# Optimizing URLLC Resource Allocation in Open-RAN: A Transformer-based Approach to Flexible Numerology

Mahdi Sharara, Antonia Maria Masucci, Yannick Carlinet, Nancy Perrot

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Mahdi Sharara, Antonia Maria Masucci, Yannick Carlinet, Nancy Perrot. Optimizing URLLC Resource Allocation in Open-RAN: A Transformer-based Approach to Flexible Numerology. IEEE INFOCOM 2025 - IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS), May 2025, London, United Kingdom. hal-04968425

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# Optimizing URLLC Resource Allocation in Open-RAN: A Transformer-based Approach to Flexible Numerology

Mahdi Sharara*, Antonia Masucci†, Yannick Carlinet†, and Nancy Perrot†

*ETIS, UMR 8051 CY Cergy Paris University, ENSEA, CNRS, Cergy-Pontoise, France

†Orange, Innovation Division, Paris, France

Emails: mahdi.sharara@ensea.fr, {firstname.lastname}@orange.com

**Abstract**—Beyond 5G networks are set to address the continuous surge in data traffic. A key enabler is the Open Radio Access Network (Open-RAN) architecture. Open-RAN aims to virtualize and decouple the network components to facilitate network management, enable AI-based control and optimization, and optimize energy efficiency and operator's costs. One of the services in 5G and beyond is Ultra Reliable Low Latency Communication (URLLC) which requires stringent delay and reliability requirements. Hence, allocating resources to satisfy these Quality of Service constraints is challenging. 5G allows for flexible numerology that controls subcarrier spacing, enabling the use of wider subcarriers to achieve shorter transmission times. This reduction in transmission delay must be paired with selecting a suitable Modulation and Coding Scheme (MCS) to meet the reliability requirements. To address this, we formulate a Mixed-Integer Linear Programming (MILP) problem to dynamically allocates Resource Blocks (RBs), MCS, numerology, time slots, and CPU resources per packet to meet URLLC traffic requirements. This dynamic model is evaluated against fixed numerology schemes. It is also compared with semi-dynamic schemes, where the numerology for all packets is unified but changes dynamically every *1ms*. Additionally, we develop a transformer-based Deep Learning (DL) model that provides sub-optimal results with significantly reduced execution time. The proposed model achieves up to 96.13% of its MILP counterpart considering the packet admission metric while reducing the execution time by more than 99.98%.

## I. INTRODUCTION

The growing demand for data and the emergence of diverse new services necessitate continuous growth and adaptation in mobile networks. Different applications would require enhanced throughput and improved latency and reliability. Enabling Extended Reality (XR), Virtual Reality, Autonomous Driving, and similar applications requires that Beyond 5G and 6G networks deliver high throughput, ultra-low latency, high reliability, and massive scalability to support these advanced use cases. Such networks must achieve the required Quality of Service (QoS) while simultaneously minimizing costs and power consumption [1].

Open Radio Access Network (Open-RAN) aims to address these goals by decoupling network components, virtualizing them, and enabling AI-driven network management. In Open-RAN, a traditional base station is mainly decomposed into three components: The Open Radio Unit (O-RU) is responsible for Radio Frequency (RF) and low Physical Layer (PHY) functions. The Open Distributed Unit (O-DU) handles high Physical Layer (PHY), Medium Access Control (MAC) layer, and Radio Link Control (RLC) layer functions. Lastly, the

Open Central Unit (O-CU) manages the Packet Data Convergence Protocol (PDCP) and Radio Resource Control (RRC) layers. These components can be software-defined to run as virtual machines or containers in the Open Cloud (O-Cloud). Additionally, Open-RAN supports AI-based closed-loop control through Radio Intelligent Controllers (RIC), which enable the training and deployment of AI models to manage the network and optimize its performance [2].

Ultra-Reliable Low-Latency Communication (URLLC) is a service that has been introduced in 5G. It has stringent delay and reliability requirements, which complicates resource allocation. High reliability is characterized by a low Block Error Rate (BLER), with reliability often measured by BLER (i.e., a reliability of $10^{-5}$ means the BLER is $10^{-5}$). 5G has proposed radio-level enhancements that allow for minimizing delay. A Resource Block (RB) consists of 12 subcarriers. For a numerology *n*, the subcarrier spacing is $15^n$ kHz, and each subcarrier has 14 consecutive OFDM (i.e., Orthogonal Frequency Division Multiplexing) symbols with a total duration $1/2^n$ ms. Traditionally, 4G only supported numerology 0. With flexible numerology in 5G, it is possible to use higher numerologies to reduce the transmission time [3].

