## 3 System Model Description and Problem Statement
### Resource Allocation Strategy  
The objective of the model implemented in the xApps is to efficiently allocate user demands to the appropriate RAN-level slice. These demands include bandwidth and latency from the radio perspective, as well as MEC resources. To achieve this, it continuously evaluates the available resources in terms of PRBs and slots, as well as CPU cores, storage, RAM, and MEC bandwidth. By analyzing this information, the model dynamically implements the allocation strategy, ensuring the creation of slices that match user demands and network policies.  
The allocation of radio resources, in terms of the transmission rate, is achieved through the allocation of PRBs according to the Shannon-Hartley channel capacity model. This model incorporates various factors, including received signal power, noise power, interference power, spectral efficiency, and interference from adjacent channels. The following expression delineates the model utilized:  
\[R=W*\log_{2}\left(1+SiNR\right) \tag{14}\]  
In this equation, \(R\) denotes the transmission rate (in bits per second), \(W\) represents the effective bandwidth (in hertz), and \(SiNR\) is the signal-to-interference-plus-noise ratio (in decibels). Furthermore, the subsequent expression is employed to evaluate the effective bandwidth.  
\[W=BW_{RB}*\eta*N_{OFDM} \tag{15}\]  
Figure 2: Iterative ILP.  
The bandwidth assigned to a PRB, denoted as \(BW_{RB}\), is determined by the Subcarrier Spacing (SCS), as expressed by the following equation: \(BW_{RB}=SCS*12\)_subcarriers_. The spectral efficiency (as indicated by the corresponding MCS index table) is represented by \(\eta\), and the number of Orthogonal Frequency Division Multiplexing (OFDM) symbols required to meet the slice request is denoted by \(N_{OFDM}\). The allocation of RAN resources to ensure a specified transmission rate is determined by the number of OFDM symbols necessary to meet this demand.  
To address the latency requirements of user demand, a mixed-numbering scenario is under consideration. This approach aligns with the implementation by [PERSON] et al [16]. The available transmission bandwidth is to be divided into multiple BWPs, each with a distinct SCS. Slice requests from time-sensitive services will be allocated in the BWP configured to provide lower latency [17].  
Taking into account the bandwidth of each PRB in its respective BWP, a resource allocation matrix is created. This matrix consists of 14 OFDM symbols for each PRB, which can be defined from a frequency point of view. This approach provides a limited amount of resources to allocate in terms of PRBs at the RAN level. The following expression can be used to calculate this:  
\[N_{PRBs}=14*(BWP_{BW}-GB)/BW_{RB} \tag{16}\]  
The number of allocable PRBs for a specific BWP is denoted by \(N_{PRBs}\), the bandwidth defined for the BWP is \(BWP_{BW}\), and the guard band associated with the selected numerology is denoted by \(GB\).  
As illustrated in the time/frequency grid of Figure 3, the channel bandwidth is apportioned into two BWPs, each configured with a distinct numerology. This configuration is used to allocate guaranteed resources to latency-critical and noncritical requests, respectively. It is important to note that each BWP consists of a finite amount of time-frequency resources, the size of which depends on the selected numerology.  
This configuration utilizes a BWP dedicated to latency-critical requests, reducing the period between radio subframe slots. This contributes to enhanced latency reduction in comparison to BWPs employing higher numerologies. As the figure above illustrates, a subframe radio slot is composed of 14 OFDM symbols. The selection of a higher numerology for BWP2 reduces the duration of the slots by half compared to BWP1, decreasing  
Figure 3: Bandwidth parts with mixed numerologies.  
the period between two symbols of the same position within the slot and contributing to reduced latency in services assigned to this BWP.