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# HGC-LSTM: A Graph Neural Network-based Model for HO Forecasting in Mobile Networks

Gwladys Ornella Djuikom Foka, Razvan Stanica, Diala Naboulsi

► To cite this version:

Gwladys Ornella Djuikom Foka, Razvan Stanica, Diala Naboulsi. HGC-LSTM: A Graph Neural Network-based Model for HO Forecasting in Mobile Networks. Computer Networks, 2025, 270, pp.111497. 10.1016/j.comnet.2025.111497. hal-05288414

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Distributed under a Creative Commons Attribution 4.0 International License
HGC-LSTM: A Graph Neural Network-based Model for HO Forecasting in
Mobile Networks

Gwladys Ornella Djuikom Foka<sup>a</sup>, Razvan Stanica<sup>b</sup>, Diala Naboulsi<sup>a</sup>

<sup>a</sup>École de Technologie Supérieure (ÉTS), Montreal, Canada

<sup>b</sup>INSA Lyon, Inria, CITI, UR3720, F-69621 Villeurbanne, France

**Abstract**

In the realm of mobile networks, the escalating growth in data traffic, primarily fueled by the proliferation of connected devices and the rising demand for data-intensive applications, poses an ongoing challenge. Ensuring seamless connectivity, mobility, and optimal user experience in such a dynamic environment is more complex than ever. In this context, effective user mobility management through handovers (HOs) emerges as a critical task. Well-managed HOs contribute to enhanced user quality of service (QoS), minimizing disruptions in connectivity as users move within the network. Conversely, poor HO management can lead to issues such as increased latency, network congestion, and elevated operational costs. Against this backdrop, our work focuses on the problem of HO forecasting, aiming to predict HOs among base stations over time. To address this challenge, we introduce the HO Graph Convolutional Long Short-Term Memory (HGC-LSTM) neural network forecasting approach. This innovative methodology incorporates Graph Neural Networks (GNNs) and Long Short-Term Memory (LSTM) networks to capture spatio-temporal dependencies and correlations among neighboring pairs of base stations during the forecasting process. Our evaluation, conducted on a real-world dataset, demonstrates that the proposed HGC-LSTM approach surpasses state-of-the-art methods in the likes of MuLSTM, transformer and ARIMA, reaching the desired trade-off between user QoS and overprovisioned resources.

**Keywords:**

HOs Forecasting, 5G and beyond, Time Series Forecasting, Machine Learning

# 1. Introduction

By the end of 2028, a number of 5 billion subscriptions to 5G mobile services is projected worldwide [1]. This surge places a considerable strain on mobile operators, who grapple with managing the exponential increase in data traffic, resulting in significant pressure on their infrastructures. A critical aspect in ensuring network stability amid this shift towards a more mobile and data-centric world is handover (HO) management. Mobile operators are in constant pursuit of solutions to accommodate the escalating traffic while guaranteeing a high quality of service (QoS) and quality of experience (QoE) for their users [2].

Notably, a proficient HO management solution, particularly in high-traffic areas, is deemed crucial for achieving these objectives [2].

In this context, various challenges have been examined, including resource allocation and network planning, for the future of 5G and beyond networks. However, HO management has not received proportional attention, despite its significant impact on user QoS and QoE. HO, referring to the process of transferring an ongoing user communication session from one base station (BS) to another while minimizing service disruptions, stands out as a key element in preserving users' satisfaction as they move within the net-
work. With the increasing number of connected
devices, diverse applications, and a significant in-
crease in data traffic demand, HO management
becomes increasingly complex. This complexity is
exacerbated for mobile operators due to the high
number of HOs and the associated overhead in
terms of signaling and resource requirements [3].

The HO management process introduces key is-
sues such as HO forecasting [4], HO triggering [5],
HO decision [6], and HO optimization [7]. This
work focuses specifically on HO forecasting, a piv-
otal aspect that enables more efficient resource
allocation schemes. Such schemes can reduce op-
erational costs, enhance scalability, and facilitate
load balancing. Additionally, effective HO fore-
casting is beneficial for network planning, includ-
ing network optimization and the dynamic con-
figuration of base stations.

The existing contributions targeting HO fore-
casting predominantly center on predicting the
next BS (or, equivalently, cell) where an HO event
will occur [8]. This is crucial for anticipating and
preparing resources for the incoming user equip-
ment (UE) on the target BS. However, the inte-
gration of network function virtualization (NFV)
into the radio access network (RAN) architec-
ture [9] brings new challenges to the HO fore-
casting problem. For example, in an open RAN
(O-RAN) approach, HO-related virtual network
functions (VNF) and resources can be dynami-
cally activated and reserved [10]. Provisioning the
necessary functions and resources at the BS level
requires an estimation of the number of HOs the
BS will need to manage in a certain time win-
dow. Moreover, if we consider that some network
functions need to be dimensioned at the level of
the X2/Xn interface, between neighboring BS, we
need to forecast the number of HOs between pairs
of BSs. This type of prediction is not tied to the
trajectory of a specific user and facilitates the al-
location of appropriate resources and activation
of the correct VNF at each BS interface.

Previous studies, specifically [4] and [11], have
recognized this forecasting challenge. In [4], re-
searchers group cells with similar HO behavior
into clusters, followed by a HO forecasting at the
level of each cluster. However, this study does not

delve into the fine-grained prediction of HOs be-
tween specific BSs, as our approach does. Instead,
it focuses on predicting the aggregated number of
HO attempts per cell. Conversely, in [11], the
authors forecast the number of HOs and traf-
fic between every pair of neighboring BSs over
time, employing a multivariate forecasting ap-
proach for resource allocation in Cloud-Radio Ac-
cess Networks (C-RANs). While this work shares
similarities with ours, we introduce a novel HO
forecasting approach based on graph neural net-
works (GNN). This approach can capture spatio-
temporal correlations among neighboring pairs of
base stations, enhancing the forecasting process.

The contributions of this paper are twofold:

* We introduce a forecasting approach named HO Graph Convolutional Long Short-Term Memory (HGC-LSTM) neural network. This method utilizes a GNN architecture along with a Long Short-Term Memory (LSTM) model to predict the number of HOs between neighboring BSs over time. The GNN architecture allows for the extraction of spatio-temporal dependencies among various pairs of base stations, enhancing the overall forecasting performance. Additionally, it enables the modeling of intricate relationships and the capture of non-linear dependencies, providing valuable insights for the forecasting task. The LSTM model, renowned for its effectiveness in handling time series data [12], further contributes to achieving more precise forecasting.

* We assess the effectiveness of our proposed HGC-LSTM solution using a real-world HO dataset and compare its performance against existing forecasting benchmarks. The results indicate that our solution surpasses the performance of baseline solutions while maintaining a reasonable balance between execution time and accuracy metrics. Furthermore, we explore the impact of LSTM parameters on the performance of the solution and conduct an in-depth investigation into its effectiveness within the context of a virtualized RAN, particularly during periods of
peak HO activity, which are typically challenging to manage in a mobile network.

