# Hotspots Analysis and Prediction for Mobile Networking Applications

Gwladys Ornella Djuikom Foka, Sachit Mishra, Razvan Stanica, Diala Naboulsi

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Gwladys Ornella Djuikom Foka, Sachit Mishra, Razvan Stanica, Diala Naboulsi. Hotspots Analysis and Prediction for Mobile Networking Applications. Annals of Telecommunications - annales des télécommunications, 2026, 10.1007/s12243-026-01144-1. hal-05511059

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Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
Hotspots Analysis and Prediction for Mobile
Networking Applications

Gwladys Ornella Djuikom Foka¹*, Sachit Mishra²,
Razvan Stanica², Diala Naboulsi¹

¹*École de Technologie Supérieure (ÉTS), City, Canada.
²INSA, INRIA, CITI, Lyon, France.

*Corresponding author(s). E-mail(s):
gwladys-ornella.djuikom-foka.1@ens.etsmtl.ca;
Contributing authors: sachit.mishra@inria.fr;
razvan.stanica@insa-lyon.fr; diala.naboulsi@etsmtl.ca;

**Abstract**

Understanding the dynamics of mobile traffic is highly valuable for a variety of fields, such as transportation and networking. In particular, analyzing hotspots, i.e., areas presenting an increased popularity at certain times, is crucial for adequate planning and management operations. Yet, despite its importance, we lack today a precise definition of the term hotspot in the community. The essential of this contribution is based on a unique mobile phone dataset collected by a French mobile operator in the city of Paris. In this work, we propose a new definition for the hotspot concept while highlighting the major weaknesses of the literature. Moreover, we provide an extensive benchmarking for the hotspot forecasting problem. Our results show that Long Short-Term Memory (LSTM) gives the best performance for the hotspot prediction problem, and we consider it for a robotic aerial base station (RABS) deployment application. In order to minimize the RABSs travel distance, we mathematically model the problem and introduce a greedy and Particle Swarm Optimization (PSO) algorithms to solve it. The results in terms of coverage ratio and travel distance showcase the difference between a prediction-based approach and a non-prediction-based approach.

**Keywords:** Hotspot, Robotic Aerial Base Stations, Machine Learning, Network Optimization
# 1 Introduction

In the realm of telecommunications, wireless and cellular networks serve as the backbone of modern connectivity, facilitating communication and data exchange for billions of users worldwide. According to the Ericsson mobility report of November 2024, global 5G subscriptions are predicted to reach 6.3 billion by the end of 2030, making up 67% of all mobile subscriptions at that time [1]. However, this growth is not uniformly distributed, and network traffic is remarkably uneven in time and space: there are moments and places when the network needs to accommodate more users and an increased demand. This is a consequence of two main factors. The first is that users move in the network, according to their daily schedules. For example, work areas are obviously more popular during the day, while residential areas are more visited during evenings and at night [2]. The second reason is that the user demand is not uniform in time: less network activity happens at night and during weekends. The result is the existence of so-called *hotspots*, areas with a high popularity among users at certain times.

As mobile devices and subscriptions continue to proliferate, cellular network operators face the challenge of managing network resources efficiently, to meet the growing demands of users. One critical aspect of this endeavor is efficiently understanding and handling hotspots in order to guarantee a certain level of quality of service (QoS), even when there is a surge of traffic demand in the network [3].

Analyzing and understanding this hotspot behavior in detail is thus crucial for network optimization purposes, as well as for guaranteeing seamless connectivity and enhancing user experience. However, we are confronted with an unexpected problem: while the term *hotspot* is a common one and easily understandable, widely accepted formal definitions are lacking in the community. Based on a review of the literature, we notice that the widely used methods for hotspot identification are threshold-based and often do not consider the combination of spatial and temporal dimensions in the identification. As examples, [4–6] consider an entire geographical area, neglecting any local phenomena.

They define hotspots as a set of cell sites and time periods where their aggregate traffic volume covers more than 50% of the total traffic in the entire dataset [4] or a region in the plane in which, the traffic density exceeds a certain threshold [5, 6]. Practically, a certain location might not be identified as a hotspot because of more significant events happening tens of kilometers away, in a completely different part of the city. Moreover, no historical dimension is considered in these definitions. This means that a location might be defined as a hotspot, despite being less visited than normal for that respective area. Furthermore, while the proposed frameworks in these studies are threshold-based, they do not incorporate temporal patterns. These patterns are crucial for hotspots detection as peak hours during weekdays differ from weekends for example, and traffic heavily depends on human mobility behaviors. Therefore, the frameworks can not distinguish between transient and persistent hotspots. To fill in the aforementioned gaps, we propose a hostpot definition that incorporates not only the spatial component but also the temporal component. The latter comes into play to leverage hourly, daily and weekly patterns which helps to distinguish regular activities from actual outliers and thus adding an extra layer to the hostpot detection framework.
While the identification of hotspots is important, predicting them can bring even higher benefits [4, 7]. This prediction is relevant specifically for cognitive and automated network optimization solutions [4]. Indeed, prediction-based solutions have been demonstrated to improve network performance, enable adaptive network management, and reduce costs [4, 8]. Accordingly, we study the performance of different algorithms for predicting hotspots, based on the proposed definition.

We also show how hotspot detection and prediction can be used to address one specific networking challenge: the deployment of RABSs. Indeed, RABSs can be used to accommodate the traffic surge observed at network hotspots. Yet, they Require strategic deployment algorithms in order to optimize the energy consumption of the flying devices transporting the base stations. Using a greedy and PSO approaches, we demonstrate how RABSs can be deployed efficiently based on the prediction of traffic hotspots.

The proposed solutions are evaluated using a real-world dataset covering the city of Paris, France. Our contributions are three-fold:

* We propose a new definition for the hotspot concept, and we argue that this definition is more adequate than the State-of-the-art when considering spatial scalability issues. Our definition takes into consideration the relative strength of a potential hotspot compared to its close vicinity, as well as its own history. These two components contribute to a more accurate and more scalable characterization considering the spatial and temporal components.

* We perform the prediction of hotspots based on the previous definition using classical machine learning (ML) methods such as eXtreme Gradient Boost (XGBoost) and Random forest (RF), as well as deep learning (DL) approaches such as Long Short-Term Memory (LSTM), Deep Neural Networks (DNN) and Transformers. We conduct a comparative analysis using a real-world dataset and the results indicate that LSTM surpasses the XGBoost and RF considering the following metrics: F1-score, precision, and recall. Furthermore, we explore the LSTM behavior when it comes to predicting one point or multiple points simultaneously.

* We illustrate how hotspot detection and prediction can help tackle a networking problem. We consider as use-case the deployment of RABS in a mobile network, to absorb peaks of traffic. We consider a greedy and PSO algorithms to place the RABSs. Our assessment is focused on showing how the algorithm behaves (in terms of coverage ratio and traveled distance) when we consider prediction-based and non-prediction-based approaches.