In this work, we consider the problem of allocating radio and computing resources for URLLC packets, where the spectrum could be sliced dynamically, so different packets use different numerologies; the most suitable numerologies that permit satisfying the QoS requirements. In fact, to satisfy delay requirements, higher numerologies could be selected leading to higher BLER, hence lower MCS should be used to satisfy the reliability requirements. We consider a Mixed Integer Linear Programming (MILP) problem aiming to assign RBs, a Modulation and Coding Scheme (MCS) index, numerology, time slots, and CPU resources. We compare this model to other MILP-based variations where a unified numerology should be used per Transmission Time Interval (TTI) and to other variations where the numerology is fixed and unified. We use MATLAB's 5G toolbox to simulate the BLER as a function of the Signal-to-Noise ratio, MCS, and numerology. As solving MILP problems is highly complex [4] and given the very small time scale requirement for scheduling (i.e., *1ms*), we train a Transformer-based Deep Learning (DL) Model aiming to learn the optimal decision of numerology, and we compare it to other baselines.

The rest of this paper is organized as follows: Section II surveys the related work. Section III discusses the proposed MILP problem, while Section IV discusses the deep learning-based solution. The simulation and results are discussed in Section V and the work is concluded in Section VI.
## II. RELATED WORK

Flexible numerology schemes have been considered in multiple works. Authors of [5] propose an Integer Linear Programming (ILP) problem that allocates RBs and allows flexible numerology aiming to respect the delay requirements without considering reliability. However, they do not solve the problem optimally. Similarly, in [6], a dynamic unified numerology could be selected every TTI where all users use the same numerology. Authors of [7] devise a theoretical closed form of the bandwidth required to guarantee specific reliability as a function of the transmission rate. They do not consider the effect of different numerology or the performance fluctuation in practical systems. Authors of [8] use deep reinforcement learning to allocate RBs and numerology. The aim is to train the model to execute actions that satisfy the QoS requirements. However, dynamic environments can lead to more cases where the model fails to meet QoS requirements, requiring additional time to relearn or adapt.

In contrast to these works, we are jointly considering multiple resource allocations as the model allocates RBs, MCS, numerology, time slots, and CPU resources. Additionally, we simulate the achievable practical BLER as a function of the Signal-to-Noise Ratio, numerology, and MCS. These practical results enable our model to account for reliability requirements, rather than focusing solely on latency requirements.

Using Deep Learning to imitate the optimal solution while reducing the execution time has been considered in multiple works. The study in [9] introduces a deep learning model utilizing BiLSTM to optimize the allocation of computing resources, enhancing both throughput and the number of users that can be admitted. In a similar vein, [10] employs BiLSTM for the dynamic placement of O-CUs and O-DUs within regional and edge clouds, taking into account constraints related to computing, links, and delays. Meanwhile, [11] focuses on the optimal allocation of resources for D2D users, formulating the model as a Mixed Integer Linear Programming Problem (MILP). Additionally, this work leverages deep learning techniques as a low-complexity alternative to the Branch and Bound algorithm by mimicking the solutions generated by the MILP solver. Inspired by these works, we opt to use a deep learning-based model that leverages the Encoder part of the Transformer architecture with the aim of imitating the MILP solver's solutions.

## III. PROBLEM MODEL

Consider one base station having a set of users $\mathcal{U}$, and each user has a set of packets $P_u$, where each packet can have different delay and reliability requirements. We consider the uplink direction where data are transmitted from users to the base station, and precisely, the O-Cloud that hosts the O-DU and O-CU. The set of Numerologies $\mathcal{N}$ contains numerologies $n$ such that $n \in \{0, 1, 2, 3\}$. Additionally, the set of arrival instances $\mathcal{T}$ has 8 instances during $1ms$, each separated by $0.125ms$. We note that the duration of one Transmission Time Interval (TTI) for a numerology $n$ equals $1/2^n ms$. Hence, different numerologies can have different arrival instances during $1ms$. As multiple numerologies can be used in this work, a TTI refers to the transmission time interval of numerology 0 and it is equal to $1ms$, while the set $\mathcal{T}$ aims to track the arrival time within this $1ms$ when a different numerology is used.

