ is a mobile charging vehicle$;m$ is the size of $\mathcal{V}$.
$Sn_{s}$ |  The source node.
$Sn_{b}$ |  The sink.
$\mathcal{R}_{s}$ |  The sensing range of node $Sn_{i}$.
$\mathcal{R}_{c}$ |  The communication range of node $Sn_{i}$.
$\mathcal{E}_{th}$ |  The residual energy threshold of node $Sn_{i}$.
$\mathcal{CE}_{th}$ |  The minimum working energy threshold of MCV $Cv_{j}$.
$\Phi_{i}^{\downarrow}$ |  The residual energy of node below threshold $\mathcal{E}_{th}$.
$\zeta_{i}$ |  The distance from MCV $Cv_{j}$ to node $Sn_{i}$.
$\eta_{i}$ |  The degree of node $Sn_{i}$.
$\ss_{i}$ |  The node $Sn_{i}$ betweenness centrality.
$\mathcal{C}_{c}$ |  The radius of circumscribed circle.
$e$ |  The Euler's Constant. Its approximate value is 2.71828.
$\pi$ |  The default value of Pi is approximately equal to 3.14159.

###  III-B Charging Queue Metric

This section describes the balanced charging load strategy for each MCV queue,
which considers the four important attributes and their respective probability
distributions to prioritize the charging queue metric. These attributes are
the residual energy of charging node Eq. (3), distance from MCV to charging
node Eq. (6), degree of a charging node Eq. (9), and charging node betweenness
centrality Eq. (12). The charging queue metric will prioritize the charging
nodes with highest value. Therefore, each MCV will have a different sequence
of prioritized charging nodes due to their different locations in the network
as described in Section III-A.

####  III-B1 Residual Energy of Charging Node

The purpose of this distribution is to prioritize the sensor nodes which have
the lower residual energy among all the charging sensor nodes. Here, we
express the residual energy of a charging sensor node
$(i.e.,\forall\,Sn_{i}\in\mathcal{N})$ as a vector,
$\Phi_{i}^{\downarrow}=(\Phi_{1}^{\downarrow},\Phi_{2}^{\downarrow},\Phi_{3}^{\downarrow},...,\Phi_{r}^{\downarrow})$,
where $\Phi_{i}^{\downarrow}$ is the residual energy of a charging sensor node
below the residual energy threshold $\mathcal{E}_{th}$. The residual energy
vector is normalized into
$\bar{\Phi}_{i}^{\downarrow}=(\bar{\Phi}_{1}^{\downarrow},\bar{\Phi}_{2}^{\downarrow},\bar{\Phi}_{3}^{\downarrow},...,\bar{\Phi}_{r}^{\downarrow})$
between $[0-1]$ using Eq. (2). Based on it by curve fitting the normalized
vector, we obtain the probability distribution function using Eq. (3),
$\tilde{\Phi}_{i}=(\tilde{\Phi}_{1}^{\downarrow},\tilde{\Phi}_{2}^{\downarrow},\tilde{\Phi}_{3}^{\downarrow},...,\tilde{\Phi}_{r}^{\downarrow})$.
Furthermore, we included a weighted factor $\lambda_{\Phi}$ to increase the
impact of the distribution, where $\lambda_{\Phi}\geq 2$ is set by default.
Nodes with lower residual energy will have higher charging priority.

$\bar{\Phi}_{i}^{\downarrow}=\frac{\Phi_{i}^{\downarrow}}{\mathcal{E}_{th}}\quad\forall\,Sn_{i}\in\mathcal{N}$
(2)

$\begin{array}[]{c@{\,}c}\tilde{\Phi}_{i}^{\downarrow}=\begin{cases}\alpha+\beta*\mathrm{e}^{\left(\gamma*\left(\bar{\Phi}_{i}^{\downarrow}\right)^{\lambda_{\Phi}}\right)}\\\
\alpha=4.1997;\quad\beta=-3.16759;\\\ \gamma=0.27897;\quad\lambda_{\Phi}=2;\\\
\end{cases}\,\forall\,Sn_{i}\in\mathcal{N}\end{array}$ (3)