The rest of the paper is organized as follows. Section 2 examines previous studies on hotspot analysis and prediction, as well as the State-of-art on the RABSs deployment solutions. Section 3 presents our proposed definition as well as the definitions from the literature and describes the dataset, the hotspots spatial distribution, and major events. Section 4 showcases the hotspot prediction benchmarking. Section 5 highlights the hotspot-based RABSs deployment technique and evaluates it on a realistic urban use case. Finally, Section 6 concludes this work.
## 2 Related Works

Problems related to hotspot identification and prediction have been tackled in different ways in the literature for numerous purposes. Hotspot analysis plays a big role in understanding and inferring human mobility patterns. Indeed, [9] defines hotspots as reflections of dense human activities in urban areas. They propose a Dynamic Spatial Network (DSN) to model the road network in a city and evaluate this on the Shanghai road network dataset. They define a hotspot as a connected subgraph of the DSN satisfying a set of properties. Using the trajectory data from 13518 taxis in Shanghai, the authors show that the DSN is better than the baselines in terms of efficiency and effectiveness. [10] takes a user-oriented definition, and it characterizes human mobility patterns by identifying hotspots as the key locations where people spend significant time. They use Hartigan's leader algorithm to cluster cell towers and logistic regression to calculate the probability of a cluster being important. A cluster is considered important if a cell tower within said cluster was contacted on more than 5% of the total studied days, the duration between the first and last contact is greater than 14 days and there is a 20% probability of importance according to the regression analysis. This method found important places for 97.5% of users and most users had 3 to 6 important places identified.

In the mobile networks community, exemplified by works such as [4–7, 11, 12], researchers concentrate on identifying and characterizing hotspots in terms of network traffic. An entropy weight-based method is proposed in [7] to identify hotspots. The authors calculate the weight of four chosen features and the score of each base station based on the computed weights; they then consider the top *N* base stations as hotspots. Results show that weekends have more hotspots than weekdays and, in both times of the week, 80% of base stations are not identified at all as hotspots during a given day. Authors in [4] define traffic hotspots as the set of cell sites and time periods where their aggregate traffic volume covers more than 50% of the total traffic in the entire dataset. Results indicate that 90% of cells have less than 20% chance of becoming a hotspot. Data hotspots exhibit an even distribution across the week and download, upload, and voice call hotspots typically occur independently. Notably, downtown areas, hospitals, and universities are almost consistently hotspots. In [5], researchers define a traffic hotspot as a region in the plane in which the traffic density exceeds a certain threshold (e.g. five or ten times the mean traffic density). Their findings showcase that hotspot densities are contingent on the chosen threshold, and deploying more small cells in larger hot zones incurs costs in terms of the ratio of covered area to serviced traffic demand. Unlike the definition in [5], the authors in [11] propose a threshold representing the minimum amount of communication traffic for an area to be considered a hotspot. In this approach, hotspots are materialized as nodes in the graph, the weights of edges represent communication strength between them. Node centrality metrics are used to quantify the importance of each hotspot and the results reveal that the node centrality metrics can be separated into two groups: one group with closeness and betweenness centralities, which favors hotspots with low weights, and another group for degree, PageRank and eigenvector centrality, which favors hotspots with high weight. It is noteworthy that authors in [6] used a similar
method to identify high communication areas and propose a smart cyber-physical-
social system (CPSS) model for analyzing hotspots in smart cities. Thus, they use
social and behavioral measures instead of the centrality methods in [11] to quantify the
importance of each hotspot. The evaluation shows that top-10 hotspots were discovered
using social network similarity and social behavioral measures. On the same lane of
threshold-based methods, researchers in [12] have opted for an approach based on 21
key performance indicators (KPIs) such as radio interference and handover success
ratio, to identify hotspots. They calculate the hotspot score for each cellular sector,
which is later integrated over different periods of time. A sector is then labeled as a
hotspot if the integrated score exceeds a predefined threshold.

In the idea of harnessing detected hotspots for more proactive network operations, researchers have been looking at the problem of hotspot prediction. Therefore, [12] emphasizes on predicting if a sector will be a hotspot or not by leveraging the aforementioned 21 KPIs. The tree-based models used for the prediction also exploit the hotspot scores, daily percentiles, and weekly profiles. The models achieve up to 14% better predictions than the Average model for regular hotspots. Authors in [4] used Support Vector Machine (SVM), Random forests (RF), and Bayesian Networks (BN) to predict if cells will become hotspots or not. The results using the data from the previous week to predict hotspots of the current week show that the accuracy and the area under the receiver operating characteristic (ROC) curve (AUC) are high for the three algorithms. As for predicting multiple weeks ahead (8 weeks), although the results show that accuracy and AUC decrease slightly with the week index, the hotspots remain predictable. Since a hotspot in [13] is determined when the traffic demand exceeds five times the mean, the authors use a two layers LSTM approach (with one fully connected layer at the top) and the measurement history of the cells over the past 24 hours to predict hotspots. The comparison with the traditional Feed forward Neural Network (FFNN) indicates that the proposed model has better performance in time sequence prediction on the one hand, and higher accuracy, precision, recall, and F1 score on the other hand.

Considering the State-of-art on hotspot analysis and prediction, we introduce a
novel definition for a hotspot. In fact, the existing works do not consider the spa-
tial and temporal aspects of the identification of hotspots. Our proposed definition
addresses this limitation by considering a relative spatial significance and the histor-
ical evolution of traffic. In addition, considering our novel definition, we evaluate the
performance of different algorithms to predict hotspots. To stress the importance of
hotspot analysis and prediction based on our definition, we target the problem of
deployment of RABSs to serve traffic hotspots. Only a few works study the problem
of RABSs deployment, so far in the literature. [14] proposes a greedy algorithm that
employs a set of rules to identify the most efficient locations for RABSs to serve in
order to maximize energy efficiency. Researchers in [15] explore the dynamic deploy-
ment of RABSs to maximize the volume of served traffic while adhering to the energy
constraints of the RABSs in 6G networks. They propose a Lagrangian heuristic algo-
rithm and a decomposition strategy to solve the problem. Since hotspots represent
areas where a large amount of activity occurs, managing them effectively is critical, to
ensure adequate quality of service is offered to users. Moreover, prioritizing the management of hotspots can help reduce deployment and management operations cost in networks when the resources are limited. We therefore introduce a greedy and PSO algorithms to deploy RABSs, while considering hotspots emergence in a target geographical area. The proposed algorithms allow to minimize the distance traveled by the RABSs. Finally, our evaluations are led using a real-world dataset describing the number of connected users per cellular base station, in the city of Paris.

# 3 Hotspots Analysis

In this section, we emphasize three points. First, we thoroughly describe the data which is the foundation of the study. Afterward, we present the definitions from the literature regarding the hotspot concept, while simultaneously proposing our definition. Moreover, we highlight how our proposed definition is more suitable in the hotspot identification process. Finally, we analyze the hotspot spatial distribution and the behavior of the proposed definition when it comes to detecting specific known locations as hotspots.

## 3.1 Dataset

Our study is based on a dataset collected by Orange, the largest French mobile operator, on the 4G network in the city of Paris for April 2019. We consider 8 days of data, from April 9 to April 16. In our analysis, we are focused on the time series of the number of users with an active radio connection to the cellular network during one-hour intervals. This metric is representative of human presence in a given area, but it also provides a direct view of the utilization of the mobile network. There are 773 base stations (BS) in the dataset, providing 4G connectivity in the city of Paris at the time of the data collection phase. We use the Voronoi diagram of these base stations on the map of the city to estimate the coverage area of each base station in the network.