While using higher numerologies allows earlier arrival, thus reducing delay, this could penalize the reliability and increase errors. We consider a set of different MCS indexes $\mathcal{M}$

corresponding to different Channel Quality Indicators (CQI) using the same method in [12], [13]. Additionally, let the set of total Resource Blocks be denoted as $\mathcal{R}$. This set is used to track the total number of RBs allocated to a packet. When a packet is assigned an element from $\mathcal{R}$, it indicates the cumulative number of RBs utilized by that packet. In the O-Cloud, there exists a set of CPUs $\mathcal{C}$. Denote by $QoS_{rel}^p$ and $QoS_{del}^p$ the required reliability and delay of a packet $p$. The BLER (i.e., Block Error Rate) of a user $u$ having SNR $SNR_u$ using numerology $n$ and MCS $m$ is measured by $err_{SNR_u}^{n,m}$. The throughput requirement of a packet $p$ is $th_p$, and the throughput achieved when using MCS $m$ and $r$ total number of resource blocks $th^{m,r}$. Additionally, $e_m^r$ tracks the processing time of a packet that uses MCS $m$ and $r$ resource blocks. We have modeled the problem of maximizing the total number of served packets as a Mixed Integer Linear Programming (MILP) Problem. Let $x_{n,t}^{p,m,r}$ be a binary decision variable that indicates if packet $p$ uses $r$ resource blocks with numerology $n$ and MCS index $m$, and arrives at the cloud at instance $t$. Additionally, let $y_{m,r,c}^p$ be a decision variable assigning packet $p$ to MCS $m$, $r$ RBs, and CPU $c$. Continuous variables $I_p^c$ and $F_c^p$ tracks the start and completion of the processing of packet $p$ at CPU $c$.

$$ \max \sum_{p \in P_u} \sum_{n \in \mathcal{N}} \sum_{t \in \mathcal{T}} \sum_{m \in \mathcal{M}} \sum_{r \in \mathcal{R}} x_{n,t}^{p,m,r} (\alpha - \beta \cdot \frac{e_m^r}{|C| \cdot 2}) \quad (1) $$

sub. to

$$ \sum_{n \in \mathcal{N}} \sum_{t \in \mathcal{T}} \sum_{m \in \mathcal{M}} \sum_{r \in \mathcal{R}} x_{n,t}^{p,m,r} \le 1, \forall u \in \mathcal{U}, p \in P_u \quad (2) $$

$$ \sum_{u \in \mathcal{U}} \sum_{p \in P_u} \sum_{m \in \mathcal{M}} \sum_{r \in \mathcal{R}} x_{n,t}^{p,m,r} = 0, \quad \{(n,t) \in (n=0, t \in \mathcal{T} \setminus \{8\}) \} \quad (3) $$

$$ \text{or } (n=1, t \in \mathcal{T} \setminus \{4, 8\}) \quad (3) $$

$$ \text{or } (n=2, t \in \{x \in \mathcal{T} \mid x \bmod 2=1\}) \} \quad (4) $$

$$ \sum_{n \in \mathcal{N}} \sum_{t \in \mathcal{T}} \sum_{m \in \mathcal{M}} \sum_{r \in \mathcal{R}} \mathrm{err}_{SNR_u}^{n,m} x_{n,t}^{p,m,r} \le QoS_{rel}^p, \forall u \in \mathcal{U}, p \in P_u \quad (4) $$

$$ \sum_{n \in \mathcal{N}} \sum_{t \in \mathcal{T}} \sum_{m \in \mathcal{M}} \sum_{r \in \mathcal{R}} w_p^{\text{queue}} x_{n,t}^{p,m,r} + \sum_c F_c^p \le QoS_{\text{del}}^p \quad (5) $$

$$ \forall u \in \mathcal{U}, p \in P_u $$

$$ \sum_{n \in \mathcal{N}} \sum_{t \in \mathcal{T}} \sum_{m \in \mathcal{M}} \sum_{r \in \mathcal{R}} th^{m,r} x_{n,t}^{p,m,r} \ge \sum_{n \in \mathcal{N}} \sum_{t \in \mathcal{T}} \sum_{m \in \mathcal{M}} \sum_{r \in \mathcal{R}} th_p x_{n,t}^{p,m,r} \quad (6) $$

$$ \forall u \in \mathcal{U}, p \in P_u $$

$$ \sum_{n \in \mathcal{N}} \sum_{t \in \mathcal{T}} x_{n,t}^{p,m,r} = \sum_{c \in \mathcal{C}} y_{m,r,c}^p \forall u \in \mathcal{U}, p \in P_u, m \in \mathcal{M}, r \in \mathcal{R} \quad (7) $$