We note that a preliminary version of this work was published as a conference paper [13]. With respect to that version, we provide a more detailed architecture of the framework as well as an extended peak analysis that includes the state-of-the-art perspective. Furthermore, we showed the impact of other parameters such as the learning rate, the time window, and the forecast horizon on the prediction. Lastly, a network analysis is provided that highlights the impact of the prediction (from the perspectives of wasted resources and underserved users) in a mobile network scenario.

The subsequent sections of the paper are organized as follows: Section 2 examines previous studies on forecasting in networks and HO forecasting. Section 3 presents the problem statement and the corresponding system model. Section 4 elaborates on the design of the proposed solution, covering the methodology and framework architecture. Section 5 focuses on the evaluation of the proposed approach. Finally, Section 6 concludes this work.

## 2. Related Works

This section provides a literature review focusing on two pivotal aspects: general HO forecasting and the application of GNN methods for predictive analytics in mobile networks. The realm of HO forecasting research typically addresses two primary problems: forecasting the next HO target cell for a mobile user and predicting the number of HOs occurring between cells (or BS) over a specific time frame.

In the domain of predicting the next HO target cell, the study conducted in [14] hones in on HO decision-making. The authors proposed a hybrid forecasting mechanism that integrates long-term and short-term forecasting models, supplemented by a fuzzy forecasting model adept at handling imprecise data. The outcomes of their research revealed a noteworthy reduction in HO failure rates. In a parallel vein, [15] and [8] also delved into the intricacies of HO decision-making. [15] focused

on using HO information to predict the next target BS, thereby minimizing network interruptions during HOs. Their prediction model relied on the historical context of serving BS and target BS during the HO process, taking into account the frequency of previous HOs between pairs of BS. On the other hand, [8] argued against the necessity of sophisticated techniques for HO forecasting in multi-access edge computing (MEC) systems. In their study, they advocated for simple probabilistic approaches to predict future cells, emphasizing the operational cost considerations in the context of complex 5G networks.

Shifting the focus to the second axis, namely predicting the number of HOs during a given time period, [4] developed a method to predict the aggregated number of HOs per cell. Their approach involved uncovering common HO patterns through an analysis of cell behavior, coupled with a clustering approach based on the K-means algorithm. The authors applied various regression models, including linear regression (LR), polynomial regression (PR), Gaussian processes (GP), and neural networks (NN) to forecast hourly HOs per cell. Their evaluation underscored the efficacy of these models, with GP demonstrating the best performance. Additionally, the study in [16] introduced a novel three-phased data clustering framework for enhancing HO forecasting performance. Utilizing a generative adversarial network (GAN) for clustering, cluster calibration, and cluster division, the authors incorporated an LSTM model to forecast the number of hourly HO occurrences per cell in a specific city. The results not only highlighted that the proposed method preserves user privacy, but also indicated improvements in HO forecasting.

It is important to note that these prior studies were predominantly focused on per-cell forecasting. This is not precise enough in a virtualized RAN, where a BS needs to reserve a sufficient amount of computing and communication resources per network interface, meaning that the needs of each VNF (including HO management) need to be closely anticipated. In contrast, the work in [11] aligns closely with our research objective. In their study, the authors undertook
the forecasting of the number of HOs between
neighboring Radio Remote Heads (RRHs) and
the traffic volume as well. Leveraging historical
data, they proposed a Multivariate LSTM model
(MuLSTM) for forecasting HOs over a future pe-
riod. Their comparative analysis demonstrated
that MuLSTM outperformed traditional methods
like Auto-Regressive Integrated Moving Average
(ARIMA) and Windowed Artificial Neural Net-
work (WANN). From a networking perspective,
the study in [11] aims to propose a RRH-BBU
mapping scheme by leveraging the prediction of
the HOs and the traffic. Although they consider
a graph-based approach for the mapping, they use
a tensor-based modeling approach to capture the
spatio-temporal dependencies for the prediction.
However, we notice that the tensor relationships
are static and, therefore, do not necessarily adapt
to changes in the environment, as the tensor fac-
torization captures general spatial relationships.
Moreover, it not only might not incorporate real-
time contextual information, but it is also compu-
tationally expensive at a larger scale. As a result,
we believe that a combination of GNN and LSTM
can provide more scalability as it handles larger
scales and changes efficiently. Furthermore, such
a representation can easily incorporate real-time
information and more context for a better predic-
tion.

Similarly, [13] combines the second aforemen-
tioned research axis and the use of GNN for fore-
casting. It introduces a forecasting model which
integrates GNN and LSTM networks to forecast
HOs between base stations over time. The evalua-
tion in terms of Root Mean Square Error (RMSE)
and execution time shows that the model outper-
forms ARIMA and MuLSTM.

Regarding the utilization of GNNs for forecast-
ing in mobile networks in a more general way,
and not specifically related to mobility manage-
ment, the study in [17] centered on mobile traf-
fic forecasting. They introduced SDGNet, a HO-
aware spatio-temporal GNN that relies on dy-
namic graph convolution and gated linear units.
Notably, their approach incorporated HO infor-
mation by modeling the cellular network as a di-
rected and weighted dynamic graph. The nodes

in the graph contain information about the traf-
fic period at a specific time, while the weights
on the edges represent the HO frequencies be-
tween the vertices over a fixed observation win-
dow. Comparative evaluations against classi-
cal baselines showcased the superior accuracy of
SDGNet in terms of Mean Absolute Error (MAE)
across short-term, mid-term, and long-term sce-
narios. Furthermore, the work in [18] addressed
the challenge of mobile traffic prediction in the
context of 5G and beyond, employing a GNN-
based approach. They proposed a Time Series
Similarity-based Graph Attention Network (TS-
GAN) designed to leverage the features of cellular
traffic usage among base stations at spatial and
temporal levels. The approach involved calcu-
lating time-series similarity between the network
traffic of every two cells, constructing a directed
graph based on these correlations, and apply-
ing stacked graph attention neural networks for
prediction. The comprehensive evaluation across
metrics such as RMSE, MAE, and Mean Absolute
Percentage Error (MAPE) demonstrated the su-
perior performance of TSGAN compared to other
solutions from the literature across long, mid, and
short-term predictions.

Considering the current state-of-art on harness-
ing GNN for prediction, it is worth highlight-
ing that studies like [19, 20, 21] use static spa-
tial graphs or simple distance-based graphs, which
fail to adapt to dynamic user patterns that vary
over time and handover patterns in the same
breath. Moreover, there is currently no study
that captures the dependencies between base sta-
tions. The study in [19] proposes a Graph At-
tention Spatial-temporal Network (GASTN) that
combines attention mechanisms, spatial relation
graphs and structural RNNs for mobile traffic
forecasting. Although GASTN captures spatial
correlations based on the time series similarity
of traffic demand in different regions, it does not
naturally represent BS-BS relationships and user
movement patterns which are crucial to handover
forecasting. Likewise, the Multi-view Spatial-
Temporal Graph Network (MVSTGN) proposed
in [20] for cellular traffic prediction does not in-
clude a view for mobility transitions, and the
model lacks means to prioritize or represent inter-
action dynamics between BS. Indeed, the tempo-
ral attention and dense convolution modules cap-
ture both the local and global spatial-temporal
correlations between the traffic time series. [21]
incorporates LSTM for the prediction of cells de-
mand and authors construct the graph based on
geographical distance between cells. However,
the proposed framework is not designed to con-
sider the spatio-temporal migrations of the users.
In the case of our contribution, we leverage the
spatial dependencies between the base stations
and their vicinity and the graph is based rather
on handover transitions (users movements) than
physical distances.

