# Joint Location-Dependent Pricing and Request Mapping in ICN-Based Telco CDNs For 5G
## 4 Joint Pricing and Request Mapping
### The Design of LDP Module  
The key design principle of the LDP module is to set the price of a CDN site according to the site's congestion level. Specifically, the principle includes two features: (a) the higher the congestion level is, the higher the price is; (b) the pricing strategy should have a location-dependent feature. Here, we define \(\theta_{m}\) as the historical congestion level of site \(m\), as Equation (3) shows. We use \(\Theta\) to represent the congestion level set of all CDN sites. \[\theta_{m}=\frac{d_{m}}{C_{m}},m\in M \tag{2}\]  
\[\Theta=[\theta_{1},\theta_{2},...,\theta_{M}]. \tag{3}\]  
According to principle (a), we first design a congestion-aware bandwidth pricing strategy (CABP). The bandwidth cost function for network provider is always modeled as no-decrease and a convex function of congestion level, for simplicity, researchers always use the piecewise linear form [44; 45]. Considering the objective of pricing is to match the bandwidth cost, we believe that it is reasonable to design a piecewise linear pricing function in CABP. Specifically, by defining two thresholds, i.e., a lower-bound threshold and an upper-bound threshold. If the congestion level of a site is lower than the lower-bound threshold, the price is set as the lowest price. If the congestion level of a site is higher than the upper-bound threshold, the price is set as the highest price. If the congestion level of a site is between two thresholds, the price is set according to a linear function of the congestion level. Given \begin{table}
\begin{tabular}{c l} \hline \hline
**Parameters or Variables** & **Meaning** \\ \hline \(M\) & Number of telco CDN sites \\ \(L\) & Number of user access regions \\ \(N\) & Set of applicaitons that adopt the telco CDN service \\ \(C_{m}\) & Bandwidth capacity of site \(m\) \\ \(d_{m}\) & Historical traffic usage of site \(m\) \\ \(t_{lm}\) & Latency between region \(l\) and site \(m\) \\ \(t_{n}\) & Expected response time of application \(n\) \\ \(\lambda_{nl}\) & Request arrival rate of application \(n\) in region \(l\) \\ \(\theta_{m}\) & Congestion level of site \(m\) \\ \(\Theta_{m}\) & Congestion level set of all CDN sites \\ \(\hat{\theta}\) & Reference congestion level to evaluate relative congestion level of a certain site \\ \(\sigma_{1}\), \(\sigma_{2}\) & Congestion level thresholds in Algorithm 1 \\ \(P_{min}\) & The lowest price of a site in LDP design \\ \(P_{max}\) & The highest price of a site in LDP design \\ \(P_{const}\) & Fix price of a site in traditional pricing strategy \\ \(P_{m}\) & Unit bandwidth price of site \(m\) \\ \(\alpha_{nlm}\) & Portion of application \(n\) requests from region \(l\) directed to site \(m\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of the parameters and decision variables. Figure 2: The relationship between the modules in our design. \(\theta_{m}\), we calculate \(p_{m}\) by comparing \(\theta_{m}\) with a reference value \(\hat{\theta}\). Define two congestion level thresholds as \(\sigma_{1}\) and \(\sigma_{2}\), respectively. Define two price thresholds as \(P_{min}\) and \(P_{max}\), respectively. Let \(P_{const}\) denote the fixed bandwidth price in a traditional CDN, then \(P_{min}\leq P_{const}\leq P_{max}\) holds. The impact of setting \(P_{min}\) and \(P_{max}\) will be discussed in Section 5. Then, \(p_{m}\) is calculated as described in Algorithm 1. If \(\theta_{m}\) is smaller than \(\sigma_{1}\hat{\theta}\), \(p_{m}\) is set as \(P_{min}\) (line 2). If \(\theta_{m}\) is between \(\sigma_{1}\hat{\theta}\) and \(\sigma_{2}\hat{\theta}\), \(p_{m}\) is set according to a linear function with a positive slope of \(\frac{P_{max}-P_{min}}{\sigma_{2}-P_{min}}\), i.e., \(p_{m}\) increases with \(\theta_{m}\) (line 4). If \(\theta_{m}\) is bigger than \(\sigma_{2}\hat{\theta}\), \(p_{m}\) is set as \(P_{max}\). Figure 3 shows the relationship between congestion level and bandwidth price.