####  III-B2 Distance from MCV to Charging Node

The purpose of this distribution is to prioritize the sensor nodes which have
the shortest distance among all the charging sensor nodes to MCV. Here, we use
the Euclidean Distance to express the distance from each MCV
$(i.e.,\forall\,Cv_{j}\in\mathcal{V})$ to charging sensor node
$(i.e.,\forall\,Sn_{i}\in\mathcal{N})$ as a vector,
$\zeta_{v_{j},i}=(\zeta_{v_{j},1},\zeta_{v_{j},2},\zeta_{v_{j},3},...,\zeta_{v_{j},r})$,
which is obtained in Eq. (4). The distance vector is normalized into
$\bar{\zeta}_{v_{j},i}=(\bar{\zeta}_{v_{j},1},\bar{\zeta}_{v_{j},2},\bar{\zeta}_{v_{j},3},...,\bar{\zeta}_{v_{j},r})$
between $[0-1]$ using Eq. (5). The probability distribution function is used
to curve fit the normalized vector, as stated in Eq. (6),
$\tilde{\zeta}_{v_{j},i}=(\tilde{\zeta}_{v_{j},1},\tilde{\zeta}_{v_{j},2},\tilde{\zeta}_{v_{j},3},...,\tilde{\zeta}_{v_{j},r})$.
Furthermore, we included a weighted factor $\lambda_{\zeta}$ to increase the
impact of the distribution, where $\lambda_{\zeta}\geq 1$ is set by default.
The shorter the distance to MCV will have higher priority of a charging sensor
node.

$\zeta_{v_{j},i}=\sqrt{(x_{j}-x_{i})^{2}+(y_{j}-y_{i})^{2}}$ (4)

$\bar{\zeta}_{v_{j},i}=\frac{\zeta_{v_{j},i}}{\zeta_{v_{j},i}+\mathcal{R}_{c}}\quad\forall\,Sn_{i}\in\mathcal{N}$
(5)

$\begin{array}[]{c@{\,}c}\tilde{\zeta}_{v_{j},i}=\begin{cases}\alpha+\beta*\mathrm{e}^{\left(\frac{\left(\left(\bar{\zeta}_{v_{j},i}\right)^{\lambda_{\zeta}}-\gamma\right)}{\mu}\right)}\\\
\alpha=1.83283;\quad\beta=-0.69354;\\\ \gamma=-0.24143;\quad\mu=1.28078;\\\
\lambda_{\zeta}=1;\\\ \end{cases}\,\forall\,Sn_{i}\in\mathcal{N}\end{array}$
(6)

####  III-B3 Degree of Charging Node

The purpose of this distribution is to prioritize the sensor nodes which have
maximum number of neighbors among all the charging sensor nodes. Here, we
express the degree of charging sensor node
$(i.e.,\forall\,Sn_{i}\in\mathcal{N})$ as a vector,
$\eta_{i}=(\eta_{1},\eta_{2},\eta_{3},...,\eta_{r})$, which is obtained in Eq.
(7). The degree vector is normalized into
$\bar{\eta}_{i}=(\bar{\eta}_{1},\bar{\eta}_{2},\bar{\eta}_{3},...,\bar{\eta}_{r})$
between $[0-1]$ using Eq. (8). The normalized vector is curve fitted with the
probability distribution function, as indicated in Eq. (9),
$\tilde{\eta}_{i}=(\tilde{\eta}_{1},\tilde{\eta}_{2},\tilde{\eta}_{3},...,\tilde{\eta}_{r})$.
Furthermore, we included a weighted factor $\lambda_{\eta}$ to increase the
impact of the distribution, where $\lambda_{\eta}\geq 1$ is set by default.
The charging sensor node with the maximum number of neighboring nodes will
have a higher priority.

$\eta_{i}=\sum_{v=1}^{r_{i}}{Sn_{i,v}}\\\ $ (7)

$\bar{\eta}_{i}=\frac{\eta_{i}}{\max\\{\eta_{i}|Sn_{i}\in\mathcal{N}\\}}\quad\forall\,Sn_{i}\in\mathcal{N}$
(8)

$\begin{array}[]{c@{\,}c}\tilde{\eta}_{i}=\begin{cases}\alpha+\beta*\left(\frac{\left(\mathrm{e}^{\left(\gamma*\left(\bar{\eta}_{i}\right)^{\lambda_{\eta}}\right)}-\mu\right)}{\gamma}\right)\\\
\alpha=0.02098;\quad\beta=1.29332;\\\ \gamma=-0.4591;\quad\mu=0.978;\\\
\lambda_{\eta}=1;\end{cases}\,\forall\,Sn_{i}\in\mathbb{N}\end{array}$ (9)

