# A Hybrid Route Selection Scheme for 5G Network Scenarios: An Experimental Approach
## 3 System Model  
There is a set of channels \(C=\{c_{1},c_{2},...,c_{|C|}\}\), each \(c_{i}\) is occupied by PU \(p_{i}\in P=\{p_{1},p_{2},...,p_{|P|}\}\). A multi-tier 5G network shown in Figures 1 and 2 is considered. The MC BSs \(MC=\{mc_{1},mc_{2},...,mc_{|N|}\}\) and femtocell nodes and BSs, \(FC=\{fc_{1},fc_{2},...,fc_{|N|}\}\) can communicate among themselves directly. For instance, a femtocell BS \(fc_{1}\) can communicate with a MC BS \(mc_{1}\) directly via \(fc_{1}-mc_{1}\). A BS can establish a multi-hop route \(k_{n}\in K=\{k_{1},k_{2},...,k_{|K|}\}\) across different layers. For instance, a femtocell source node \(fc_{s}\) establishes a multi-hop route \(fc_{s}-mc_{1}-fc_{d}\) to MC BS \(mc_{1}\) and then to the femtocell destination node \(fc_{d}\). The traffic intensity \(\Psi_{t_{n}}^{k_{n}}\in\Psi=\{\Psi_{t_{1}}^{k_{1}},\Psi_{t_{2}}^{k_{2}},..., \Psi_{t_{|N|}}^{k_{|K|}}\}\) is one of the parameters that source nodes consider before selecting a route. The \(CC\) and the \(MC\) BSs are located in the control plane \(C^{cc}\), while the \(FC\) BSs are located in the data plane \(D^{/c}\).  
A source node selects a route based on the PU activities, which can either be ON (busy) or OFF (idle). The \(ON\)/\(OFF\) duration of PUs in channel \(c_{C}\in C\) and link \(L=\{l_{1},l_{2},...,l|n|\}\) follows the _Poisson model_, which is exponentially distributed with rates \(\lambda_{ON}^{c_{C},PU}\) for active time and \(\lambda_{OFF}^{c_{C},PU}\) for idle time of the \(PU\) activities, respectively. The channel availability \(\Phi_{t,OFF}^{c_{C},J_{n}}\) determines the average availability of the link in the time instant \(t\) as follows [54]:  
\[\begin{split}\Phi_{t,OFF}^{c_{C},J_{n}}=&\frac{ \lambda_{ON}^{c_{C},PU}}{\lambda_{ON}^{c_{C},PU}+\lambda_{OFF}^{c_{C},PU}}+\\ &\frac{\lambda_{OFF}^{c_{C},PU}}{\lambda_{ON}^{c_{C},PU}+\lambda _{OFF}^{c_{C},PU}}\times e^{-(\lambda_{ON}^{c_{C},PU}+\lambda_{OFF}^{c_{C},PU })^{t}}\end{split} \tag{2}\]  
The \(PU\) and SU avoid any possible collision, but if that happens, it has to be less than the IEEE requirement [45]. In this setup, the appearance of PUs follows the Poisson model that creates a random pattern for ON and OFF. The SU node estimates the average channel available time \(\Phi_{t,OFF}^{c_{C},J_{n}}\) of channel \(c_{C}\in C\) on a link of a route \(k_{n}\in K\). This ON-OFF time assignment is exponentially distributed and shows the duration of the PU transitions(the traffic in each channel). The duration of this random appearance follows the ON-OFF time period shown in Table 2. For example, the PU ON time period can be 50 s and the PU OFF time period can be from 50 to 250 s. This allows PUs to utilize their licensed channels whenever they want during their OFF time. Meanwhile, SUs utilize white spaces opportunistically.  
The time horizon in a channel for SU is segregated into the sense-transmit time window [55]. The sensing time is the duration of the channel sensing and processing time. The _processing time_ is the duration that the USRP/GNU radio takes for hardware and software initiation, such as packet encoding and decoding, digital conversion, and transmission or reception. The _transmit time_ is the duration that a SU node takes to send or receive a data packet.