In summary, the landscape of HO forecasting
research predominantly gravitates towards pre-
dicting the next cell from a user perspective.
However, our research diverges by concentrating
on forecasting the number of HOs between pairs
of neighboring base stations, offering a perspec-
tive suitable in a network virtualization context.
While [11] closely aligns with our focus, our pro-
posed GNN-based approach introduces advanced
techniques capable of accurately capturing spatio-
temporal dependencies between different pairs of
base stations like in [13]. This leads to enhanced
performance across both regular and complex HO
patterns, distinguishing our work in the topic of
predictive analytics for virtualized RANs.

3. System Model and Problem Statement

In this section, we introduce the problem state-
ment and describe our modeling of the HO fore-
casting problem.

3.1. *System model*

We consider a set of BS deployed in a target
area of study. As users move between BS, the
network needs to manage HOs. We denote a pair
of BSs between which users move as *p*, and HOs
are therefore assigned to each *p*. Each pair *p* is
associated with a time series *H*<sub>*p*</sub><sup>*T*</sup>, representing the
evolution of the number of HOs between the two
BS of pair *p* over time, up to timestamp *T*. The

set of all pairs of connected BS in the target area
is denoted as $P$.

As illustrated in Figure 1, this network is mod-
eled as an undirected graph $G = (P, E)$, where
$P = \{p_1, ..., p_N\}$ represents the set of nodes in the
graph, corresponding to the $N = |P|$ pairs of BSs,
and $E$ is the set of edges. Referring to the scenario
in Figure 1, nodes $p_1, p_2, p_3$, and $p_4$ represent pairs
(BS-A, BS-B), (BS-B, BS-C), (BS-C, BS-D), and
(BS-D, BS-A), respectively, where HOs occur. An
edge between nodes $p_i$ and $p_j$ exists if there is at
least one common base station between them, and
the edge weight is set to $w_{i,j} = 1$.

<figure><img src="image_3.png" /><figcaption>Figure 1: Graph modeling of the HO information.</figcaption></figure>

3.2. *Problem statement*

In our problem, we aim to forecast the num-
ber of HOs between each pair of BSs, over a set
of future time intervals. We aim to do so while
considering the historical evolution of the num-
ber of HOs for all pairs. More precisely, we define
$H_{(p,t)} = \{h_p^{T-t}, ..., h_p^T\}$ as a time series that repre-
sents the evolution of the number of HOs for the
pair $p$ between time slots $T-t$ and $T$. In this no-
tation, the index $t$ denotes the time intervals from
the historical data used in the prediction process.
Moreover, $h_p^{T-t}$ denotes the number of HOs for
pair $p$ at time interval $T-t$. Given $H_{(p,t)}$, our
objective is to forecast the next $m$ data points,
from $h_p^{T+1}$ to $h_p^{T+m}$.

This handover forecasting problem exhibits in-
herent spatial and temporal correlations. HO
rates between a couple of BSs are often influenced
by the HO rates among nearby BSs. Such local-
ized interdependencies arise from common mobil-
ity patterns and shared land use features. These
correlations can be effectively captured using a graph structure, which in turn can be leveraged and processed by GNN [22]. From a temporal point of view, daily commuting patterns and event-based mobility create complex temporal dynamics that LSTMs can succeed at modeling [23]. The interplay between spatial network structure and temporal evolution creates a quite challenging forecasting problem. Combining GNN and LSTM allows to effectively capture the corresponding spatial and temporal dimensions, which can then be harnessed for the forecasting in the context of HO management.

# 4. Framework Design

To address the aforementioned problem, this section outlines the methodology we employed to develop the proposed solution, followed by a discussion of the framework architecture.

## 4.1. Methodology

The HGC-LSTM model proposed in this study integrates GNNs and LSTM to predict HO occurrences between pairs of BS. Our architecture, depicted in Figure 2, comprises two key components: the Graph Convolutional Network (GCN) and the LSTM layer.

The first component involves obtaining node representations by passing a training dataset through the GCN layer. This layer is designed to capture local and global dependencies within the graph using a message-passing mechanism to aggregate information from neighboring nodes. In our context, neighboring nodes correspond to pairs of base stations that share a common BS, enabling us to consider BS-level phenomena while facilitating fine-grained forecasting at the link level. The GCN layer learns representations that encode both local features of the node and its structural context within the graph for accurate forecasting. We note that $H(G, t)$ describes the graph G that encompasses all the pairs where each pair (node) has as feature the historical data used considered for the prediction (t).

For the second component, the LSTM layer is dedicated to forecasting the time series associated

with each node in the graph. During this stage, we leverage the corresponding adjacency matrix of our graph along with the node representations updated by the GCN layer, to serve as input for the LSTM layer. We denote as $H'(G, t)$ the graph information updated by GCN and used as an input for LSTM (see Figure 2).

## 4.2. Framework architecture

Below, we delve into a more detailed description of each component, starting with the GCN segment and subsequently exploring the LSTM part. This combination of GCN and LSTM allows the model to use spatial and temporal information. GCN, through the message passing mechanism, aggregates information from a node's neighbors (spatial information) to generate the node embedding. This is used by the LSTM part to capture the temporal dynamics of each node's time series. This improves prediction, as feeding GCN-generated embeddings into a LSTM layer enhances the temporal model with spatially informed features.

### 4.2.1. Message Passing Mechanism

Depicted in Figure 2, message passing is a fundamental aspect of the GCN layer, as it facilitates the aggregation of information between nodes of the graph. For each node $p$ in the graph, the following steps are considered to compute node representations:

* **Initialization:** A node $p$ is linked to $p_{i \in 1,...,n}$ neighbors, where $n$ is the number of neighbors of the considered node. In our model, a node $p$ represents a pair of BS and connects to all other BS pairs with a common base station. Each node $p$ is assigned as a feature $H_{(p,t)}$, representing its historical data of length $t$. In our case, these historical data represent the number of HOs associated with node $p$. Later, these $t$ points from the past will be considered in the forecasting process. The initial representation of each node is calculated as:

$$p^{init} = w_{p,p_i} \cdot H_{(p,t)}$$
<figure><img src="image_4.png" /><figcaption>Figure 2: HGC-LSTM framework.</figcaption></figure>

where $w_{p,p_i}$ is the weight of the edge between $p$ and its neighbor $p_i$. In our model, where there is no inherent distinction between BS relationships, $w_{p,p_i} = 1$.