####  III-B4 Charging Node Betweenness Centrality

The purpose of this distribution is to prioritize the sensor nodes, which act
as a bridge between the source node and sink node most of the time. Here, we
express the betweenness centrality of a charging sensor node
$(i.e.,\forall\,Sn_{i}\in\mathcal{N})$ as a vector,
$\ss_{i}=(\ss_{1},\ss_{2},\ss_{3},...,\ss_{r})$, which is obtained in Eq.
(10). The betweenness centrality vector is normalized into
$\bar{\ss}_{i}=(\bar{\ss}_{1},\bar{\ss}_{2},\bar{\ss}_{3},...,\bar{\ss}_{r})$
between $[0-1]$ using Eq. (11). The probability distribution function, as
described in Eq. (12),
$\tilde{\ss}_{i}=(\tilde{\ss}_{1},\tilde{\ss}_{2},\tilde{\ss}_{3},...,\tilde{\ss}_{r})$,
is used to curve fit the normalized vector. Furthermore, we included a
weighted factor $\lambda_{\ss}$ to increase the impact of the distribution,
where $\lambda_{\ss}\geq 1$ is set by default. The maximum time a node acts as
a betweenness will have a higher priority of a charging sensor node.

$\ss_{i}=\sum_{Sn_{s}\neq Sn_{i}\neq
Sn_{b}}\frac{\sigma_{Sn_{s}Sn_{b}}(Sn_{i})}{\sigma_{Sn_{s}Sn_{b}}}\\\ $ (10)

$\bar{\ss}_{i}=\frac{\ss_{i}-\min(\ss_{i})}{\max(\ss_{i})-\min(\ss_{i})}$ (11)

$\begin{array}[]{c@{\,}c}\tilde{\ss}_{i}=\begin{cases}\alpha+\mathrm{e}^{\left(-\mathrm{e}^{\left(-\beta*\left(\left(\bar{\ss}_{i}\right)^{\lambda_{\ss}}-\gamma\right)\right)}\right)}\\\
\alpha=1.343494;\quad\beta=2.88956;\\\
\gamma=0.57881;\quad\lambda_{\ss}=1;\end{cases}\,\forall\,Sn_{i}\in\mathcal{N}\end{array}$
(12)

The purpose of charging queue metric is to use the above four distributions to
efficiently prioritize the charging queue of each MCV. As discussed in Section
III-A, the initial position of each MCV is divided into $k$ regions using Eq.
(1). Therefore, charging sensor nodes will be prioritized differently for each
MCV queue due to the distance distribution Eq. (6) from each MCV to the sensor
node. In this work, the sink node is in charge of prioritizing each MCV queue
based on the charging queue metric determined in Eq. (13). The charging queue
metric obtained the highest priority value based on the average term of four
probability distributions.

$\tilde{\mathcal{C}}_{qm}=(\tilde{\Phi}_{i}^{\downarrow}+\tilde{\zeta}_{v_{j},i}+\tilde{\eta}_{i}+\tilde{\ss}_{i})/4\quad\quad\forall\,Sn_{i}\in\mathcal{N}$
(13)

###  III-C Charging Factor Strategy

This section focuses on the efficient probabilistic partial charging model by
developing a charging factor strategy for all charging nodes prioritized in
each MCV queue. For instance, we express a queue of an MCV with charging
sensor nodes as $\mathcal{Q}_{Cv_{j}}=\\{Sn_{1},Sn_{2},Sn_{3},...,Sn_{r}\\}$.
Here, we consider the residual energy of a charging node distribution Eq. (3)
in the queue, where the higher probability of a node is considered to be more
critical than the rest of the nodes.

Therefore, to efficiently evaluate the charging factor strategy and optimize
the partial charging in the queue, we first determine the minimum criticality
$\mathcal{C}_{min}$ and the maximum criticality $\mathcal{C}_{max}$ of the
charging sensor nodes using residual energy priority values, and then obtain
the probabilistic weighted factor $\mathcal{P}_{wf}$ in Eq. (14).

$\mathcal{P}_{wf}=\frac{\mathcal{C}_{max}(\tilde{\Phi}_{i}^{\downarrow})-\mathcal{C}_{min}(\tilde{\Phi}_{i}^{\downarrow})}{\mathcal{C}_{max}(\tilde{\Phi}_{i}^{\downarrow})}\\\
$ (14)

The charging factor strategy based on Eq. (14) is obtained in Eq. (15) to
determine the charging factor for each sensor node in the charging queue
$\mathcal{Q}_{Cv_{j}}$.