$$ \sum_{m \in \mathcal{M}} \sum_{r \in \mathcal{R}} \sum_{c \in \mathcal{C}} y_{m,r,c}^p \le 1, \forall u \in \mathcal{U}, p \in P_u \quad (8) $$

$$ F_c^p = I_c^p + \sum_{m \in \mathcal{M}} \sum_{r \in \mathcal{R}} e_m^r \cdot y_{m,r,c}^p, \forall u \in \mathcal{U}, p \in P_u, c \in \mathcal{C} \quad (9) $$

$$ \sum_c I_c^p \ge \sum_{n \in \mathcal{N}} \sum_{t \in \mathcal{T}} \sum_{m \in \mathcal{M}} \sum_{r \in \mathcal{R}} \frac{t}{8} x_{n,t}^{p,m,r}, \forall u \in \mathcal{U}, p \in P_u \quad (10) $$

$$ F_c^p \le M \cdot \sum_{m \in \mathcal{M}} \sum_{r \in \mathcal{R}} y_{m,r,c}^p, \forall u \in \mathcal{U}, p \in P_u, c \in \mathcal{C} \quad (11) $$

$$ F_c^p \le I_c^{p'} + M(1 - z_c^{p,p'}), \forall u, u' \in \mathcal{U}, p \in P_u, p' \in P_{u'}, p \ne p', \quad c \in \mathcal{C} \quad (12) $$

$$ F_c^{p'} \le I_c^p + M(z_c^{p,p'}), \forall u, u' \in \mathcal{U}, p \in P_u, p' \in P_{u'}, p \ne p', c \in \mathcal{C} \quad (13) $$

$$ z_c^{p,p'} + z_c^{p',p} = 1, \forall u, u' \in \mathcal{U}, p \in P_u, p' \in P_{u'}, p' \ne p', c \in \mathcal{C} \quad (14) $$

$$ N_n^t = \sum_{u \in \mathcal{U}} \sum_{p \in P_u} \sum_{m \in \mathcal{M}} \sum_{r \in \mathcal{R}} r \cdot x_{n,8,m,r}^p, \forall t \in [1, 8] \cap \mathbb{Z}, n = 0 \quad (15) $$

$$ N_n^t = \sum_{u \in \mathcal{U}} \sum_{p \in P_u} \sum_{m \in \mathcal{M}} \sum_{r \in \mathcal{R}} 2^n \cdot r \cdot x_{n,t',m,r}^p, n = 1, \quad (16) $$

$$ t' \in \{4, 8\}, t \in \{t' - i, i \in \{0, 1, 2, 3\}\} $$
$$ N_n^t = \sum_{u \in \mathcal{U}} \sum_{p \in \mathcal{P}_u} \sum_{m \in \mathcal{M}} \sum_{r \in \mathcal{R}} 2^n \cdot r \cdot x_{n,t',m,r}^{p} \quad (17) $$

$$ N_n^t = \sum_{u \in \mathcal{U}} \sum_{p \in \mathcal{P}_u} \sum_{m \in \mathcal{M}} \sum_{r \in \mathcal{R}} 2^n \cdot r \cdot x_{n,t}^{p,m,r} \quad (18) $$

$$ w_n^t \ge N_{n+1}^{t'} \quad (t \in \{2, 4, 6, 8\}, t' \in \{t-i, i \in \{0, 1\}\}, n=2 \quad (19) $$

$$ w_n^t \ge N_{n+1}^{t'} + w_{n+1}^{t''}, \quad t \in \{4, 8\}, \quad t' \in \left\{\frac{t}{2}, t\right\}, \quad t'' \in \left\{\frac{t}{2}, t\right\}, n=1 \quad (20) $$

$$ w_n^t \ge N_{n+1}^{t'} + w_{n+1}^{t''}, \quad t=8, \quad t' \in \left\{\frac{t}{2}, t\right\}, \quad t'' \in \left\{\frac{t}{2}, t\right\}, n=0 \quad (21) $$

$$ N_n^t \le N^{RB} - \left(w_n^t + \sum_{n' < n} N_{n'}^t\right), \quad (n, t) \in \{(0, 8), (1, 4), (1, 8), (2, 2), (2, 4), (2, 6), (2, 8)\} \quad (22) $$

$$ x_{n,t}^{p,m,r} \in \{0,1\}, \forall u \in \mathcal{U}, p \in \mathcal{P}_u, n \in \mathcal{N}, t \in \mathcal{T}, m \in \mathcal{M}, \quad (23) $$

