# Optimized Architecture for Efficient OFDMA Network Design
## 4 Validation and Robustness Study of the Analytical Model
### Simulator Description  
The simulator developed for this study is designed to rigorously model and analyze the behavior of WiMAX systems under various conditions, outperforming existing solutions in both accuracy and performance. One of its key features is the ability to alternate between ON and OFF periods for each mobile station (MS), ensuring a highly realistic representation of user behavior during data transmission and idle times. At any given moment, a mobile station is either in an ON period (downloading data) or an OFF period (waiting between downloads). When an MS enters an ON period, it is assigned a number of bits corresponding to the size of the download, which is randomly determined following an exponential or Pareto distribution depending on the \(\overline{x}_{on}\) parameter. Similarly, when an MS enters an OFF period, it is assigned a waiting time before the next download, following an exponential distribution dependent on \(\overline{t}_{off}\). At the start of a simulation, the initial states of all MSs are defined. For example, all users may begin in an ON period. In the case of a single MS, once it finishes downloading (\(x_{on}=0\)), it transitions to an OFF period and is assigned a new (\(t_{off}\)). After a certain number of frames corresponding to (\(t_{off}T_{F}\)), the MS returns to an ON period, and a new (\(x_{on}\)) is drawn for the next download. This cycle repeats until the simulation concludes. When multiple users are considered (\(N>1\)), the simulator tracks the number of active users (in ON periods) at each frame. The simulator's role is to calculate various performance parameters, which are then compared to the results from the analytical model. While the analytical model averages all possible cases based on their probabilities, the simulation achieves results by averaging across a large number of frames. For example, to calculate \(\overline{U}\), the frame utilization rate, the utilization of each individual frame is summed over the entire simulation and divided by the total number of frames. The simulator ensures precise and reliable performance metrics through multiple steps, including the initialization of frame counters, user allocations, and slot assignments. To provide a clearer understanding of how these performance parameters are derived, the following sections will detail the steps executed by the simulator. As shown in the Figure 3, the simulator functions as follows:  
1. Frame Counter Initialization: In this step, a frame counter is initialized at \(0\), which will be incremented in the next step, but it will not exceed a predefined maximum value. 2. User Setup: A specific number of users is set. A random \(x_{on}\) value is assigned to all mobile stations (MS). This value is determined differently in the validation phase compared to the robustness phase (following an exponential distribution for validation and a Pareto distribution for robustness). The traffic parameters on which \(x_{on}\) depends are provided as input. 3. MCS Assignment: For each MS, a Modulation and Coding Scheme (MCS) is randomly assigned based on the channel model. 4. Scheduling Algorithm: The selected scheduling algorithm is applied to calculate the number of slots to allocate to each station. 5. Updating \(x_{on}\): The value of \(x_{on}\) is updated for each frame. The downloaded bits and the number of slots allocated to each MS are saved. The frame counter is incremented by \(I\). 6. Frame Counter Check: Ensure that the frame counter does not exceed the predefined maximum value. If it hasn't, proceed to step 7. Otherwise, jump to step 10. 7. Download Completion Check: For each station, check if it has completed downloading the assigned \(x_{on}\). If completed, proceed to step 8; if not, return to step 3 while ensuring the new MCS satisfies the following conditions:  
* For the validation study: The new MCS should be different from the previous one. * For the robustness study: The MCS assigned for two consecutive frames should be identical. 8.