$\begin{array}[]{c@{\,}c}\mathcal{C}_{fs}=\left\lceil\left(\sqrt{(\tilde{\Phi}_{i}^{\downarrow})^{2}*\mathcal{P}_{wf}}-\partial_{\tilde{\Phi}_{i}^{\downarrow}}\right)*100\right\rceil\end{array}$
(15)

Here, $\partial_{\tilde{\Phi}_{i}^{\downarrow}}$ is the charging control
factor, which is set to 10% of the residual energy priority Eq. (3) of each
queue node. The reason is that the distance between the MCV and each node, as
well as the charging time required for each node, must keep in mind to give
the MCV a fair chance to successfully partially charge each node in the queue.
This helps to improve charging efficiency, coverage, and the network lifetime
by preventing nodes from dying during MCV service time. The probabilistic
weighted factor, however, is equal to residual energy priority when an MCV
only has one sensor node in its request queue.

###  III-D ISAC-based MCV detection

In this section, we employ the integrated sensing and communication (ISAC)
approach, in which the prioritized charging sensor node sends the ISAC signal
to the first arriving MCV in its sensing range based on its sensing capability
and received echo to analyze which is affected by noise and interference and
obtain the distance, and then directly communicate with the sink to prevent
other MCVs from visiting the same nodes to overcharge. Due to this, it reduces
the travel time and the charging delays. The sink then updates the charging
queue priority of the other MCVs. The received echo signal $x(t)$ affected by
noise and interference is given in Eq. (16).

$x(t)=s(t-\tau)+n(t)$ (16)

where $s(t-\tau)$ is the combination of the original transmitted signal,
delayed by the travel time $\tau$ of the echo. $n(t)$ is the additive noise.

Our goal is to detect the presence of the signal $s(t)$ in the noisy received
signal $x(t)$. Hence, the sensor node will apply matched filtering to the
received signal. The matched filter $h(t)$ is designed to maximize the
correlation between the received signal $x(t)$ and the signal $s(t)$
transmitted by the MCV. The output of the matched filter $y(t)$ is given by
Eq. (17).

$y(t)=\int x(\tau)h(t-\tau)d\tau$ (17)

where $h(t)$ is the impulse response of the matched filter.

To obtain the time delay $\tau$ that maximizes the cross-correlation function
Eq. (17), we first rewrite the cross-correlation function as a function of the
time delay $\tau$ in Eq. (18) and then take the derivative of the cross-
correlation function with respect to $\tau$.

$y(t)=\int x(\tau)h(t-\tau)d\tau=\int x(t-\tau)h(\tau)d\tau$ (18)

According to the concept of waveform matched filter in [17], the time delay
that maximizes the cross-correlation function is given in Eq. (19)

$\tau=\arg\max{\int x(t)s^{*}(t)d\tau}=\arg\max[x(t)*s^{*}(t)]$ (19)

where $*$ denotes convolution. In other words, the time delay that maximizes
the cross-correlation function is the one that maximizes the convolution of
$x(t)$ and $s^{*}(t)$.

To detect the MCV by the charging sensor node $Sn_{i}$, we estimate the
distance between them using a time delay $\tau$ that maximizes the cross-
correlation function Eq. (19) and speed of light $c=\frac{d}{\tau}$. Hence,
the two-way signal distance from charging sensor node to MCV is
$2d_{Sn_{i},Cv_{j}}$. Consequently, it determines the distance in Eq. (20).

$d_{Sn_{i},Cv_{j}}=\frac{c*\tau}{2}$ (20)

Based on the probabilistic sensing model [3], if the distance between a sensor
node and the MCV $d_{Sn_{i},Cv_{j}}$, is within the sensing region
$\mathcal{R}_{s}$, the sensor node can detect the MCV and communicate with the
sink. Subsequently, the sink updates the priority queues of other MCVs by
removing that node.

##  IV Performance Evaluation and Discussion

The proposed scheduling protocol, Poised, is implemented and evaluated through
simulations. Initially, the simulator was developed to assess data routing
schemes with both static [1] and mobile [4] sinks using NS3 models. Later on,
it was modified to evaluate WRSN techniques [5]. The WRSN network is
constructed on a square-shaped monitoring area. The sensor nodes are
distributed at random, with the sink node in the center of the area. The sink
serves as a depot for MCVs to recharge their batteries. The sink is also in
charge of scheduling charging requests for each MCV as well as network
management. To ensure the accuracy of the results, we took into account the
average of $20$ random simulations. Table II contains a summary of the key
simulation parameters.