* **Aggregation:** In this step, messages containing the initial representations are exchanged between neighboring nodes. We note that, for our system, neighboring nodes actually mean pairs of BS with a BS in common, so this message exchange happens internally, and it does not require actual communication in the network. An aggregated message $p^{agg}$ is calculated by each node $p$, based on the messages received from its neighbors. The messages are aggregated to derive a new representation for each node. In our work, since we do not account for any weight in the node interactions, the aggregation function is simply defined as the average of the neighbors' representations:

$$p^{agg} = \frac{1}{n} \sum_{i=1}^{n} p_{i}^{init},$$

where $p_{i}^{init}$ is the initial representation of neighbor $i$.

* **Update:** The final representation of node $p$, denoted as $H'_{(p,t)}$, is calculated using the aggregated messages $p^{agg}$ and the initial representation of node $p^{init}$. After aggregating the messages, each node updates its representation as follows:

$$H'_{(p,t)} = p^{init} \oplus p^{agg},$$

where $\oplus$ represents the concatenation operation. Generally speaking, this update step usually involves applying an activation function to the final node representation. However, for our problem, the activation function is directly included in the LSTM layer.

The output of this block provides node representations over time and is combined with LSTM units. We underline the fact that these node representations include information about the node's neighbors, a consequence of the update step.

### 4.2.2. LSTM layer

The output of the message passing, explained above, serves as the input for the LSTM layer which includes LSTM units, as illustrated in Figure 2. The objective here is to capture the temporal dependencies in our data. However, since the node representations also include spatial information in the form of the aggregated neighbor messages, we have in fact a spatio-temporal point
of view. In the remainder of this section, to simplify the notations, we denote the representation over time of a generic pair p as $H_t$.

The LSTM network builds upon the information of the input sequence to make predictions for future times steps. The process can be described as follows:

* **Initialization and input processing:** The hidden state $h_{(t-1)}$ and the cell state $c_{(t-1)}$ of the LSTM neural network (see the bottom part of Figure 2) are initialized with random values. The goal here is to prepare the LSTM cell memory for information propagation across various time steps.

* **Input gate $i_t$:** In this step, the input and the hidden state are processed by passing them through a sigmoid activation function. This explains why an activation function was not used in the GCN layer. This step helps in deciding whether the new information should be incorporated into the current state, according to the formula:

$$i_t = \sigma(W_{H'i}H'_t + W_{hi}h_{t-1} + W_{ci}c_{t-1} + b_i),$$

where $W_{H'i}$, $W_{hi}$ and $W_{ci}$ are weight matrices for the input, hidden state, and cell state, respectively. $b_i$ is the bias term, and $\sigma(\cdot)$ is the sigmoid activation function that forces the input to a value that is either 0 or 1.

* **Forget gate $f_t$:** This step determines the information to be omitted from the previous cell state $c_{(t-1)}$, by applying a sigmoid function to the input value and the preceding hidden state, as expressed in the following formula:

$$f_t = \sigma(W_{H'f}H'_t + W_{hf}h_{t-1} + W_{cf}c_{t-1} + b_f),$$

where $W_{H'f}$, $W_{hf}$ and $W_{cf}$ are weight matrices for the input, hidden state, and cell state, respectively and $b_f$ is the bias term. It produces the values 0 (forget) or 1 (keep).

* **Cell state update:** At this stage, the LSTM merges the new information provided

by the input gate $i_t$ and the forget gate $f_t$ to determine the extent to which the old state, represented by the cell state $c_{(t-1)}$, should be retained. The cell state is then updated according to:

$$c_t = f_t \odot c_{t-1} + i_t \odot \tanh(W_{H'c}H'_t + W_{hc}h_{t-1} + b_c),$$

where $\odot$ represents element-wise multiplication. $W_{H'c}$ and $W_{hc}$ are weight matrices for the input and hidden state, respectively. $b_c$ is the bias term, and $\tanh(\cdot)$ is the hyperbolic tangent activation function that forces the input to a value of -1 or 1.

* **Output gate $o_t$:** The output is determined by incorporating information from the previous hidden state $h_{t-1}$, the updated cell state $c_t$, and the current input $H'_t$. The output gate plays a crucial role in controlling which portions of the cell state are utilized to compute the hidden state, as expressed in the formula:

$$o_t = \sigma(W_{H'o}H'_t + W_{ho}h_{t-1} + W_{co}c_t + b_o),$$

where $W_{H'o}$, $W_{ho}$, and $W_{co}$ are weight matrices for the input, hidden state, and cell state, respectively and $b_o$ is the bias term.

* **Prediction:** The forecast value is denoted as the hidden state $h_t$, representing the output of the LSTM network. It is derived by combining the cell state $c_t$ and the output gate $o_t$ through the following expression:

$$h_t = o_t \odot \tanh(c_t)$$

This procedure iterates for each time step within the input sequence, allowing the LSTM layer to capture dependencies across extended sequences. The output $H''(G, t)$ is the graph with the forecasts of the number of HOs for each node (pair of base stations).

## 5. Evaluation

In this section, we present the evaluation of the proposed HGC-LSTM approach. For this, we discuss the dataset used in our study, followed by
the details of our experimental set-up. To understand how HGC-LSTM is situated in the state of the art, we measure its performance against other methods from the literature and analyze in detail the obtained results.

## 5.1. Dataset

Our evaluation is based on an authentic dataset obtained from 59 base stations within the Orange 4G network in Poitiers, France. The geographical distribution of these 59 cellular sites is visualized in Figure 3.

<figure><img src="image_5.png" /><figcaption>Figure 3: 4G site locations in Poitiers, France.</figcaption></figure>

The dataset encompasses information on the count of HOs between pairs of base stations at 30-minute intervals. The data spans from March 15th, 2019, to April 16th, 2019. In the context of our graph-based approach, the dataset provides details for a total of 537 pairs of BSs experiencing HOs, forming the basis for constructing the graph, as outlined in Section 3. As shown in Figure 1, the pairs of BS between which HOs occur in the dataset are modeled as nodes in our graph. Each graph node obtained like this in the model has an associated time series as a feature, representing the number of HOs which occur between the two corresponding BS.

## 5.2. Baselines Algorithms

We conduct a comparative analysis of our proposed HGC-LSTM framework against two

alternative approaches: a transformer-based model [24], ARIMA [25], a classical univariate time series method, and MuLSTM as proposed in [11], the closest existing work to ours in the literature.

Transformer models are neural networks that track relationships in sequential data using self-attention mechanisms, allowing them to process entire sequences simultaneously rather than step-by-step. Those models have gained popularity in the literature for time series forecasting as they have proven to be efficient in capturing long-range dependencies in the data. Initially, transformer models follow an encode-decoder architecture but, for the time series forecasting problem, only the encoder part is used [26]. The transformer architecture consists of two main components: the encoder block (including the normalization, multi head attention, convolutional layers) to capture temporal dependencies, and the Multi-Layer Perceptron (MLP) layer for the prediction. It is worth noting that, in our work, we train the same transformer model, but for each pair of BSs individually.

