## Line Chart: Average k vs. Number of Interferers ### Overview The image is a line chart comparing the average value of 'k' against the number of interferers 'r'. There are four data series, each representing a different configuration of parameters 'c' and 'k_max'. The chart illustrates how the average 'k' changes as the number of interferers increases for each configuration. ### Components/Axes * **X-axis:** "number of interferers (r)". The axis ranges from 1 to 7 in integer increments. * **Y-axis:** "average k". The axis ranges from 1 to 7 in integer increments. * **Legend:** Located in the top-right corner of the chart. It defines the four data series: * Dotted Blue Line: "Prop.-c = 0.3, k_max = 10" * Purple Line with X markers: "Prop.-c = 0.3, k_max = 50" * Green Dashed Line with Diamond markers: "Prop.-c = 0.6, k_max = 10" * Yellow Line with Circle markers: "Prop.-c = 0.6, k_max = 50" ### Detailed Analysis * **Prop.-c = 0.3, k_max = 10 (Dotted Blue Line):** * Trend: Generally increasing, but with a slower rate of increase compared to other series. * Data Points: * r = 1, average k ≈ 1.7 * r = 2, average k ≈ 1.9 * r = 3, average k ≈ 2.1 * r = 4, average k ≈ 2.5 * r = 5, average k ≈ 3.1 * r = 6, average k ≈ 3.2 * r = 7, average k ≈ 3.3 * **Prop.-c = 0.3, k_max = 50 (Purple Line with X markers):** * Trend: Increasing, with a steeper initial slope that flattens out. * Data Points: * r = 1, average k ≈ 1.7 * r = 2, average k ≈ 2.1 * r = 3, average k ≈ 2.2 * r = 4, average k ≈ 2.6 * r = 5, average k ≈ 3.9 * r = 6, average k ≈ 4.0 * r = 7, average k ≈ 4.3 * **Prop.-c = 0.6, k_max = 10 (Green Dashed Line with Diamond markers):** * Trend: Increasing, similar to the purple line but slightly higher. * Data Points: * r = 1, average k ≈ 1.7 * r = 2, average k ≈ 2.0 * r = 3, average k ≈ 2.2 * r = 4, average k ≈ 2.7 * r = 5, average k ≈ 4.0 * r = 6, average k ≈ 4.0 * r = 7, average k ≈ 4.3 * **Prop.-c = 0.6, k_max = 50 (Yellow Line with Circle markers):** * Trend: Increasing, with a significant jump between r = 4 and r = 5. * Data Points: * r = 1, average k ≈ 1.7 * r = 2, average k ≈ 2.1 * r = 3, average k ≈ 2.3 * r = 4, average k ≈ 2.6 * r = 5, average k ≈ 5.5 * r = 6, average k ≈ 5.6 * r = 7, average k ≈ 6.2 ### Key Observations * For a given 'c' value, increasing 'k_max' generally results in a higher average 'k'. * The yellow line (Prop.-c = 0.6, k_max = 50) shows a much more significant increase in average 'k' as the number of interferers increases, especially after r = 4. * The dotted blue line (Prop.-c = 0.3, k_max = 10) consistently has the lowest average 'k' values. ### Interpretation The chart demonstrates the relationship between the number of interferers and the average value of 'k' under different parameter configurations. The parameter 'c' and 'k_max' significantly influence the average 'k'. Specifically, a higher 'k_max' value allows for a greater average 'k', especially when combined with a higher 'c' value. The jump in the yellow line suggests a threshold effect, where increasing the number of interferers beyond a certain point (r=4) has a disproportionately large impact on the average 'k' when both 'c' and 'k_max' are high. The data suggests that the system's behavior is highly sensitive to the interplay between these parameters and the number of interferers.

## Line Chart: Average k vs. Number of Interferers ### Overview This image presents a line chart illustrating the relationship between the average value of 'k' and the number of interferers ('r'). The chart compares four different parameter settings: two different values for 'Prop.-c' (0.3 and 0.6) combined with two different values for 'kmax' (10 and 50). ### Components/Axes * **X-axis:** "number of interferers (r)", ranging from 1 to 7, with tick marks at each integer value. * **Y-axis:** "average k", ranging from 1 to 7, with tick marks at each integer value. * **Legend:** Located in the top-left corner, identifying four data series: * "Prop.-c = 0.3, kmax = 10" (represented by a dotted blue line) * "Prop.-c = 0.3, kmax = 50" (represented by a purple line with 'x' markers) * "Prop.-c = 0.6, kmax = 10" (represented by a green line with diamond markers) * "Prop.-c = 0.6, kmax = 50" (represented by a yellow line with circle markers) ### Detailed Analysis Here's a breakdown of each data series, including observed trends and approximate data points: 1. **Prop.-c = 0.3, kmax = 10 (Dotted Blue Line):** This line shows a generally increasing trend, but with diminishing returns. * r = 1: k ≈ 1.8 * r = 2: k ≈ 2.1 * r = 3: k ≈ 2.4 * r = 4: k ≈ 2.7 * r = 5: k ≈ 3.0 * r = 6: k ≈ 3.2 * r = 7: k ≈ 3.4 2. **Prop.-c = 0.3, kmax = 50 (Purple Line with 'x' Markers):** This line also increases, but at a faster rate than the previous one, and appears to plateau towards the end. * r = 1: k ≈ 1.9 * r = 2: k ≈ 2.2 * r = 3: k ≈ 2.6 * r = 4: k ≈ 3.1 * r = 5: k ≈ 3.6 * r = 6: k ≈ 4.0 * r = 7: k ≈ 4.2 3. **Prop.