TABLE II: Simulation Parameters Parameter |  Value
---|---
Number of nodes |  Varies from $100$ to $500$
Communication range |  $50m$
Sensing range |  $25m$
Sensor battery capacity |  $0.5J$
Threshold for charging requests |  $30\%$ residual energy
MCV battery capacity |  $10kJ$
The charging rate |  $0.05J/s$
MCV travel speed |  $5m/s$
MCV travel cost |  $5J/m$
MCV mobility model |  Random waypoint

Poised is evaluated using a number of parameters that includes: i) Energy
Usage Efficiency $(\%)$: It is expressed as the ratio of total energy
transferred to sensor nodes to total energy transmitted from sink to MCVs. ii)
Charging Delay $(s)$: It is expressed as the time it takes the MCVs to
complete the energy requirements of the sensor nodes. iii) Survival Rate
$(\%)$: It is expressed as the ratio of number of alive sensor nodes to the
total number of sensor nodes in the network. iv) Travel Distance $(m)$: It is
expressed as the total distance covered by MCV during a single charging tour.

###  IV-A Simulation Results

The proposed protocol Poised compares the outcomes with two state-of-the-art
protocols: FLCSD [6] and DMCP [7].

(a)

(b)

(c)

(d)

Figure 1: Performance over number of nodes

Fig. 1(a) depicts the results of energy usage efficiency, demonstrating how
the result gradually increases with the number of nodes for all protocols. The
proposed protocol Poised outperforms cutting-edge protocols for the following
reasons. First, it employs a well-balanced charging load strategy for each MCV
based on the probability distribution of each attribute to fairly prioritize
charging nodes in each MCV queue. Second, it provides an effective charging
factor strategy in each MCV queue to partially charge all the nodes in the
network based on the residual energy of charging node distribution. Finally,
it employs the ISAC concept to reduce the travel cost of each MCV in the
network. For these reasons, it maximizes the amount of energy transferred to
each requested node in the network. FLCSD and DMCP both fell short to consider
the efficient charging load for each MCV in the network and to prioritizes the
charging queue to partially charge them in order to maximize energy usage
efficiency.

Fig. 1(b) depicts the results of charging delay, demonstrating how the results
gradually increases with the number of nodes in the network for all protocols.
The proposed protocol Poised outperforms cutting-edge protocols because it
utilizes probabilistic partial charging, which covers more nodes in each MCV
queue. The nodes in each MCV queue are assigned a probabilistic charging
factor based on their relative criticality. The charging factor strategy
incorporates the charging control factor, assisting in maximizing the
reachability of each sensor node in the queue in order to efficiently
partially charge the nodes. It also employs the ISAC concept, which revokes
multiple MCVs to charge the same node multiple times in a single request,
reducing travel costs while increasing the chance of charging the required
waiting node in the queue in an efficient manner. FLCSD lacked partial
charging, while DMCP included it but only focused on relative criticality,
neglecting a probabilistic charging factor strategy with a charging control
factor that can minimize charging delay.

Fig. 1(c) depicts the results of survival rate, demonstrating how the results
gradually decreases with the number of nodes in the network for all protocols.
The proposed protocol Poised outperforms cutting-edge protocols with the same
reasons given in the charging delay result.

Fig. 1(d) depicts the results of travel distance, demonstrating how the
results gradually increases with the number of nodes in the network for all
protocols. The proposed protocol Poised outperforms cutting-edge protocols by
utilizing the distance from MCV to charging node distribution in Eq. (6) which
gives priority to nodes in the queue that are closer to MCV. Also, it employs
the ISAC approach; for more information, see charging delay result. FLCSD and
DMCP made no attempt to reduce MCV travel distance in the network.

##  V Conclusion

This paper presented a probabilistic on-demand charging scheduling for ISAC-
assisted WRSNS with multiple mobile charging vehicles. It focuses on the load
balanced strategy in charging scheduling for each MCV, the efficient charging
factor strategy to partially charge the nodes in the network, and the
integrated sensing and communication approach to reduce the traveling cost of
each MCV. Therefore, it first considers the four attributes to balance the
charging load, along with their probability distributions, in order to
prioritize the relatively critical nodes for charging. The attributes are the
residual energy of charging node, distance from MCV to charging node, degree
of charging node, and charging node betweenness centrality. Second, it focuses
on an efficient charging factor strategy to partially charge the nodes based
on the charging node residual energy distribution. It also includes a charging
control factor to reduce charging delay while increasing charging coverage and
survival rate. Finally, the proposed protocol employs the ISAC concept to
detect the first arriving MCV within the sensing range of the charging sensor
node. This reduces the traveling distance of other MCVs and avoids the
conflict of charging the same the node with a single request. According to the
simulation results, the proposed protocol Poised outperforms the cutting-edge
protocols.

## Acknowledgment

This work is supported in part by National Natural Science Foundation of China
under Grant 62101232, and in part by the Guangdong Provincial Natural Science
Foundation under Grant 2022A1515011257.

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