## 3 System Model Description and Problem Statement
### Resource-Aware Slice Decision Problem and DQN Validation of Resource Allocation
In our scenario, all weight values are equal, indicating that all components of this function are equally important. In addition, to prevent any term from dominating the others, their magnitudes were normalized. Constraints (3), (4), (5), and (6) ensure that the sum of the MEC resources demanded by the current slice request and all the previous allocated slices do not exceed its available capacity in terms of CPU, RAM, storage, and BW resources. Constraint (7) guarantees that the current request is assigned to only one slice type, which will be the most suitable. Moreover, constraint (8) uses an external function to determine if there are sufficient RAN resources to assign the current slice request using the RAN resource allocation strategy explained in Section 3.3. If no such resources exist, the request will not be allocated even if the MEC has enough capacity. The nonlinear constraints (9) and (10) are implications that define the dependency between the variables \(x_{s}\) and \(z\), establishing that \(z\) is equal to 1 if the current slice request is allocated, and it is equal to 0 if insufficient availability exists to place the request. Using linearization techniques, both nonlinear constraints can be linearized. Thus, constraint (9) is equivalent to  
\[w_{3}\cdot(\text{MEC}^{ ST}-x_{s}\cdot D^{ ST})+w_{4}\cdot(\text{MEC}^{ DW}-x_{s}\cdot D^{ DW})]-z \tag{2}\]2  
and constraint (10) is linearized with the following expression:  
\[w_{3}\cdot(\text{MEC}^{ ST}-x_{s}\cdot D^{ ST})+w_{4}\cdot(\text{MEC}^{ DW}-x_{s}\cdot D^{ DW})]-z \tag{2}\]3  
Finally, all variables are defined as binary in (11). The iterative algorithm in Figure 2 utilizes a One-RSDP ILP to determine the outcome of a slice request. This process is continuously iterative until all demands are satisfied. The system evolves iteratively for each request received, following a defined probability distribution, such as the Poisson distribution, to determine the optimal slice type. Each time one slice is assigned, the corresponding resources are reserved during a specified period. When finishing, these resources are released. The ILP model was implemented using the Python-based package Pyomo [13; 14] and Gurobi [15] as its underlying solver, whereas the rest of the iterative algorithm was coded in the Python 3.10 programming language. For each experiment, we ran the solutions 100 times, which enabled us to present results with confidence intervals of 95%. The simulations were performed on a workstation with a 3.30 GHz Intel Core-i9 processor and 64 GB of RAM. Using an ILP is costly in terms of the time required to provide a solution, which makes it unfeasible to use in real time. For instance, in a scenario with the input data defined in Section 4.2, the average computation time required to obtain a result with the defined ILP is 22.32 ms in average, while the time spent on the proposed solution is about 395.4 us. An approximately 56 times faster system response time is achieved compared to the ILP, running both systems on machines with equal computational power. Consequently, the mathematical model is evaluated in this study solely as a performance benchmark. For this reason, approximation functions such as neural networks with methods based on DRL were selected in this work. These methods enable the identification of a satisfactory solution that is close to optimal, with processing speeds suitable for real-time applications, once the trained model is obtained.