# Joint Location-Dependent Pricing and Request Mapping in ICN-Based Telco CDNs For 5G
## 5 Evaluation
### Experiment Results
#### 5.2.3 Impact of \(\xi\) and \(P_{max}\) on Performance of PARM
** In our design, the differentiated prices imply the difference in the sites' congestion level and affect the procedure of request mapping. Thus, it is essential to evaluate the impact of price range on the performance of PARM. For simplicity, we make \(P_{min}\) fixed as 0.2 and make \(P_{max}\) vary from 0.35 to 0.8. The trend of four observed metrics are shown in Figures 16-19, respectively. In Figure 16, we observe that four curves are stable around certain values, whose numerical relationship conforms with that in Figure 12. This is because given a fixed \(\xi\), the various price only influence the optimized value of Equation (4a), not the variables. On the basis of the stability in Figure 16, it is not surprising that the trend of total bandwidth cost is also stable, as shown in Figure 17.  
Figure 14: Impact of \(\tau\) on total payment in PARM. Figure 15: Impact of \(\tau\) on average latency in PARM. In Figure 18, we observe that the rank of four traffic patterns at every \(P_{max}\) conforms with the respective rank in Figures 16 and 17, i.e., the higher the overall congestion level of a traffic pattern, the higher the total payment. In addition, four curves all increase but with different gradients, specifically, the higher the overall congestion level of a traffic pattern, the bigger the gradient. Note that the curves of Traffic Pattern 3 and Traffic Pattern 4 are both linear. Thus, for simplicity, we take these two patterns as examples to analyze the observation above. First, the sites' prices are location-independent (all sites have the same price) in these two patterns, as shown in Figures 6 and 7. Therefore, the total payment could be formulated as Equation (9), where \(P_{fixed}\) is the bandwidth price in Traffic Pattern 3 or 4. \(d^{\prime}_{m}\) is the traffic demand of site \(m\) after request mapping under PARM. Note that as \(P_{max}\) increases, the slope of CABP also increases. Under the same pricing function, \(P_{fixed}\) in Traffic Pattern 4 increases faster because it is calculated with a bigger variable (the average congestion level) in the linear function. Therefore, the curve of Traffic Pattern 4 has a bigger gradient. Figure 16: Impact of \(P_{max}\) on sites’ variation in PARM. Figure 17: Impact of \(P_{max}\) on total bandwidth cost in PARM. Finally, it is easy to understand the curves in Figure 19, considering that price variables do not have direct relationship with latency optimization. Figure 11:0  
From the above analysis, three conclusions could be obtained as follows:  
* \(\xi\) is effective in affecting the sites' variation and the total bandwidth cost. Note that if \(\xi\) is too big, the total bandwidth cost will grow rapidly when sites become too congested (as Traffic Pattern 4 in our simulation). Therefore, the overall congestion level should be taken into account when setting \(\xi\);
* \(P_{max}\) is effective in affecting the application providers' total payment. If the overall congestion level is high, a bigger \(P_{max}\) will give more economic incentives to help a telco CDN match its increasing bandwidth cost. Certainly, the tolerance of CDN users (i.e., application providers) should be taken into account when a telco CDN is making the decision of raising \(P_{max}\);
* Average latency does not have a direct relationship with \(\xi\) or \(P_{max}\). Figure 11:1 Impact of \(P_{max}\) on average latency in PARM. Figure 11:2 Impact of \(P_{max}\) on total payment in PARM.