ARIMA is a well-known and widely used statistical univariate model designed for the analysis and prediction of single time series data. It employs autoregressive (AR), differencing (I), and moving average (MA) components to model patterns and behaviors in a single variable over time. The AR component captures the linear relationship with lagged observations, the I component removes trends through differencing, and the MA component models dependencies on residual. The ARIMA parameters, namely autoregressive order (a), differencing order (d), and moving average order (q), are determined based on the characteristics of the time series data and are estimated using statistical techniques. In our case, since ARIMA is not inherently designed for multivariate forecasting, we constructed individual models for each pair of BSs with HOs to be predicted, resulting in personalized parameters for each pair.

MuLSTM, on the other hand, is a neural network architecture tailored for processing and predicting a feature that depends on multiple other features. This model is designed to capture de-
pendencies and patterns across multiple variables in a time series dataset [27]. Leveraging LSTM architecture, MuLSTM effectively handles sequential data and captures long-term dependencies, using the same principles as those described in Section 4. Each MuLSTM model is specific to a pair of BSs, utilizing historical data for that pair and its neighbors, based on the defined graph structure.

Our main evaluation metrics are RMSE, Mean Absolute Error (MAE) and Mean Absolute Percentage (MAPE), which are classical choices in forecasting problems. The metrics assess the performance of these algorithms by comparing predicted values against the ground truth in the dataset. The dataset is split into training and testing sets, with 70% training, 30% testing for ARIMA and 80% training, 20% testing for MuLSTM. For HGC-LSTM, we need an extra step for the GCN layer, hence we use a split of 70% training, 10% validation, and 20% testing. The validation step is essential for HGC-LSTM due to its GCN model involving graph topology, helping to avoid overfitting or underfitting by tuning hyperparameters. ARIMA and MuLSTM, not involving any convolutional layer, do not require a validation step. For the transformer model, we consider a split of 80% training, 20% test and we consider a 0.2 validation split during training (20% of training data) to effectively monitor overfitting.

Predictions are executed on the test set for each algorithm, and the model with the lowest RMSE, MAE and MAPE values is deemed the most effective.

## 5.3. Feature selection and Training Methodology

In this section, we provide details about the different settings we used in our experiments. The key factors, outlined in Table 1, include parameters for both the GCN and the LSTM network in our framework. Notably, when working with ARIMA, we created a distinct model for each pair of BSs, each model having its own set of parameters. Similarly, MuLSTM operated on a per-pair basis, sharing the same batch size as HGC-LSTM and using 50 LSTM units. This approach allowed

us to fine-tune configurations for each model, ensuring a thorough exploration of the experimental conditions. The transformer model operates on a per-pair basis with a batch size of 64.

<table><caption>Table 1: Framework variables.</caption><thead><tr><td>Variable</td><td>Description</td><td>Value</td></tr></thead><tbody><tr><td>N</td><td>Number of nodes (pairs)</td><td>537</td></tr><tr><td>E</td><td>Number of edges</td><td>21098</td></tr><tr><td>batch</td><td>Batch size (number of time series samples in each batch)</td><td>64</td></tr><tr><td>inputs</td><td>Number of input features</td><td>1</td></tr><tr><td>outputs</td><td>Number of output features</td><td>1</td></tr><tr><td>t</td><td>Number of time steps considered for the prediction</td><td>4</td></tr><tr><td>epochs</td><td>Number of epochs</td><td>300</td></tr><tr><td>units</td><td>Number of LSTM units</td><td>64</td></tr></tbody></table>

The input features for HGC-LSTM are the time series of the number of handovers between each pair of base station where HOs occur. The features are normalized using the train set mean and standard deviation, and the input shape is (*batch*, *t*, *N*, *inputs*).

During the fine tuning process, we used the optimizer RMSprop [28] with a learning rate of 0.0002 as the RMSprop optimizer is well-suited for recurrent architectures like LSTMs. This low learning rate helps preventing overshooting optimal weights when dealing with spatio-temporal dependencies through GNN and LSTM. Additionally, since the time series are spatial and temporal dependent, a smaller learning rate helps ensure stable convergence. We used four steps in the past to perform the prediction as it provides a trade-off between providing enough historical context and the computational efficiency as four time steps capture relevant short-term patterns. The number of LSTM units provides sufficient capacity to capture complex temporal patterns across
multiple nodes and the batch size helps to provide a stable gradient. A batch size of 64 is often a rule of thumb for many deep learning applications and it ensures a balance between computational efficiency and stable gradient updates.

The training methodology of HGC-LSTM involves key components to optimize the performances of the handover forecasting:

* **Training Configuration**: We considered Z-score standardization for the normalization and the loss function is the Mean Squared Error (MSE). The optimizer is RMSprop as aforementioned and it considered 300 epochs which is large enough to ensure convergence on complex patterns.

* **Training Process**: Early stopping (patience of 200 epochs) allows the training to halt when the validation loss stops improving to prevent overfitting by stopping the training when the model performance degrades. The regularization via the dropout layers (rate:0.5) also reduces overfitting by randomly deactivating 50% of neurons during training.

Additionally, we provided an algorithm breakdown in the subsection Algorithmic Breakdown of the section Evaluation which encompasses three components: the graph construction, the message passing mechanism and the prediction itself through the LSTM layer.

Our HGC-LSTM model is constructed using TensorFlow-GPU, an open-source machine learning library. We primarily employed PyCharm for data preprocessing and utilized the PyCharm Integrated Development Environment (IDE) for coding purposes. The training of all algorithms was conducted on Compute Canada, the national high-performance computing (HPC) infrastructure, which provides advanced research computing resources across Canada.

For the device configuration in our experiments, we used Intel Xeon Silver 4110 Skylake 2.10 GHz and Intel Xeon Gold 6238 Cascade Lake 2.10 GHz as the Central Processing Units (CPUs). The graphical processor employed was Tesla T4, and

the memory capacity used was 16 GB. This setup ensured a robust and efficient computational environment for our experiments.

### 5.4. Algorithmic Breakdown

Our proposed algorithm leverages a combination of GNNs and LSTM networks to accurately forecast HO occurrences between BSs. Below we provide a comprehensive explanation of our approach through an algorithmic breakdown. HGC-LSTM encompasses three components: the graph construction, the GCN layer and the GCN+LSTM part.