$$ y_{m,r,c}^p \in \{0,1\}, \forall u \in \mathcal{U}, p \in \mathcal{P}_u, m \in \mathcal{M}, r \in \mathcal{R}, c \in \mathcal{C} \quad (24) $$

$$ z_c^{p,p'} \in \{0,1\}, \forall u, u' \in \mathcal{U}, p \in \mathcal{P}_u, p' \in \mathcal{P}_{u'}, p' \in \mathcal{P}_{u'}, \quad (25) $$

$$ I_c^p \in \mathbb{R}_{\ge 0}, \forall u \in \mathcal{U}, p \in \mathcal{P}_u, \forall c \in \mathcal{C} \quad (26) $$

$$ F_c^p \in \mathbb{R}_{\ge 0}, \forall u \in \mathcal{U}, p \in \mathcal{P}_u, \forall c \in \mathcal{C} \quad (28) $$

$$ N_n^t \in \mathbb{N}_{\ge 0}, \forall n \in \mathcal{N}, t \in \mathcal{T} \quad (29) $$

$$ w_n^t \in \mathbb{N}_{\ge 0}, \forall n \in \mathcal{N} - 3, \quad t \in \mathcal{T}, t \bmod 2^{3-n} = 0 \quad (30) $$

<figure><img src="image_2.png" /><figcaption>Fig. 1. Fusing RBs according to the used numerology</figcaption></figure>

Eq. (1) is the objective function. It aims to maximize the number of processed packets while at the same time it prioritizes choosing MCS and RBs decisions that lead to the least CPU usage. The weights $\alpha = 100$ and $\beta = \frac{1}{2|C|}$ are chosen in a way that ensures that minimizing the CPU load will never be prioritized over admitting another packet. Eq. (2) ensures the decisions for each packet are unique. We note that numerology 0 has a $1ms$ TTI and packets can arrive at the last instant (i.e., $t \in \{8\}$), numerology 1 has two $0.5ms$ TTIs and packets can arrive at $t \in \{4, 8\}$, numerology 2 has four $0.25ms$ TTIs and packets arrive at $t \in \{2, 4, 6, 8\}$, while numerology 3 has eight $0.125ms$ TTIs and packets use any $t \in \mathcal{T}$. Eq. (3) handles this condition. In this paper, and unless otherwise specified, we use the term TTI to refer to the TTI of numerology, which is equal to $1ms$. Eq. (4) and (5) handle the reliability and delay requirements of each packet, while (6) ensures the allocated MCS and RBs are enough to transmit the packet. Eq. (7) and (8) mandate a CPU is only allocated if all the other decisions are made, and no more than one CPU can be selected. Eq.(9) tracks the completion time of packet processing while Eq. (10) ensures the packet can only be processed after it arrives. Eq. (11) ensures no processing can happen if there is no CPU assigned to the packet. Here, $M$ is the big-M notation where $M = 10000$. A CPU can't process two packets at the same time. Hence we introduce an auxiliary binary variable $z_c^{p,p'}$ used in Eq. (12),(13),(14) to enforce this condition. The set $\mathcal{R}$ defines the total number of RBs if numerology 0 is used. However, using higher numerology $n$, one RB would take $2^n$ RBs fused together (as the subcarrier spacing increases by $2^n$) but for a shorter amount of time that equals $\frac{1}{2^n}ms$. We use the integer auxiliary variable $N_n^t$ to track the total number of RBs used by each numerology $n$ at each instant $t$. This is done in Eq. (15)-(18). Although we can multiplex multiple numerologies, some considerations should be made. Using 1 RB with $n = 0$ means that the transmission spans all $t \in \mathcal{T}$. However, it is possible to use 1 RB with $n = 3$ (i.e., eight RBs of $n = 0$ fused together for $0.125ms$) arriving at $t = 1$, but at $t = 3, 4, n = 2$ is used. In the latter case, The initially eight fused RBs (i.e., RBs of $n = 0$) will be divided on 2 separate RBs (each consisting

of 4 fused), while the transmission time starts at $t = 2$ and completes at $t = 4$ taking $0.25ms$. Fig. 1 demonstrates an example where RBs could be fused together depending on the used numerology. To distinguish between such cases, we introduce the variable $w_n^t$ in Equations (19)-(22) ensure such cases are considered for the various permitted numerology and TTI pairs. Here we denote by $N^{RB}$ the total available number of RBs. These RBs are numerology-0 RBs. They can be interpreted as the total available spectrum resources during $1ms$, and these RBs could be fused and sliced dynamically to modify the used numerology. We assume that sufficient guard bands are present in the spectrum to mitigate inter-numerology interference. Finally, Eq. (23)-(30) list the decision variables used in the model.