Figure 1 and Figure 2 collectively provide insights into user behavior patterns across different temporal granularities. Figure 1a presents the 24-hour cycle of average user activity and highlights a lower activity in the night hours (0-5 AM). Moreover, we observe a gradual increase during morning hours (5-10 AM) with a peak activity during business hours (7 AM - 5 PM) and, as expected, a gradual decline in evening hours. Figure 1b on the other hand shows a view of user activity during working hours (9 AM - 5 PM), revealing distinct patterns. The average number of users oscillates between approximately 30,000 and 45,000, with regular peaks occurring throughout the day. The standard deviation band extending from nearly 0 to 100,000 users indicates high variability in the number of users during these hours, suggesting significant fluctuations in the network. Figure 2 breaks down activity by hour and day of the week. The darker blue colors, indicating a higher number of users (more than 45,000 users), are concentrated during business hours (7 AM - 5 PM) on weekdays. However, there are distinctly different patterns on days 13-14, showing significantly lower activity due to the fact that those days are during a weekend.
<figure><img src="image_2.png" /><figcaption>Fig. 1 Daily and weekly patterns of users with ±1 standard deviation</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 2 Average users by day and hour</figcaption></figure>

## 3.2 Hotspot Definitions

In this section, we elaborate on the hotspot definitions proposed in the literature. Moreover, we propose what we consider a more adequate definition, while highlighting its advantages compared to the State-of-art.

Identifying and analyzing a hotspot Requires proposing an adequate and precise definition. Indeed, the term *hotspot*, denoting a place with significant activity of a specific type, is part of the common language. However, formally defining a hotspot in a data analysis context proves to be a challenge, as multiple parameters and points
of view can be considered. From a network traffic perspective, several possible definitions were proposed in the literature. We consider the following two representative definitions from the State-of-art as baselines.

**Definition 3.1.** [6, 11] - A hotspot is a base station *i* which fulfills the following inequality:

$$I_i \geq \frac{1}{N} \cdot \sum_{j=1}^{N} I_j + \Delta,$$

where $I_i$ is the user density of base station *i*, *N* is the number of base stations, and the value of $\Delta$ is calculated as follows:

$$\Delta = \left( MaxDensity - \frac{1}{N} \cdot \sum_{j=1}^{N} I_j \right) \cdot p,$$

where *MaxDensity* is the maximum density in all the regions (base stations) regardless of the time slot and *p* is a parameter to determine the cutoff threshold.

**Definition 3.2.** [4] - A hotspot is constituted of a set of cell sites and time periods where the aggregate user density encompasses over 50% of the total user density in the dataset.

From our perspective, the definitions provided above lack an acknowledgment of the relative strength of a potential hotspot compared to its closely surrounding areas. Additionally, they do not consider any historical element in the definition of the hotspot. Therefore, we propose the following definition:

**Definition 3.3.** A hotspot is a BS that satisfies the following properties during a given time slot:

* it has a higher user density than its *k* closest neighbors (geographically) during the time slot;

* it has a higher user density than its own mean historic density at that specific time of the day.

In this definition, we consider that a hotspot should not be defined with respect to the entire studied area, but with respect to its neighbors. We also add a second condition, to account for the history of the location. The idea here is that a given location should not be seen as a hotspot if it presents a below-average user density with respect to its own history.

### 3.2.1 Hotspots Temporal Distribution

Considering these definitions, we conduct a non-exhaustive analysis of the temporal distribution of the hotspots and the spatial scalability of the definitions. for the rest of our study, we pick specific values for the important parameters of each definition.
<figure><img src="image_4.png" /><figcaption>Fig. 3 Distribution of the number of hotspots for all the definitions</figcaption></figure>

for Definition III.1, we consider *p* = 0.75, as proposed in [11]. For Definition III.3, we choose *k* = 10 because it is the smallest value guaranteeing a stable hotspot evolution. Indeed, Figure 5 depicts the impact of *k* on the number of hotspots. As shown, we observe the distribution of the number of hotspots in the considered week for *k* = 2, 3, 5, 7, 10, 12, 15. As we can see, all curves exhibit a clear daily cycle: hotspots counts rise during the day and drop sharply at night. Furthermore, there is a pronounced global drop around April 13th and 14th which are the weekends. Regarding the effect of *k*, for any given date and time, smaller values of *k* (e.g., 2, 3, 4) yields substantially more hotspots, while larger values of *k* (10, 12, 15) track each other closely with lower hotspot counts. Figure 3 shows that for definitions III.2 and III.3, there is a significant decrease in the number of hotspots between the 13th (Saturday) and the 14th (Sunday). This observation is in line with the overall user data pattern noted in subsection 3.1: there is naturally less activity on the mobile network during the weekend. However, significant differences can be noticed between the different definitions. Definition III.2 is on the higher end when it comes to the number of detected hotspots (80 to 160), while Definition III.3 detects fewer hotspots (0 to 70 approximately). As for Definition III.1, we note a very consistent pattern for all the days revealing that this definition is ineffective to find hotspots because it disregards the differences in patterns for weekdays and weekends in the studied dataset.

### 3.2.2 Spatial Scalability

In this section, we discuss a scalability problem which represents, in our view, the main weakness of the State-of-art definitions. To showcase this problem, we compute the hotspots considering two areas: a larger map considering the entire city of Paris (Paris
<figure><img src="image_5.png" /><figcaption>Fig. 4 Scalability Assessment</figcaption></figure>

intra-muros) and a smaller sub-map considering a neighborhood of 2,5 km radius, centered around the Opera - Galeries Lafayette area. We considered a specific temporal example for the assessment: April 15th, 2019 at 6 PM. Figure 4 shows the hotspots detected based on the three definitions. As we can see in Figure 4d and Figure 4e, we have fewer hotspots than in Figure 4a and Figure 4b respectively, which indicates that some hotspots disappear depending on the size of the area for both definitions. On the other hand, as we can see in Figure 4f and Figure 4c, regardless of the size of the area that we consider to identify the hotspots, our proposed definition succeeds at identifying the same hotspots.

We believe this scalability property to be essential for the definition of the concept of hotspot. Indeed, we argue that a given area should be identified as a hotspot regardless whether we consider a dataset covering a smaller area around it, or an entire country. The fact that we detect a hotspot in a given neighborhood in Paris should not depend on the fact that we consider data only from that neighborhood, from the entire city, or from the entire country. From the best of our knowledge, Definition III.3, which we propose in this work, is the first hotspot definition in the literature respecting this intuitive and important property. Therefore, in the following, this definition will be analyzed in detail, and it will represent the foundation for the hotspot prediction process.
<figure><img src="image_6.png" /><figcaption>Fig. 5 Distribution of the number of hotspots over for Definition III.3</figcaption></figure>

## 3.3 Hotspots Spatial Distribution

We investigate the spatial distribution of the hotspots detected using our proposed definition. for this, we compute the frequency of being detected as a hotspot for every BS. More precisely, for each BS, we calculate the percentage of time slots for which the BS is detected as a hotspot. We plot these results as heat maps in Figure 6, distinguishing between weekdays (Figure 6a), week-end (Figure 6b), morning (Figure 6c) and evening (Figure 6d) times. In these Figures, warmer colors indicate areas that are more frequently detected as hotspots.