<caption>**Algorithm 1 Graph Construction**</caption>

1: **Input:** $H_P^T$
2: **Output:** $H(G, t)$
3: $G \leftarrow \text{EmptyGraph()}$
4: $H(G, t).addGraph(G)$
5: **for** $pair_i$ **in** $P$ **do**
6: &nbsp;&nbsp;&nbsp;&nbsp; $G$.addNodes($pair_i$)
7: &nbsp;&nbsp;&nbsp;&nbsp; $H(G, t)$.pair_i.addfeature($H_{(pair_i,t)}$)
8: &nbsp;&nbsp;&nbsp;&nbsp; **for** $pair_i$ **in** $G$ **do**
9: &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; **for** $pair_j$ **in** $G$ **do**
10: &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; **if** ($pair_i$ &amp; $pair_j$ share BS) and ($pair_i \neq pair_j$) **then**
11: &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $G$.addEdge($pair_i, pair_j, W = 1$)
12: &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; **end if**
13: &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; **end for**
14: &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; **end for**
15: **end for**

#### 5.4.1. Graph Construction

The Algorithm 1 takes as input $H_P^T$ which represents the time series all of the pairs in $P$ over $T$ time slots (line 1). It also gives as output $H(G, t)$ which is the graph $G$ including all the pairs and for each pair (node) we have $H(p, t)$ as feature (line 2). Therefore, each pair $pair_i$ is added as a node in the graph and the feature $H_{(pair_i,t)}$ too (lines 5-6). $H_{(pair_i,t)}$ represents the time series of the historical data considered for the prediction ($t$ time steps). An edge exists between two nodes if they share at least one base station in common and the weight $W$ will be 1 (lines 8-11).
**Algorithm 2 Graph Convolution Layer**
1: **Input:** $H(G, t)$
2: **Output:** $H'(G, t)$
3: **for** pair$_i$ in G.nodes **do**
4:     $p^{init} \leftarrow H(pair_i, t)$
5:     **neighborsList** $\leftarrow$
       ExtractNeighbors($H(G, t)$, pair$_i$)
6:     $p^{init}_{neigh} \leftarrow EmptyList()$
7:     **for** neighbor$_j$ in neighborsList **do**
8:         $p_j^{init} \leftarrow$
           ComputeNeighbors(neighbor$_j$, pair$_i$)
9:         $p^{init}_{neigh}$.append($p_j^{init}$)
10:      **end for**
11:    $p^{agg} \leftarrow$ Mean($p^{init}_{neigh}$)
12:    $H$.pair$_i \leftarrow$
        addFeature(<concatenate($p^{init}$, $p^{agg}$)>)
13:    **end for**

**Algorithm 3 HGC-LSTM Architecture**
1: **Input:** $H'(G, t)$
2: **Output:** $H''(G, T)$
3: $H''(G, T) = \text{LSTM}(H'(G, t))$

5.4.2. Graph Convolution Layer

The Graph Convolutional (GC) layer in Algorithm 2 layer processes node features by aggregating information from adjacent nodes, allowing the model to lean spatio-temporal dependencies. This is the layer used for the message passing mechanism described in section 2 which has three steps: initialization, aggregation and update. This algorithm takes as input $H(G, t)$ where each pair (node) has as feature the historical data used considered for the prediction as previously mentioned (line 1). Additionally, the output is $H'(G, t)$ which is the graph with all the nodes representations after the message passing mechanism. This mechanism is performed for each node in the graph and the algorithm first computes each node's neighbors representation $p_{\text{neigh}}^{\text{init}}$ (lines 6 - 10) as well as the initial representation of the node itself $p^{\text{init}}$ (line 4). Then, there is the aggregation of the computed representations (line 11) using the Mean to obtain the aggregated messages $p^{\text{agg}}$. The aggregation enables each node to incorporate information from its neighborhood,

capturing the correlations between connected BSs pairs. Finally, the updated node representation of the pair $pair_i$ is computed doing the concatenation of the aggregated messages and the initial node representation (line 12).

5.4.3. LSTM + GCN

This component (Algorithm 3) is basically our proposed framework which combines the GCN and LSTM layers. The input of this algorithm which is the previously obtained $H'(G, t)$ is fed through a LSTM layer (line 3) which captures the temporal dependencies in the data. It is worth nothing that a dense layer projects the LSTM outputs to the desired forecast horizon $f$, generating the predictions. The output $H''(G, T)$ describes the graph where each node carries the prediction of each pair for $T$ time steps.

5.5. Metrics Analysis

Figure 4 illustrates the global average RMSE for the four considered prediction techniques: ARIMA, HGC-LSTM, transformer and MuLSTM. Across the dataset comprising 537 pairs of BSs, HGC-LSTM exhibits the lowest average RMSE, indicating superior overall performance compared to transformer, ARIMA and MuLSTM.

To offer a more visual representation of the forecast performance, Figure 5 presents the predicted numbers of HOs on the test data for four arbitrarily selected pairs of BS, comparing HGC-LSTM, ARIMA, transformer and MuLSTM. The plots suggest that HGC-LSTM consistently outperforms the other methods, closely aligning with the ground-truth time series.

To provide a quantitative comparison on specific pairs of base stations, Figure 6 displays the individual RMSE, MAE and MAPE for the four specific pairs of BS. While HGC-LSTM may exhibit lower performance for certain pairs, its stability and capacity to handle diverse patterns contribute to an overall superior performance. For example, for pair 203, the best RMSE according to Figure 6a is obtained by ARIMA. However, the performance of HGC-LSTM is more uniform, reaching a good forecasting performance for every pair of BS. Our observation is that MuLSTM faces
<figure><img src="image_6.png" /><figcaption>Figure 4: RMSE, MAE, MAPE for the algorithms</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Figure 5: Forecasting for the pairs 334, 329, 267, and 203 with HGC-LSTM, transformer, ARIMA and MuLSTM.</figcaption></figure>

challenges in predicting time series with a limited seasonal pattern, showcasing the effectiveness of
<figure><img src="image_8.png" /><figcaption>Figure 6: RMSE, MAE, MAPE for the selected pairs per algorithm</figcaption></figure>

<table><caption>Table 2: Best ranked solution.</caption><thead><tr><th>HGC-LSTM</th><th>MuLSTM</th><th>ARIMA</th><th>transformer</th></tr></thead><tbody><tr><td>55.02%</td><td>18.03%</td><td>9.65%</td><td>17.3%</td></tr></tbody></table>

HGC-LSTM in capturing such more complex patterns. However, as we can observe in Figure 6c, the difference in values all the algorithms is quite marginal for the pairs 334, 329 and 267 but we also notice that MuLSTM is significantly worse than the others. For the MAE comparison in Figure 6b, HGC-LSTM presents on average, the best results across the four pairs although ARIMA is the lowest for pair 329. It is worth noticing that pair 267 shows the smallest gap between models performances and the performance differences are less dramatic in MAPE than in MAE.

For a more in-depth analysis, we rank the three algorithms based on their RMSE performance for each pair of BS in the dataset, and we select the best method in each case. These results are shown in Table 2. HGC-LSTM attains the top-ranking solution in the majority of cases, showcasing its consistent effectiveness in terms of RMSE. However, ARIMA, transformer and MuLSTM outperform HGC-LSTM in certain instances.

## 5.6. Peaks Analysis

Going beyond classical metrics in the forecasting community, we examine the efficacy of HGC-LSTM in predicting peak values within our dataset, a crucial metric for mobile operators who need to propose efficient network management solutions at these peak hours. For example, in the context of a virtualized RAN, accurate predictions during these peak moments empower operators to proactively allocate computational and

<figure><img src="image_9.png" /><figcaption>Figure 7: Peaks distribution.</figcaption></figure>

communication resources. Defining a peak as a juncture in the time series where the *k* values preceding and following that point exhibit lower values than the focal point, we employ *k* = 4 for this analysis.

The scatter plot in Figure 7 visualizes the predicted versus actual values of the peaks, revealing a tendency for the predicted values to be smaller than the actual values. Notably, HGC-LSTM encounters challenges in accurately forecasting higher peaks, a phenomenon visually affirmed by the selected examples in Figure 5, wherein high-value peaks in the ground truth are frequently underestimated.