IV. DEEP LEARNING

As solving a MILP problem is highly complex given the small time scale scheduling requirements, we opt to use a deep learning model that aims to learn the optimal solutions of the solver. However, we restrict the model to only aim at outputting a numerology that is used on all RBs per TTI but can change from one TTI to another. For the other decisions, we apply the following simple procedure: After the DL agent outputs the numerology, each packet defines its demand such that it uses the least number of RBs, and the highest MCS that permit respecting the BLER requirement. Then packets are ranked in the increasing order of required RBs. In case of a tie, another ranking is done prioritizing the packets with the earliest deadline. Then packets are allocated one by one, as long as radio and CPU resources are sufficient to satisfy a packet requirement. The choice of the time slot is made by selecting the earliest slot that has sufficient RBs, and that permits respecting the latency requirement for the packet.

Given that the DL model focuses on outputting the numerology, we consider a sequence-to-one architecture where the input represents a sequence of packets, each represented by the different features of the packet, while the output represents the selected numerology. As Fig. 2a shows, the model takes a sequence of packets as an input. A packet $i_p$ is represented by the SNR, delay and reliability requirements. Additionally, per each numerology, the selected MCS, the number of RBs, and the time slots that permit respecting the required QoS are all included in the features representation. The sequence of packets is then passed to a network. First, we consider a network based on the transformer architecture presented in [14]. We only consider the encoder part shown in Fig. 2b, and we remove the word embeddings and positional encoding as they are irrelevant to our application, knowing that the transformer was proposed initially for natural language processing applications. We have two encoder blocks, each consisting of multi-head attention, which permits the model
<figure><img src="image_3.png" /><figcaption>Fig. 2. The architecture of deep learning models: a) Full model b) Transformer-based c) LSTM-based</figcaption></figure>

to calculate the attention weights of the input sequence and then use it to decide how much attention should be given to each element during inference. The attention layer has to determine which parts in the input sequence should be given larger weights in the decision making. The attention outputs are added to the original input then layer normalization is applied. Then a network of two consecutive feed-forward layers are used where a ReLU activation layer is used between them. Then the output of the feed-forward networks is added to its input and layer normalization is applied. The output is fed to the second encoder block which has an identical mechanism. The model takes the last element from the output of the encoder block (i.e., sequence-to-one) and feeds it into two consecutive feed-forward layers; the first has a ReLU activation, and the second has softmax activation to output one of the numerologies. For the sake of comparison, we consider an LSTM based network to replace the transformer part, where a Bidirectional LSTM is used in the first layer followed by an LSTM in the second layer. In LSTM layer, the output for each element depends on the previous outputs from previous inputs. In contrast to the Encoder-Only transformer, the calculation in LSTM has to be done sequentially. This gives the transformer-based architecture an advantage in parallel processing, leading, in theory, to a faster execution time [14].

# V. SIMULATION AND RESULTS

## A. Simulation setup

1) **Simulation Parameters:** Our study considers one base station having 24 RBs (i.e., numerology 0) where a subset of these RBs could be fused together to modify the numerology and the transmission time. The URLLC packet's arrival rate follows a Poisson point process that ranges from 5 to 20 packets per millisecond. This includes all packets from all users. Each packet has a delay requirement that follows a uniform distribution between 0.5 and 2 ms, while the reliability requirement is uniformly distributed between 0.001 and 0.05. We reuse the mappings of CQI to MCS used in [13]. We also assume that each URLLC packet carries 32 bytes of data as in [15]. The throughput as a function of the MCS and number of resource blocks can be calculated according to the 5G standardization. We reuse the model used in [16] to model

<figure><img src="image_4.png" /><figcaption>Fig. 3. Probability distribution of SNR</figcaption></figure>

the required processing time at the CPU as a function of the MCS index, the number of used RBs, and the CPU frequency, which is based on Open Air Interface simulations.

2) **SINR distribution:** We consider a real traffic simulation done locally at Orange Labs. The curve is shown in Fig. 3. We use it to sample the SINR of each user.