Figure 6a shows high intensity around areas such as the Opera and Châtelet les Halles, which are major business and commercial centers in Paris. Moreover, there is strong activity near major train stations like Gare du Nord (biggest train station in Europe) and Gare de l'Est. These observations reveal that the proposed definition succeeds in detecting the overall activity pattern of Paris. Regarding the weekend
<figure><img src="image_7.png" /><figcaption>Fig. 6 Spatial distribution of hotspots occurrences</figcaption></figure>

pattern in Figure 6b, we see that there is intensity around tourist areas, likely Notre-Dame and Champs-Elysées. There is a persistence of activity in central areas that matches Parisian weekend patterns. For the 8 AM pattern depicted in Figure 6c, we observe concentrated hotspot occurrences near major transportation hubs and business districts, which is typical of morning rush hours. The pattern suggests movement toward central business areas. In contrast, for the 9 PM pattern, depicted in Figure 6d, we notice a decrease in hotspot concentration in business areas, marked by less intense colors in said areas, with a remaining activity in areas like the Marais that matches where entertainment takes place.

## 3.4 Major Events

During the studied period, two major events happened in Paris: the Notre Dame Cathedral fire and the Paris Marathon. We consider that these events likely attracted a high level of interest from the population, and we investigate whether they resulted in the detection of hotspots. For the Notre Dame Cathedral fire, we consider the corresponding area, during the day of the fire (April 15), but also during the day after the fire. Indeed, as already observed in [16], more people actually visited the site the day after the fire, to observe its consequences. For the Paris Marathon, we consider the area around the Arc de Triomphe, which was the starting point of the marathon.

<table><caption>**Table 1** Major events in the dataset, detected as hotspots by Definition III.3.</caption><thead><tr><th>Date</th><th colspan="2">Event</th><th>Places</th></tr></thead><tbody><tr><td>April 15th, 2019</td><td colspan="2">Notre Dame Cathedral Paris burned</td><td>Notre Dame Cathedral Paris</td></tr><tr><td>April 16th, 2019</td><td colspan="2">The day after the Notre Dame Cathedral Paris burned</td><td>Notre Dame Cathedral Paris</td></tr><tr><td>April 14th, 2019</td><td colspan="2">Paris Marathon</td><td>Arc de Triomphe</td></tr></tbody></table>
The results are presented in Table 1, where we notice that our definition detects the majority of the aforementioned locations as hotspots, which highlights its effectiveness at detecting hotspots, due to those events.

## 4 Hotspot Prediction

In this section, we leverage machine learning and deep learning techniques to perform binary classification of cells, determining whether a given cell is a hotspot or not. Specifically, we utilize various tree-based models such as Decision Tree (DT), Random forest (RF), and XGBoost. Additionally, we explore other machine learning models, including Logistic Regression (LR) and Naive Bayes (NB), to enhance prediction accuracy. The dataset we are working with is imbalanced, containing a significantly higher number of non-hotspot (102999) cases than hotspot cases (8313). Our objective in building the prediction model is to improve its performance specifically for the hotspot cases. To achieve this, we assigned a value of 1 to hotspot cases during model training. We aimed to ensure that metrics such as precision, recall, and F1 score for the hotspot class (value 1) achieved consistently high values.

<table><caption>**Table 2** Performance metrics of the ML models for hotspot and non-hotspot class.</caption><thead><tr><th>ML Model</th><th>Class</th><th>Precision</th><th>Recall</th><th>F1-Score</th></tr></thead><tbody><tr><td rowspan="2">XGBoost</td><td>0</td><td>0.93</td><td>0.99</td><td>0.96</td></tr><tr><td>1</td><td>0.86</td><td>0.72</td><td>0.78</td></tr><tr><td rowspan="2">Random forest</td><td>0</td><td>0.93</td><td>0.99</td><td>0.97</td></tr><tr><td>1</td><td>0.86</td><td>0.14</td><td>0.24</td></tr><tr><td rowspan="2">Decision Tree</td><td>0</td><td>0.93</td><td>0.99</td><td>0.96</td></tr><tr><td>1</td><td>0.56</td><td>0.15</td><td>0.24</td></tr><tr><td rowspan="2">Logistic Regression</td><td>0</td><td>0.93</td><td>0.99</td><td>0.96</td></tr><tr><td>1</td><td>0.54</td><td>0.10</td><td>0.17</td></tr><tr><td rowspan="2">Naive Bayes</td><td>0</td><td>0.96</td><td>0.87</td><td>0.91</td></tr><tr><td>1</td><td>0.25</td><td>0.53</td><td>0.34</td></tr><tr><td rowspan="2">Neural Network</td><td>0</td><td>0.98</td><td>0.97</td><td>0.98</td></tr><tr><td>1</td><td>0.72</td><td>0.71</td><td>0.71</td></tr><tr><td rowspan="2">LSTM</td><td>0</td><td>0.99</td><td>0.98</td><td>0.99</td></tr><tr><td>1</td><td>0.81</td><td>0.85</td><td>0.83</td></tr><tr><td rowspan="2">Transformers</td><td>0</td><td>0.97</td><td>0.95</td><td>0.96</td></tr><tr><td>1</td><td>0.56</td><td>0.70</td><td>0.63</td></tr></tbody></table>

As previously demonstrated in section 3.1, hotspot patterns for weekdays and weekends differ significantly, potentially introducing further bias into the predictions. To mitigate this, we first filter the data to include only weekdays. Additionally, we incorporate prior information for training the model by performing a shift operation. for this, we conducted an extensive analysis by evaluating model accuracy across various lags, referred to as Time Windows (TW), as illustrated in Figure 7. Figure 7 clearly shows that as we increase the value of TW, the performance of the model also increases in the context of the F1 score for hotspots until TW reaches 8, after which it starts to diminish. Additionally, we tested TW only up to 12, as increasing it further
<figure><img src="image_8.png" /><figcaption>Fig. 7 Impact of time windows over the F1 score.</figcaption></figure>

would result in the removal of too many data points. So, we selected TW as 8 for all the models. This step enhances the model's performance by considering previous data points in the prediction process.

After the shift operation, we split the time-series data using the standard 80:20 ratio. Specifically, the model is trained on data from all BS for the first 80% of the timestamps. Finally, We use grid search to fine-tune the hyperparameters of different models to optimize their performance. Since we employ multiple machine learning models, we focus on tuning only the key parameters for each, for example, in tree-based models, we optimize the tree depth for DT, while for RF, we primarily tune the number of trees and their depth. In the case of XGBoost, we additionally fine-tune the learning rate for step size shrinkage and the gamma factor for minimizing loss during splits. for Naïve Bayes, we adjust the smoothing parameter, and in LR, we fine-tune the model using L1 and L2 regularization.