To quantify the prediction accuracy on all peak values, we compute the error percentage using the formula:

$$ error(\%) = ((prediction - real)/real) \cdot 100, $$

where *prediction* is the predicted value of the peak and *real* is the real value of the peak. The global error, represented by the mean of all errors,
<figure><img src="image_10.png" /><figcaption>Figure 8: Probability distribution of the error percentage for HGC-LSTM.</figcaption></figure>

stands at 37.55%. This implies that, on average, the model deviates by this percentage when the network experiences elevated user mobility (as indicated by a high number of HOs).

Further scrutiny involves analyzing the distribution of peak errors through the cumulative distribution function (CDF). This is defined as:

$$F(x) = P(X \leq x),$$

where X is a random variable and x signifies the error value. Considering the absolute values of the error percentage, as illustrated in Figure 8a, we juxtapose the error distribution obtained by HGC-LSTM for all data points with that for peak values. We notice that more than 60% of peak values exhibit errors exceeding 25%, while only 40% of all data points (not only peak values) register errors of a similar magnitude. This contrast underscores the heightened error levels associated with peak values compared to the broader dataset.

For more details, Figure 8b presents the CDF of errors, encompassing both positive and negative values. Notably, the majority of errors associated with peaks manifest as negative values, indicating that the HGC-LSTM approach consistently underestimates values at peak moments. This prevalence of negative errors diminishes to 60% when considering all data points, suggesting a nuanced performance variation across peak and non-peak instances.

We also investigate how ARIMA, transformer and MuLSTM perform on peaks. Similarly to

Figure 7, we can observe in Figure 9 that the predicted values tend to be smaller than the actual values. This means that ARIMA, transformer and MuLSTM have as much trouble predicting higher values as HGC-LSTM.

The CDFs in Figure 10, Figure 11 and Figure 12 show that the peak error percentage for MuLSTM and ARIMA is similar to the one for HGC-LSTM. However, the CDFs obtained for all the data points are much more alike to those obtained for the peaks, in the case of these baseline approaches. This means that HGC-LSTM obtains its better performance by mainly reducing the prediction error for non-peak points. For peak values, HGC-LSTM shows the same performance as the state-of-the-art solutions.

## 5.7. Execution Time

In evaluating computational efficiency, the comparison among HGC-LSTM, ARIMA, transformer and MuLSTM reveals noteworthy insights. The analysis of the total execution time for the three methods, as illustrated in Table 3, underscores the efficiency of HGC-LSTM, outperforming transformer, ARIMA and MuLSTM by requiring less execution time (including the training). We note that the four solutions were evaluated on the same hardware as described above. A closer examination reveals that ARIMA faces challenges in this aspect, primarily stemming from the need to build individual models per pair of BS. This intricate process involves tuning distinct parameters for each model, resulting in a considerable computational burden. Given
<figure><img src="image_11.png" /><figcaption>Figure 9: Peaks distribution for baselines.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Figure 10: Probability distribution of the error percentage for MuLSTM.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Figure 11: Probability distribution of the error percentage for ARIMA.</figcaption></figure>

that the entire parameter tuning, model training, and forecasting process must be repeated 537 times for our dataset, ARIMA experiences prolonged execution times compared to alternative approaches. In contrast, MuLSTM adopts a similar one-model-per-pair structure, yet manages to achieve more efficient execution times. This efficiency can be attributed to the utilization of the Tesla T4 GPU, specifically designed for train-

ing workloads and equipped with dedicated tensor cores for deep learning operations. GPU optimization contributes to faster computations, a crucial advantage when handling neural networks, as evident in both MuLSTM and HGC-LSTM. Despite these optimizations, it should be noted that MuLSTM still incurs an execution time that is one order of magnitude higher than our proposed solution. Since for the transformer model
<figure><img src="image_14.png" /><figcaption>Figure 12: Probability distribution of the error percentage for transformer.</figcaption></figure>

we wanted to achieve the best possible performances, we performed the forecasting for one pair at the time. However, despite the use of high-end GPU and hardware infrastructure, the execution time is still quite significant in comparison to MuLSTM and HGC-LSTM considering that the model that we use is trained with 100 epochs.

In essence, the computational efficiency of HGC-LSTM shines through, offering a streamlined approach that balances effective forecasting with reduced execution times. The challenges faced by ARIMA in handling multiple models and the optimized GPU utilization in MuLSTM and transformer highlight the distinct advantages of HGC-LSTM in terms of computational efficiency.

<table><caption>Table 3: Total execution time per algorithm</caption><thead><tr><td>Algorithms</td><td>Execution time (s)</td></tr></thead><tbody><tr><td>ARIMA</td><td>312422</td></tr><tr><td>HGC-LSTM</td><td>775.97</td></tr><tr><td>MuLSTM</td><td>6276</td></tr><tr><td>transformer</td><td>19223</td></tr></tbody></table>

## 5.8. Parametric Study of the HGC-LSTM Model

In this section, we evaluate the impact of the different HGC-LSTM parameters on the prediction. We consider the following parameters: LSTM units, learning rate, time window, and forecast horizon. We choose RMSE to evaluate their impact.

### 5.8.1. LSTM Units

In examining the HGC-LSTM model and its various parameters, an essential facet to explore is the influence of the number of LSTM units on the predictive accuracy. As depicted in Figure 13, a discernible trend emerges, showcasing a substantial decrease in the average RMSE when transitioning from 4 to 8 units. Following this initial decline, the decrease becomes more gradual as the number of units increases, albeit with a local peak observed at 200 units. This analysis underscores the pivotal role that the number of LSTM units plays in shaping the performance of the HGC-LSTM framework. The findings suggest that this parameter warrants careful consideration and evaluation across diverse datasets.

In our specific investigation, unless specified otherwise, the choice of 64 units during training represents a deliberate trade-off. This decision seeks to strike a balance between optimizing the overall performance of the model and managing execution time. The rationale behind this lies in the acknowledgment that a higher number of units not only extends execution times but also increases the risk of overfitting. As such, the chosen configuration of 64 units aims to achieve a nuanced equilibrium in the trade-off, aligning with our objectives and dataset characteristics.

### 5.8.2. Learning Rate

Next, we investigate the impact of the learning rate on the prediction of HGC-LSTM. Since this parameter determines how quickly our algorithm will converge, our aim is to assess the best value
<figure><img src="image_15.png" /><figcaption>Figure 13: Average RMSE by number of units for HGC-LSTM.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Figure 14: RMSE as a function of the HGC-LSTM learning rate.</figcaption></figure>

for this outcome. The obvious observation in Figure 14 is that the RMSE is relatively constant for values of the order of $10^{-4}$ to $10^{-2}$. Moreover, we observe that, despite the fact that it decreases from $10^{-1}$ to $10^{-2}$, there is a sudden increase from $10^{-5}$. Thus, we can say that the best range for this parameter, in our scenario, includes values between $10^{-4}$ and $10^{-2}$.