3) **Block Error Rate (BLER) simulation:** To simulate the (BLER) as a function of the Signal-to-Noise ratio, CQI, and numerology, we use the 5G toolbox in MATLAB. Starting by encoding data at the Uplink Shared Channel (USC), the data undergoes Physical Uplink Shared Channel (PUSCH) modelated followed by precoding and adding Cyclic Prefix to the OFDM symbols. Then, the block is subject to the Tapped Delay Line (TDL) propagation model where the TDL-C model is used to present an outdoor case. Additionally, we assume the carrier frequency is 3.5 GHz and that we are considering a static case, so the Doppler spread is 0Hz. Then the transmission undergoes Timing synchronization followed by removing the Cyclic Prefix. Channel estimation is done next and followed by PUSCH demodulation and decoding.

4) **Simulation tools:** The simulation is coded in MATLAB. We use MATLAB's 5G toolbox to simulate the BLER as a function of the CQI (i.e., MCS), numerology, and SNR, and we use the Deep Learning toolbox for deep learning-related tasks. Additionally, we use the Optimization toolbox to solve the optimization problems.

## B. Algorithms

In the simulation, we consider six MILP-based algorithms. Additionally, we use two DL models and one Random model each selecting a unified numerology during 1ms, while the MCS, RBs, and time slot are selected according to the procedure presented in sec IV.

* **Intra-Dyn: Intra-TTI Dynamic MILP.** This is the model presented in sec III.

* **Inter-Dyn: Inter-TTI Dynamic MILP.** This is a variation where all the spectrum uses a unified numerology during 1 TTI, but this numerology can change from TTI to another.

* **Fixed-0:** The numerology is fixed to $n = 0$.

* **Fixed-1:** The numerology is fixed to $n = 1$.

* **Fixed-2:** The numerology is fixed to $n = 2$.

* **Fixed-3:** The numerology is fixed to $n = 3$.

* **DL-Tran: Transformer-based algorithm.**

* **DL-LSTM: LSTM-based algorithm.**

* **Random: Random selection of numerology.**

## C. DL Model and Training

Each of the DL models represent the input features with 131 neuron. The attention output has to have the same output
size, while the size of its key channels is 128, and it has 8
heads. The feed-forward layer size inside the encoder block is
set to 128. On the other hand, in *DL-LSTM*, the parameter of
hidden units in the BiLSTM layer is set 96 while that of the
following LSTM layer is set to 35. In total we have around
208.1 thousand learnable in *DL-Tran* and 208.3 thousand
learnable in *DL-LSTM*. To train the deep-learning models, we
solved 1000000 different instances of the MILP model (i.e.,
*Inter-Dyn*) using MATLAB Optimization toolbox solver. We
considered 1000 run for 4 different packets arrival rate, and
each run persisted for 25 TTIs. We trained each of the DL
models for 1000 epochs, where the training set consisted of
65% of the total, while the validation set consisted of 35%.
After 1000 epochs, the accuracy of the validation set reached
96.726% and 98.09% for *DL-Tran* and *DL-LSTM* respectively.

D. Simulation results

We run the simulation 25 times each with 25 TTIs (i.e., total of 25ms) for the different average packet arrival rates (i.e., the Poisson distribution expected value) ranging from 5 to 20 packets per 1ms. First, we consider the results of the MILP-based algorithms with respect to the metrics of processed packets and delay as a function of the average packet arrival rate, along with the 95% confidence intervals, as shown in Fig. 4. *Intra-Dyn* outperforms all the others given the highest level of freedom it enjoys followed by *Inter-Dyn* which has restricted freedom (i.e., unified numerology during 1ms). On the other hand, *Fixed-0* achieves the least performance, although it could provide the highest reliability (i.e., increasing the numerology could lead to a higher error rate). The reason is that packets take 1ms to arrive at the O-Cloud, and this reduces the amount of available delay budget, and some packets may have a delay budget of less than 1ms, making it impossible to satisfy their needs with this numerology. Interestingly, both *Fixed-1* and *Fixed-3* outperforms *Fixed-2*. *Fixed-1* has lower numerology, thus higher reliability but less time budget for processing. On the other hand, *Fixed-3* allows for faster arrival at the O-Cloud, increasing the available time budget for processing. *Fixed-3* would mitigate the higher error rate by using more RBs and a lower MCS index that permits higher reliability. Considering the delay metric in Fig. 4b, *Fixed-0* leads to the highest delay, as it uses the lowest numerology. On the other hand, *Intra-Dyn* achieves the least average delay. We note that the objective function does not enforce reducing the average delay as an objective. The only mandate is to respect the delay requirement for each admitted packet. However, to admit more packets benefiting from the additional degree of freedom, *Intra-Dyn* would choose higher numerologies to allow some packets to arrive as early as possible to process them before the arrival of other packets that need to use lower numerology due to BLER requirements.