While training different machine learning models, we achieve high accuracy on the training set, with an average prediction accuracy of around 0.97 (as shown in Table 2). However, as expected, the F1 score for the hotspot class is not very high across all models. This indicates that the model overfits due to the class imbalance in the data. The best results are achieved with XGBoost for the hotspot class, yielding an F1 score of 0.78. However, the recall value remains low at 0.72, suggesting that the high F1 score is primarily driven by high precision rather than balanced performance across both precision and recall.

As different machine learning models struggled to achieve high F1 and recall scores, we turned to state-of-the-art deep learning architectures, specifically Deep Neural Networks (DNN), Long Short-Term Memory networks (LSTM), and Transformers, for time-series prediction. Among these, LSTM models consistently outperform the others. While Transformers require large amounts of training data to capture long-range temporal patterns, DNNs lack explicit mechanisms for modeling sequence dependencies, LSTMs excel by integrating information from the current timestep while simultaneously modeling long-term dependencies. This makes LSTM networks particularly
<figure><img src="image_9.png" /><figcaption>**Fig. 8** Boxplot showing the distribution of traffic across each hour of the day, with lines representing the precision and recall corresponding to each hour.</figcaption></figure>

well-suited for our scenario. With LSTM as shown in Table 2, we achieve an F1 score of 0.83, which is 6% higher than that of the XGBoost model (second best model in terms of accuracy of F1 score). The key highlight is that LSTM achieves a recall value of 0.85, outperforming XGBoost by 18%. Additionally, LSTM also achieves a score of 0.81 for precision, making it a well-balanced combination of precision and recall.

Figure 8 presents the hourly variation in precision and recall achieved by the LSTM model, highlighting the strong influence of temporal dynamics on hotspot prediction performance. The results reveal that the model performs poorly during daytime hours, particularly between 10:00 AM and 4:00 PM. This degradation is most evident in the recall values, which reach their lowest point between 11:00 AM and 1:00 PM. Such a decline suggests that the model struggles to detect a large proportion of true hotspots during these hours. A likely explanation lies in the increased randomness and irregularity of hotspot occurrences in the daytime, driven by both planned and unplanned events that cause sudden fluctuations in user concentration. These non-periodic patterns introduce instability that the LSTM model fails to capture effectively, resulting in significantly reduced recall while precision decreases more modestly.

In contrast, the model demonstrates stronger predictive performance during commuting hours and at night. These time periods exhibit high regularity due to the repetitive and predictable nature of human mobility: individuals travel between home and work during morning and evening commutes, and nighttime activities often involve consistent visits to restaurants, malls, or entertainment venues. Such regular patterns enhance the model's ability to learn temporal dependencies, enabling it to anticipate hotspot occurrences with much greater accuracy. Consequently, both recall and precision improve, with recall benefiting particularly from the increased temporal periodicity that allows the model to detect a larger proportion of true hotspots.
<figure><img src="image_10.png" /><figcaption>**Fig. 9** Impact of time on the performance of multi-step prediction in the LSTM model for hotspot prediction.</figcaption></figure>

Next, we aim to develop LSTM model capable of predicting multiple time steps ahead. This approach is particularly valuable for the next phase of our experiment, where we need to optimize RABSs deployment to address hotspot issues. By anticipating multiple future hotspot patterns, we can make more informed decisions and improve resource allocation, ultimately ensuring smoother network performance. We use TW = 7 and aim to predict 5 time steps ahead. The F1 score for hotspot prediction is slightly lower than expected, reaching approximately 0.78. Similarly, both precision and recall have decreased to 0.76 and 0.79, respectively. However, the performance for non-hotspot regions remains largely unchanged.

To analyze the factors contributing to the performance reduction, we plotted precision and recall values for different prediction steps. Figure 9 clearly shows that these values remain nearly the same for time step 1, similar to what we achieve with the LSTM model when predicting a single time step. However, as the prediction horizon increases, both precision and recall gradually decline. This degradation is a consequence of predicting further into the future, ultimately increasing the model's bias.

# 5 RABSs Deployment

In the following, we discuss one possible application of the hotspot identification and prediction process in the field of network management. Concretely, by leveraging the outcome of the hotspot prediction phase, in this section, we focus on the problem of RABSs placement in a mobile network. As a flexible infrastructure deployment technique, RABSs can temporarily reinforce the mobile network, and provide supplementary capacity in specific places at specific times. However, moving aerial vehicles from one point to another is a costly operation. Therefore, we address the RABSs placement problem with the objective of minimizing the traveled distance by RABSs in mind.
## 5.1 System Model

In a 2D grid (12×12) scenario, we consider a set of locations $\mathcal{L} = \{1, 2, ..., N\}$ where $N$ is the total number of hotspots on the grid. We define $\mathcal{T} = \{1, 2, ..., T\}$ as the set of time periods and where each time period is one hour and $T$ as the total number of considered time periods. In addition, we consider a set of RABSs $\mathcal{R} = \{1, 2, ..., M\}$ where $M$ is the number of available RABS. We define the position of each RABS at time $t$ as $\mathbf{q}_r(t) = [x_r(t), y_r(t), h_r(t)]$, $\forall r \in \mathcal{R}, t \in \mathcal{T}$. Similarly, each location's coordinates is defined by $\mathbf{w}_l = [x_l, y_l, h_l]$, $\forall l \in \mathcal{L}$. Each RABS has a maximum movement distance of $d_{max}$. Considering that one RABS covers one hotspot, we propose two algorithms for the placement: greedy and PSO.

The step-by-step instructions of Algorithm 1 (greedy) are covered as follows:

* In line 1, the Requirements for the algorithm are defined. Firstly, the algorithm takes as inputs the list of dataframes containing the locations each timestep $t \in \mathcal{T} = \{1, 2, ..., T\}$ and each location is flagged as 0 (not hotspot) or 1 (hotspot). Other inputs are the number of RABS $M$ to cover the hotspots and the maximum $d_{max}$ which is the maximum distance a RAB has to cover to reach a hotspot.

* In lines (2 - 7), the algorithm calculates the distance between a RABS and a hotspot using the *HAVERSINEDISTANCE*.

* In lines (8 - 21), the algorithm creates the function *FINDNEARESTHOTSPOT* to find the nearest hotspot which is not already covered by a RABS and which is within a distance $d_{max}$ using the haversine distance. The function returns the location of the nearest hotspot and the distance between that hotspot and the considered RABS.

* In lines (22 - 23), the algorithm iterates over each timestep $t$ and considers the dataframe $df_t$ for that timestep.

* In lines (24 - 27), at the first timestep ($t = 1$), the algorithm places the RABSs randomly on the locations regardless of the flag and retrieves the hotspots for the current time step $t$.

* In lines (28 - 30), the algorithm iterates over each RABS. If the RABS is already on a hotspot, then that hotspot is marked as covered.

* In lines (31 - 34), Otherwise, the algorithm moves the RABS to the nearest hotspot which is within the maximum RABS movement distance $d_{max}$.

* At the final stage, the algorithm calculates the overall coverage ratio of the hotspots across all the time steps as well as the overall travel distance of the RABS.

The step-by-step instructions of Algorithm 2 (PSO) are covered as follows:

* In line (1), the algorithm initializes the current positions $\mathbf{P}_{current}$ to an empty set for the first timestep.