-c = 0.6, kmax = 10 (Green Line with Diamond Markers):** This line shows a moderate increasing trend. * r = 1: k ≈ 1.8 * r = 2: k ≈ 2.1 * r = 3: k ≈ 2.5 * r = 4: k ≈ 3.0 * r = 5: k ≈ 3.4 * r = 6: k ≈ 3.8 * r = 7: k ≈ 4.0 4. **Prop.-c = 0.6, kmax = 50 (Yellow Line with Circle Markers):** This line exhibits the most significant increase, especially between r = 4 and r = 6. * r = 1: k ≈ 1.9 * r = 2: k ≈ 2.2 * r = 3: k ≈ 2.6 * r = 4: k ≈ 3.4 * r = 5: k ≈ 5.2 * r = 6: k ≈ 5.5 * r = 7: k ≈ 5.7 ### Key Observations * Increasing 'kmax' from 10 to 50 generally leads to higher average 'k' values for both 'Prop.-c' settings. * Increasing 'Prop.-c' from 0.3 to 0.6 also tends to increase average 'k', but the effect is more pronounced when 'kmax' is higher. * The most dramatic increase in 'k' occurs when 'Prop.-c' is 0.6 and 'kmax' is 50, particularly as the number of interferers increases. * The dotted blue line (Prop.-c = 0.3, kmax = 10) shows the smallest increase in 'k' across all values of 'r'. ### Interpretation The chart demonstrates the impact of 'Prop.-c' and 'kmax' on the average value of 'k' as the number of interferers increases. 'k' likely represents some measure of performance or cost, and 'r' represents the level of interference. The data suggests that increasing 'kmax' and 'Prop.-c' can mitigate the negative effects of interference (higher 'r'), leading to improved performance (higher 'k'). The significant jump in the yellow line (Prop.-c = 0.6, kmax = 50) between r=4 and r=6 suggests a threshold effect. Beyond a certain level of interference, increasing both 'Prop.-c' and 'kmax' becomes crucial for maintaining performance. The relatively flat slope of the blue line indicates that with low values of both parameters, the system is highly susceptible to interference. The choice of 'Prop.-c' and 'kmax' appears to be a trade-off. Higher values may improve performance under interference, but could also introduce other costs or complexities not reflected in this chart. Further investigation would be needed to understand the implications of these parameter settings in a broader context.

## Line Graph: Average k vs. Number of Interferers (r) ### Overview The image is a line graph comparing the relationship between the number of interferers (r) and the average value of k across four distinct scenarios defined by propagation coefficient (Prop.-c) and maximum k (k_max). The graph uses four distinct line styles and markers to differentiate the scenarios. ### Components/Axes - **X-axis**: "number of interferers (r)" with integer values from 1 to 7. - **Y-axis**: "average k" with a scale from 1 to 7. - **Legend**: Located in the top-left corner, with four entries: 1. **Dotted blue line**: Prop.-c = 0.3, k_max = 10 (marked with "x"). 2. **Purple dashed line**: Prop.-c = 0.3, k_max = 50 (marked with "x"). 3. **Green dash-dot line**: Prop.-c = 0.6, k_max = 10 (marked with "□"). 4. **Yellow solid line**: Prop.-c = 0.6, k_max = 50 (marked with "○"). ### Detailed Analysis 1. **Dotted Blue Line (Prop.-c = 0.3, k_max = 10)**: - Starts at (1, 1.8) and increases linearly to (7, 3.2). - Slope: ~0.2 per unit increase in r. 2. **Purple Dashed Line (Prop.-c = 0.3, k_max = 50)**: - Starts at (1, 1.9) and increases linearly to (7, 4.1). - Slope: ~0.4 per unit increase in r. 3. **Green Dash-Dot Line (Prop.-c = 0.6, k_max = 10)**: - Starts at (1, 1.7) and increases linearly to (7, 4.0). - Slope: ~0.4 per unit increase in r. 4. **Yellow Solid Line (Prop.-c = 0.6, k_max = 50)**: - Starts at (1, 1.6) and increases linearly to (7, 6.2). - Slope: ~0.7 per unit increase in r. ### Key Observations - **Trend**: All lines show a positive correlation between the number of interferers (r) and average k. - **Impact of k_max**: Higher k_max values (50 vs. 10) result in significantly higher average k across all r values. - **Impact of Prop.-c**: Higher Prop.-c (0.6 vs. 0.3) increases average k, especially at larger r values. - **Steepest Growth**: The yellow line (Prop.-c = 0.6, k_max = 50) exhibits the steepest slope, indicating the strongest sensitivity to interferers. ### Interpretation The graph demonstrates that both the propagation coefficient (Prop.-c) and the maximum k (k_max) are critical factors in determining the average k in the presence of interferers. Higher values of Prop.-c and k_max mitigate the negative effects of interferers, with k_max having a more pronounced impact. For example: - At r = 7, the yellow line (Prop.-c = 0.6, k_max = 50) reaches an average k of ~6.2, while the dotted blue line (Prop.-c = 0.3, k_max = 10) only reaches ~3.2. - The purple and green lines (same Prop.-c but differing k_max) show that increasing k_max from 10 to 50 improves performance by ~1.1 units at r = 7. This suggests that optimizing k_max is more effective than adjusting Prop.-c for improving system performance under interference. The linear trends imply a predictable relationship between these variables, which could inform resource allocation or interference management strategies in network systems.