### 5.8.3. Time Window

The time window in HGC-LSTM defines the length of the sequence that we take as input to predict the values for the next time steps. We used it to feed a sequence of past observations into the LSTM model for predicting the next data point in the time series, while capturing temporal dependencies and patterns in the data. We want to assess the influence of this parameter on the accuracy of the prediction, so we consider a set of values for that sake. Figure 15 shows that, if we take 6 time steps in the past to predict the

<figure><img src="image_17.png" /><figcaption>Figure 15: RMSE as a function of the HGC-LSTM time window.</figcaption></figure>

future, it gives the best results. However, we also note that the results are generally stable in terms of RMSE and that the impact of this parameter is reduced. We also note that a higher value for the time window naturally implies a higher execution time for HGC-LSTM.

### 5.8.4. Forecast Horizon

The forecast horizon represents the number of data points *f* that we want to predict. In predicting future values, we can choose one of the following methods:

* **Predict multiple points simultaneously**: Considering our aforementioned time series $h_p^T$, the goal would be to predict, at each time step, all values from $h_p^{T+1}$ to $h_p^{T+f}$ simultaneously. This implies that one value $h_p^{T_k}$ will be predicted at multiple time steps, more precisely *f* times.

* **Predict one point at a time**: Taking into account the settings mentioned above, the goal here would be to predict only $h_p^{T+f}$ at a given time step *T*.

Since in all the results above we predicted one point in the future, with *f* = 1, we now investigate both prediction cases, with different values of *f*. Figure 16 shows that not only the prediction is better overall when we predict multiple points simultaneously, but also that the optimal forecast horizon for our algorithm is *f* = 2.
<figure><img src="image_18.png" /><figcaption>Figure 16: RMSE value depending on the forecast horizon.</figcaption></figure>

5.9. Mobile network evaluation

From the mobile network operator point of view, evaluating a network forecasting solution in terms of RMSE is not very meaningful. What matters is whether the prediction obtained is accurate enough to have a positive impact on the network. To evaluate HGC-LSTM from this perspective, we consider the problem of mobility management in a virtualized RAN. In this case, only the antenna unit of the BS remains installed on-site, while all the computation is conducted on shared resources in a proximity data center [9]. In this scenario, each BS (more precisely, each baseband unit, located in the datacenter) needs to be dynamically allocated computation and communication resources to manage HOs. This dynamic allocation needs to include a HO forecasting mechanism. Moreover, HO management also implies communication between the source BS and the target BS, meaning that a technique such as HGC-LSTM, which predicts the number of HOs between every pair of BS, is particularly appropriate for the task.

In an ideal scenario, the prediction of the num-
ber of HOs would be perfect, allowing a perfect
HO resource allocation. Of course, in practice,
a perfect prediction is not possible. For an im-
perfect prediction, the consequences are different
if the error is positive or negative. Practically,
in case of an over-estimation, resources are al-
located, but remain unused. This is mainly a
cost problem for an operator, who is using more

resources than necessary. In case of an under-
estimation, there are not enough resources to
manage all HOs, which will most likely result in a
QoS penalty for some users. Preserving the QoS
level is generally more important from the oper-
ator perspective. For this reason, we consider in
the following that an operator reserves a number
of additional resources with respect to the pre-
dicted values. Practically, if the number of pre-
dicted HOs is *x*, we consider the operator will
reserve resources for (1 + *r*) · *x* HOs. In the fol-
lowing, we vary *r* between 5% and 50%. The goal
is to determine how many users are going to be
blocked and how many resources we are wasting,
depending on *r* and for the different prediction so-
lutions we studied. For simplicity and to remain
generic, we make the assumption that conduct-
ing one HO requires one unit of resources in the
following analysis.

We show this tradeoff between the number of
underserved users and the amount of resources
reserved in Figure 17, for one arbitrarily chosen
pair of BS. Indeed, the results are very similar in
shape for all the BS in the studied dataset, hence
we decided to show only one representative exam-
ple. As expected, as we increase *r*, more resources
are reserved, but not always used. This is able to
satisfy more users when an under-estimation hap-
pens, hence the decreasing blue curve, but more
resources are wasted in case of over-estimation, as
shown by the red curve.

In order to assess the gain brought by a dy-
<figure><img src="image_19.png" /><figcaption>Figure 17: Network performance evaluation for pair 329 with HGC-LSTM.</figcaption></figure>

namic resource allocation solution for HO management, we compare with a static approach, where the BS are configured to cope with the maximum number of HOs. We note that this static approach can be seen as a best case scenario in current networks, as it still implies the knowledge of the highest peak of HOs during the day, in order to perfectly dimension the network. Since user mobility is mainly concentrated during morning and evening hours, we focus our analysis on two time intervals: i) 6AM to 10AM, and ii) 5PM to 9PM. We compute the gain in terms of reserved resources with respect to a static approach for the prediction algorithms studied in this paper: HGC-LSTM, MuLSTM, ARIMA and transformer. We use two values for r, namely 10% and 50%.

Figure 18 shows that the four algorithms manage to save resources compared to a traditional static approach. It is interesting to note that, when considering these average results for specific time intervals, the impact of *r* is less significant than the individual BS results shown in Figure 17. The average gain for *r* = 50% is only slightly lower than the one obtained for *r* = 10% for the four considered algorithms. However, HGC-LSTM produces a slight improvement over the other two solutions, both in the morning and in the evening. Considering the significant gains brought about by the predictive solutions in this case, as well as the much shorter execution time

measured for HGC-LSTM, we believe that its usage in an anticipatory mobile network framework can bring interesting benefits to a network operator.

## 6. Conclusion

This study addresses the challenge of forecasting the number of HOs between pairs of base stations in a mobile network. We introduce HGC-LSTM, a novel framework that leverages GNNs in conjunction with LSTM networks to capture both spatio-temporal dependencies and intricate patterns within the data. Our methodology is developed and evaluated using a real-world HO dataset obtained from all the 4G base stations in the city of Poitiers. In comparison to three established baselines, namely ARIMA, transformer and MuLSTM, known for their efficacy in time series forecasting, our model demonstrates superior performance in terms of the global RMSE, MAE and MAPE. Additionally, we illustrate the efficiency of HGC-LSTM in terms of execution time. Moreover, we conduct a comprehensive analysis of the parameters employed in HGC-LSTM, highlighting the impact of factors such as the number of LSTM units, time window, and forecast horizon on the forecasting accuracy. Given the focus of this contribution on networking applications, we explore the prediction of peak HO occurrences during periods of heightened mobility, typically observed during commuting hours. Our findings reveal that all the examined algorithms, including HGC-LSTM, face challenges in accurately forecasting these peak values. Nevertheless, we illustrate that integrating HGC-LSTM into a dynamic HO resource allocation framework can offer substantial advantages to a mobile operator when contrasted with a conventional static approach.

## References

[1] Ericsson, Ericsson Mobility Report (November 2022).

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<figure><img src="image_20.png" /><figcaption>(a) Morning Hours</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>(b) Evening Hours</figcaption></figure>

<caption>Figure 18: Resource savings with respect to a static solution.</caption>

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