* In line (2), the algorithm begins the main loop that processes each timestep from $t = 1$ to $T$ to handle dynamic hotspot coverage over time.
<caption>**Algorithm 1 Greedy RABSs Placement with Dynamic Hotspot Coverage**</caption>

**Require:**
1: Set of RABSs $\mathcal{R}$, Maximum coverage distance $d_{max}$
2: **for** $t = 1$ to $T$ **do**
3: &nbsp;&nbsp;&nbsp;&nbsp;**if** $t = 1$ **then**
4: &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Place RABSs randomly on locations
5: &nbsp;&nbsp;&nbsp;&nbsp;**end if**
6: &nbsp;&nbsp;&nbsp;&nbsp;$C_t \leftarrow \{(x_l, y_l, h_l) \text{ where } flag_l = 1\}$
7: &nbsp;&nbsp;&nbsp;&nbsp;**for all** $rabs \in$ current RABSs positions **do**
8: &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;**if** $rabs \in C_t$ **then**
9: &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;covered_hotspots $\leftarrow$ covered_hotspots $\cup$ $\{rabs\}$
10: &nbsp;&nbsp;&nbsp;&nbsp;**else**
11: &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;($nearest, dist$) $\leftarrow$ FINDNEARESTHOTSPOT($rabs, C_t, covered_hotspots$)
12: &nbsp;&nbsp;&nbsp;&nbsp;**if** $nearest \neq$ null **then**
13: &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Move RABS to nearest position
14: &nbsp;&nbsp;&nbsp;&nbsp;**end if**
15: &nbsp;&nbsp;&nbsp;&nbsp;**end if**
16: &nbsp;&nbsp;&nbsp;&nbsp;**end for**
17: &nbsp;&nbsp;&nbsp;&nbsp;**end for**
18: Calculate average coverage ratio, the overall travel distance
19: **function** FINDNEARESTHOTSPOT($rabs_pos, hotspots, covered_hotspots$)
20: &nbsp;&nbsp;&nbsp;&nbsp;$d_{min} \leftarrow \infty$
21: &nbsp;&nbsp;&nbsp;&nbsp;$nearest \leftarrow$ null
22: &nbsp;&nbsp;&nbsp;&nbsp;**for all** $h \in$ hotspots **do**
23: &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;**if** $h \notin$ covered_hotspots **then**
24: &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$d \leftarrow$ HAVERSINEDISTANCE($rabs_pos, h$)
25: &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;**if** $d \le d_{max}$ **and** $d < d_{min}$ **then**
26: &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$d_{min} \leftarrow d$
27: &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;nearest $\leftarrow$ h
28: &nbsp;&nbsp;&nbsp;&nbsp;**end if**
29: &nbsp;&nbsp;&nbsp;&nbsp;**end if**
30: &nbsp;&nbsp;&nbsp;&nbsp;**end for**
31: &nbsp;&nbsp;&nbsp;&nbsp;**return** ($nearest, d_{min}$)
32: **end function**

* In line (3), the algorithm identifies hotspots $\mathcal{H}_t = \{(x_l, y_l, h_l) \text{ where } flag_l = 1\}$ for the current timestep. RABSs can only be placed on hotspot positions (exact coordinates), so $\mathcal{A}_t = \mathcal{H}_t$.

* In lines (4 - 7), the algorithm checks if this is the first timestep and randomly initializes RABSs positions from hotspot locations.

* In line (8), the algorithm stores the previous positions $\mathbf{P}_{prev}$ before processing the current timestep to calculate movement costs later.

* In line (9 - 15), the algorithm initializes the swarm by creating $n_p$ particles with random positions and velocities, where each particle represents a candidate solution for all RABS placement.
**Algorithm 2 PSO for Dynamic RABSs Placement**

**Require:** Number of RABSs $n_{rabs}$, Maximum movement distance $d_{max}$, Number of particles $n_p$, Number of iterations $n_{iter}$

**Ensure:** Optimized RABSs positions for each timestep

1: Initialize current positions $\mathbf{P}_{current} \leftarrow \emptyset$

2: **for** each timestep $t = 1$ to $T$ **do**

3: $\mathcal{H}_t \leftarrow \{(x_l, y_l, h_l)\}$ where $flag_l = 1$

4: RABSs can only be placed on hotspot positions: $\mathcal{A}_t \leftarrow \mathcal{H}_t$

5: **if** $\mathbf{P}_{current} = \emptyset$ **then**

6: Randomly initialize $\mathbf{P}_{current}$ from $\mathcal{H}_t$

7: **end if**

8: $\mathbf{P}_{prev} \leftarrow \mathbf{P}_{current}$

9: **Initialize Swarm:**

10: **for** $i = 1$ to $n_p$ **do**

11: Create particle $p_i$ with random positions from $\mathcal{H}_t$

12: Initialize velocity $\mathbf{v}_i \leftarrow$ random values

13: Set personal best $\mathbf{pBest}_i \leftarrow$ current positions

14: Calculate fitness $f_i \leftarrow$ fitness($p_i$, $\mathcal{H}_t$, $\mathbf{P}_{prev}$)

15: **end for**

16: Set global best $\mathbf{gBest} \leftarrow$ best particle's positions

17: Set global best fitness $f_{gBest} \leftarrow$ best fitness

18: **PSO Optimization Loop:**

19: **for** iteration $iter = 1$ to $n_{iter}$ **do**

20: **for** each particle $p_i$ in swarm **do**

21: Calculate fitness $f_i \leftarrow$ fitness($p_i$, $\mathcal{H}_t$, $\mathbf{P}_{prev}$)

22: **if** $f_i > f_{pBest_i}$ **then** $\triangleright f_{pBest_i}$: Fitness value of the personal best position for particle $i$. Calculated using the Fitness Function algorithm on position $\mathbf{pBest}_i$.

23: Update personal best: $\mathbf{pBest}_i \leftarrow$ current positions

24: Update personal best fitness: $f_{pBest_i} \leftarrow f_i$

25: **end if**

26: **if** $f_i > f_{gBest}$ **then**

27: Update global best: $\mathbf{gBest} \leftarrow$ current positions

28: Update global best fitness: $f_{gBest} \leftarrow f_i$

29: **end if**

30: **Update Velocity:**

31: **for** each RABS $j = 1$ to $n_{rabs}$ **do**

32: $r_1, r_2 \leftarrow$ random numbers in $[0, 1]$

33: $pb_{diff} \leftarrow$ index($pBest_{i,j}$) - index($p_{i,j}$) $\triangleright$ $p_{i,j}$: Position of particle $i$ for RABS $j$

34: $gb_{diff} \leftarrow$ index($gBest_j$) - index($p_{i,j}$)

35: $v_{i,j} \leftarrow w \cdot v_{i,j} + c_1 \cdot r_1 \cdot pb_{diff} + c_2 \cdot r_2 \cdot gb_{diff} \triangleright v_{i,j}$: Velocity of particle $i$ for RABS $j$

36: **end for**

37: **Update Position:**

38: **for** each RABS $j = 1$ to $n_{rabs}$ **do**

39: $idx_{change} \leftarrow$ round($v_{i,j}$)

40: $new_{idx} \leftarrow$ (current_index + idx_change) mod $|\mathcal{H}_t|$

41: $p_{i,j} \leftarrow \mathcal{H}_t[\mathit{new}_{idx}] \mathit{1}$

42: **end for**

43: **end for**

44: **end for**

45: Set $\mathbf{P}_{current} \leftarrow \mathbf{gBest}$

46: Calculate coverage and movement metrics

47: Store metrics for timestep $t$

48: **end for**

49: **return** Optimized positions and metrics for all timesteps
* In lines (16 - 17), the algorithm sets the global best positions **gBest** and global best fitness $f_{gBest}$ to the best particle found during initialization.