Next, we compare, in Fig. 5 the DL models to the MILP *Inter-Dyn* which they aim to imitate. *DL-Tran* remains within 90.5% to 96.13% of *Inter-Dyn*, while the Random remains within 83.2% to 86.38%. Surprisingly, the *Random* still surpasses the *DL-LSTM* which achieves between 81.94% and 76.03%. In fact, the data set was generated such that each TTI generates the optimal solution. During inference, the solution of each TTI is not optimal and some packets that failed to be admitted could still have a chance during the next TTI, so they will be included in the features representation of the DL models. Hence, there is a slight deviation between the training and test sets. Additionally, LSTMs do embed the positions of the packets in the sequence unlike our proposed Transformer-Encoder-Only in which the attention mechanism

<figure><img src="image_5.png" /><figcaption>(a) Number of Processed Packets</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>(b) Average delay</figcaption></figure>

<caption>Fig. 4. MILP algorithms performance</caption>

is independent of the position of the packets in the input
sequence. This could explain why *DL-Tran* outperforms *DL-
LSTM*. Considering the delay metric in Fig. 5b *DL-Tran* also
outperforms *Random* and *DL-LSTM*. It is important to note
that the simple procedure to assign time slots to packets
was designed such that it prioritizes using the first TTIs and
immediately processes packets when they arrive if resources
are idle. Considering the execution time in Fig. 5c, *DL-
Tran* managed to reduce the execution time by more than
99.9882% with respect to *Inter-Dyn*. On the other hand, *DL-
LSTM* took less execution time although calculations should
be done recursively in LSTM. The reason is that MATLAB
does optimization for the layer reducing the overhead of
function calls compared Transformer layers that only recently
got supported. Finally, *Random* has an execution time in the
order of a few microseconds.

E. Implementation in Open-RAN context and Potential im-
provements

Practically, our model requires data accustomed to the
scenario of the environment it operates in. While we used
the MATLAB 5G toolbox to estimate the BLER as a function
of the numerology, SNR, and CQI considering the specified
environment, it would be necessary to generate such a model
either through practical experimentation, historical data, etc. or
through Digital-Twins. In the context of Open-RAN, solving
MILPs and training the models could be done in the non-RT-
RIC. The MILP-based algorithms serve as benchmarks, but
remain impractical for implementation. Hence, the DL model
must run in the DU or close to it. To run every 1ms, it could be
run as a dApp, recently proposed by [17], which supports time
scales of 1ms. While running the model on MATLAB required
more than 1ms due to the overhead imposed by MATLAB
and the operating system, accelerated hardware should permit
the model to run faster, given it supports parallelization.
Otherwise, in case the dynamicity is low, it may be possible to
run the model in the near-RT-RIC or non-RT-RIC supporting
time scales of 10ms and 1s respectively. A reinforcement
<figure><img src="image_7.png" /><figcaption>(a) Processed Packets</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>(b) Average delay</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>(c) Execution time of algorithms</figcaption></figure>

<caption>Fig. 5. Performance evaluation of the DL-based solutions</caption>

learning agent could be trained to decide when to rerun the
DL model depending on how much dynamic the network is.

We have opted to take *Inter-Dyn* as a reference model for training, as initially, *DL-Tran* failed to output the same time slots as *Intra-Dyn* without violating the constraint of available RBs. Ideally, a DL model that can predict the MCS, RBs, numerology, and time slots without violating the radio constraint is desirable. However, further research and training on the model should be done to achieve such performance.

VI. CONCLUSION

In this work, we have considered multi-resource allocation for URLLC in Open-RAN. The proposed MILP model aims to allocate RBs, MCS, numerology, time slots, and CPU resources while satisfying the reliability and delay requirements of URLLC packets. As this model permits dynamic numerology selection for each packet, the performance of this model is compared to other fixed and semi-dynamic versions. Given the high complexity of solving MILP problems, we opt to use a transformer-based Deep-Learning (DL) model that learns to output the optimal solution with lower complexity. As the results demonstrate, the DL-based algorithm could achieve up to 96.13% of its MILP counterpart. Given the DL model only decides a unified numerology per TTI, we plan to develop it to allocate other types of resources simultaneously and validate it on Open-RAN testbeds.

ACKNOWLEDGMENT

This work is mainly funded by the ANR HEIDIS
(https://heidis.roc.cnam.fr/; ANR-21-CE25-0019) project. It is in part
funded by CY Initiative (grant "Investissements d'Avenir" ANR-16-IDEX-
0008)

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