* In lines (18 - 20), the algorithm begins the PSO optimization loop that runs for $n_{iter}$ iterations to iteratively improve the solution. The algorithm iterates through each particle $p_i$ in the swarm to process all particles during each iteration (line 20).

* In line (21), the algorithm calculates the fitness $f_i$ for the current particle by evaluating coverage ratio minus movement penalty, which measures how good the particle's solution is.

* In lines (22 - 25), the algorithm updates the personal best **pBest**$_i$ if the current fitness is better than the particle's previous best, ensuring each particle remembers its own best experience.

* In lines (26 - 29), the algorithm updates the global best **gBest** if the current particle's fitness exceeds the swarm's global best, ensuring the best solution found by any particle is preserved and shared.

* In lines (30 - 36), the algorithm updates the velocity for each RABS using the PSO formula, which combines inertia term (maintains momentum), cognitive component (attraction to personal best), and social component (attraction to global best) with random factors.

* In lines (37 - 44), the algorithm updates the position of each RABS by converting the velocity to an index change, calculating the new index using modulo arithmetic, and selecting the new position from hotspot locations only.

* In line (45), the algorithm sets the current positions $P_{current}$ to the global best positions found after all iterations, using the best solution as the final RABS placement.

* In line (46), the algorithm calculates and stores coverage and movement metrics for the current timestep to evaluate performance.

* In line (49), the algorithm returns the optimized positions and metrics for all timesteps after processing the entire time series.

## 5.2 Evaluation and results

The algorithms will be evaluated on the same period as the prediction and assessed for different cases:

* **Perfect case (ground-truth)**: the algorithms are ran with the perfect knowledge of the hotspots and we leverage the results obtained from Definition III.1.

* **Prediction-based case**: the algorithms are ran with the predicted hotspots obtained in section 4.

We evaluate the algorithms by showcasing how $d_{max}$ can influence the placement while emphasizing on the coverage ratio and the RABSs traveled distance. We will first present the results obtained using the greedy algorithm followed by those obtained using the PSO algorithm, as well as the computational complexity for both.
<figure><img src="image_11.png" /><figcaption>Fig. 10 Evolution of the coverage ratio and the number of hotspots over time per $d_{max}$ for Ground-Truth and LSTM (10a, 10b). Evolution of the travel distance and the number of hotspots over time per $d_{max}$ for Ground-Truth and LSTM (10c, 10d)</figcaption></figure>

### 5.2.1 Greedy algorithm

In this subsection, we present the evaluation results of the greedy algorithm in terms of coverage ratio and travel distance.

**a) Coverage Ratio:**

The coverage ratio is the ratio between the covered and uncovered hotspots. We can observe on Figures 10a and 10b that when we consider values of $d_{max}$ greater than or equal to 3.0, the change in the coverage ratio is inexistent or marginal at most (case of LSTM). We also note for both cases that it rapidly decreases for small values of $d_{max}$ (1.0) which is normal considering that the average distance between those locations is around 4.0 km. Therefore, unless, we consider very low values of $d_{max}$, the value of this parameter does not have a high incidence on the coverage. This is shown further in figure 11a where we have the depiction of the average coverage across time steps which is between 70% and 80% for LSTM and the ground-truth. As we can see, the difference in the global average coverage for each value of $d_{max}$ is not significant considering both. This suggests that using LSTM for hotspot prediction is relevant for anticipatory RABSs deployment.

**b) Travel Distance:** The travel distance is the number of kilometers covered by all the M RABSs across all the timesteps. Figures 10c, 10d suggest that $d_{max}$ has a more significant impact on the travel distance in comparison to the coverage
<table><caption>**Table 3** PSO Parameters</caption><thead><tr><th>Parameters</th><th>Values</th><th>Description</th></tr></thead><tbody><tr><td>w</td><td>0.7</td><td>Inertia weight</td></tr><tr><td>c1</td><td>1.5</td><td>Cognitive coefficient</td></tr><tr><td>c2</td><td>1.5</td><td>Social coefficient</td></tr><tr><td>α</td><td>0.2</td><td>Movement penalty</td></tr><tr><td>n<sub>p</sub></td><td>35</td><td>Number of particles</td></tr><tr><td>n<sub>iter</sub></td><td>60</td><td>Number of iterations</td></tr></tbody></table>

ratio. The main observation is that the travel distance increases proportionally with the value of $d_{max}$. Figure 11b corroborates this observation as we note that the increase in the total travel distance is exponential for both LSTM and the ground-truth. The histogram highlights not only that increase, but also the significant differences when it comes to the total travel distances. Indeed, the total travel distance for the ground truth is significantly higher than for LSTM although still be exponential as we increase $d_{max}$.

As we can see from the aforementioned curves, the results obtained from the ground-truth and the prediction are somewhat close which corroborates the fact that having a prediction-based placement is beneficial because it gives a fairly good idea of the real hotspots. Moreover, it is obvious that the number of hotspots in Figure 10 is inversely proportionate to the travel distance and the coverage ratio.

<figure><img src="image_12.png" /><figcaption>**Fig. 11** Average Coverage (fig 11a) and Total Travel Distance (fig 11b) per $d_{max}$ for Greedy</figcaption></figure>

### 5.2.2 PSO Algorithm

In this subsection, we present the evaluation results of the PSO algorithm in terms of coverage ratio and travel distance. Table 3 shows the different parameters (values and descriptions) used for the algorithm.
<figure><img src="image_13.png" /><figcaption>Fig. 12 Evolution of the coverage ratio and the number of hotspots over time per $d_{max}$ for Ground-Truth and LSTM (12a, 12b). Evolution of the travel distance and the number of hotspots over time per $d_{max}$ for Ground-Truth and LSTM (12c, 12d)</figcaption></figure>

a) **Coverage Ratio:** Figure 12a presents the ground-truth coverage ratio achieved by the PSO algorithm. The results demonstrate a clear relationship between $d_{max}$ and coverage performance. Specifically, $d_{max} = 10.0$ (red line) consistently achieves the highest coverage ratios, with peaks between 0.90 and 0.98. For $d_{max} = 6.0$ (green) and $d_{max} = 3.0$ (orange) we observe a slightly lower coverage performance, while $d_{max} = 1.0$ (blue) consistently shows the lowest coverage, often dipping below 0.75. This pattern indicates that greater movement flexibility enables the PSO algorithm to well adapt to dynamic hotspot distributions, resulting in improved coverage. We also observe a higher variation in the case of PSO for different values of $d_{max}$ in contrast to greedy where there is less significant variation for different values of $d_{max}$ and as we can see, the greedy algorithm maintains more stable coverage ratios for Ground-truth and LSTM. Figure 12b shows the coverage ratio results considering the LSTM predictions. While the overall trends align with the ground-truth, the maximum coverage peaks around 0.85 compared to 0.98 in the ground-truth. Interestingly, the values of $d_{max} = 3.0$ and $d_{max} = 6.0$ achieve the highest coverage between 16th, 06:00 and 16th, 12:00, which differs from the ground-truth where $d_{max} = 10.0$ consistently performs best. As illustrated in Figure 13a the ground-truth approach consistently achieves higher average coverage compared to the LSTM-based method across all tested $d_{max}$ values.
The obvious difference between both algorithms for ground-truth and LSTM is that in the case of greedy, for the considered values of $d_{max}$ we observe that the distribution are very similar for $d_{max} = 3, 6, 10$ except between 16th, 02:00 and 16th, 13:00 where it is slightly different when $d_{max} = 3$ in the case of ground-truth. Moreover, for LSTM, we observe the same pattern for all the values of $d_{max}$ in previously mentioned time frame. In contrast with greedy, for PSO we observe less homogeneity when it comes to the different distributions for both ground-truth and LSTM. Higher values of $d_{max}$ consistently achieve high coverage overall of greedy and PSO.

b) **Travel Distance:** Figure 12c displays the ground-truth travel distance for the PSO algorithm. As expected, higher $d_{max}$ values (6.0 and 10.0) result in higher travel distances reaching peaks of 120 and 140 kilometers for $d_{max} = 10.0$ and $d_{max} = 6.0$ respectively. The travel distances are highly volatile, with sharp peaks and drops; $d_{max} = 1.0$ (blue) consistently shows the lowest travel distance demonstrating the effectiveness of the movement constraint in limiting RABSs mobility. Figure 12d presents the LSTM predictions for travel distance and the model leads generally to lower travel distances compared to the ground-truth. Figure 13b demonstrates the total travel distance for both ground-truth and LSTM. The ground-truth approach generally requires greater travel distance, even though for $d_{max} = 6.0$ both methods converge to an identical travel distance.

Similarly to the coverage ratio, we observe more homogeneity in the travel distance distributions for the ground-truth and LSTM in the case of greedy. Moreover, higher values of $d_{max}$ achieve high travel distances for both PSO and greedy despite the fact that the difference is more significant for greedy than PSO. From the travel distances curves in the case of PSO, we observe significant variations depending on the values of $d_{max}$.

The obvious difference between both algorithms for ground-truth and LSTM is that in the case of greedy, for the considered values of $d_{max}$ we observe that the distribution are very similar for $d_{max} = 3, 6, 10$ except between 16th, 02:00 and 16th, 13:00 where it is slightly different when $d_{max} = 3$ in the case of ground-truth. Moreover, for LSTM, we observe the same pattern for all the values of $d_{max}$ in previously mentioned time frame.

### 5.2.3 Computational Complexity

Tables 4 and 5 show the runtime of greedy and PSO respectively for each value of $d_{max}$. As we observe, for both ground-truth (average of 0.0158) and LSTM (average of 0.0163), greedy achieves the best performances in terms of runtime. For PSO on the other hand, the average runtime for ground-truth and LSTM are 1.8478 and 1.8556 respectively. By extending the analysis to the theoretical complexity analysis, we observe:

* **Greedy (Overall):** $O(T \cdot n_{abs} \cdot H)$ where T = number of timesteps, H = number of hotspots. This complexity makes greedy suitable for real-time applications with hundreds of hotspots.
<figure><img src="image_14.png" /><figcaption>Fig. 13 Average Coverage (fig 13a) and Total Travel Distance (fig 13b) per $d_{max}$ for Greedy</figcaption></figure>

<table><caption>Table 4 Greedy Runtime</caption><thead><tr><th>d<sub>max</sub></th><th>Ground-truth</th><th>LSTM</th></tr></thead><tbody><tr><td>1</td><td>0.0048</td><td>0.0044</td></tr><tr><td>3</td><td>0.0037</td><td>0.0041</td></tr><tr><td>6</td><td>0.0035</td><td>0.0039</td></tr><tr><td>10</td><td>0.0158</td><td>0.0039</td></tr></tbody></table>

* PSO (overall): $O(T \cdot O \cdot I \cdot n_{rabs} \cdot H)$ where P = particles, I = iterations. While more computationally intensive, PSO remains feasible for offline optimization.

# 6 Conclusion

Hotspots are a common phenomenon in mobile networks, a result of non-uniform user presence and user demand. Carriers need to carefully manage these hotspots, in order to ensure that user QoS is preserved above an acceptability threshold. However, as we observed in this work, the literature does not provide scalable solutions to define and identify hotspots for the RABSs deployment. Therefore, we proposed a more scalable definition using a real 4G network users dataset from Paris, France and performed hotspots prediction with the findings. We showed that LSTM gives the best results
<table><caption>Table 5 PSO Runtime</caption><thead><tr><th>d<sub>max</sub></th><th>Ground-truth</th><th>LSTM</th></tr></thead><tbody><tr><td>1</td><td>0.4771</td><td>0.4604</td></tr><tr><td>3</td><td>0.4597</td><td>0.4664</td></tr><tr><td>6</td><td>0.4553</td><td>0.4681</td></tr><tr><td>10</td><td>0.4557</td><td>0.4607</td></tr></tbody></table>

in terms of F1-score, precision and recall with values between 80% and 85%. On top of that, we proposed a prediction-based methodology for RABSs deployment as an application for the hotspot prediction. We propose a greedy and a PSO algorithms that aim to minimize the total RABSs travel distance. The evaluation in terms of coverage ratio and travel distance for both algorithms showed that the results for LSTM and the ground-truth are somewhat similar, suggesting that using prediction for RABSs deployment can be beneficial. Moreover, from a time complexity point of view, greedy appears to be more suitable for real-time applications when PSO is more computationally extensive. Future works will include the investigation of hotspots in terms of network traffic, the consideration of other networking applications and studies on a large dataset. Indeed, considering that, 8 days of data on one city might not be sufficient to generalize, we are planning on complementing our study by carrying it out to an extended period of time of data on one hand, and other cities on the other hand.

## Declarations

* **Funding** : This work was supported by the École de Technologie Supérieure (ÉTS), the National Natural Sciences and Engineering Research Council of Canada (NSERC) through research grant RGPIN-2020-06050. This work was partially funded by the CHIST-ERA ECOMOME project and the ANR COCO5G (ANR-22-CE25-0016) project. This work was partially funded by the ANR Mob Sci-Dat Factory (ANR-23-PEMO-0004) project.

* **Author Contribution** : Sachit Mishra drafted the section Hotspot Prediction. Gwladys Djuikom drafted the following sections: Abstract, Introduction, Related Works, Hotspots Analysis, RABSs Deployment and Conclusion. Razvan Stanica, Gwladys Djuikom and Diala Naboulsi contributed on the section 5. Razvan Stanica contributed on section 3. All authors reviewed the manuscript.

## References

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