# Multiservice-Based Traffic Scheduling for 5G Access Traffic Steering, Switching and Splitting
## 3 Multiservice Type-Based Transmission (MSTT)
Thus, the effective network capacity, \(E_{k}^{L}(\theta_{k}^{L})\), for service \(k\) of UE \(i\) on the NR link is expressed as follows:  
\[E_{k}^{L}\Big{(}\theta_{k}^{L}\Big{)}=-\frac{1}{\theta_{k}^{L}}\log\Big{(} \mathbb{E}_{\gamma_{k}^{L}}\Big{\{}e^{-\theta_{k}^{L}R_{k}^{L}}\Big{\}}\Big{)}= -\frac{1}{\theta_{k}^{L}}\log\Big{(}\mathbb{E}_{\gamma_{k}^{L}}\Big{\{}e^{- \theta_{k}^{L}R_{k}^{L}}\log_{2}\left(1+P_{k}^{W}\gamma_{k}^{W}\right)\Big{\}} \Big{)}, \tag{17}\]  
where \(\theta_{k}^{L}\) is the impact factor of the characteristics of service \(k\) on the effective network capacity of the NR link, i.e., the DQoS index of the service is \(\theta_{k}^{L}\). \(B_{k}^{L}\) is the uplink bandwidth allocated to service \(k\) on the NR link, \(P_{k}^{L}\) is the power allocated to the UE in the NR uplink, \(\gamma_{k}^{L}\) is the instantaneous rate when service \(k\) is transmitted over the NR link, and \(\mathbb{E}_{\gamma_{k}^{L}}(\cdot)\) is the expectation regarding \(\gamma_{k}^{L}\). Similarly, the effective network capacity, \(E_{k}^{W}\big{(}\theta_{k}^{W}\big{)}\), for service \(k\) of UE \(i\) on the WLAN link can be expressed as follows:  
\[E_{k}^{W}\Big{(}\theta_{k}^{W}\Big{)}=-\frac{1}{\theta_{k}^{W}}\log\Big{(} \mathbb{E}_{\gamma_{k}^{W}}\Big{\{}e^{-\theta_{k}^{W}R_{k}^{W}}\Big{\}}=- \frac{1}{\theta_{k}^{W}}\log\Big{(}\mathbb{E}_{\gamma_{k}^{W}}\Big{\{}e^{- \theta_{k}^{W}R_{k}^{W}}\log_{2}\left(1+P_{k}^{W}\gamma_{k}^{W}\right)\Big{\}} \Big{)}, \tag{18}\]  
where \(\theta_{k}^{W}\) is the impact factor of the characteristics of service \(k\) on the effective network capacity of the WLAN link.\(B_{k}^{W}\) is the uplink bandwidth allocated to service \(k\) on the WLAN link, \(P_{k}^{W}\) is the power allocated to the UE in the WLAN uplink, \(\gamma_{k}^{W}\) is the instantaneous rate when service \(k\) is transmitted over the WLAN link, and \(\mathbb{E}_{\gamma_{k}^{W}}(\cdot)\) is the expectation regarding \(\gamma_{k}^{W}\). For simplicity, it was assumed that service \(k\) has the same influence on the effective network capacities of the NR and WLAN links, i.e., \(\theta_{k}=\theta_{k}^{L}=\theta_{k}^{W}\). Thus, the total effective network capacity of service \(k\) on the NR and WLAN links can be expressed as follows [43]:  
\[E(\theta_{k})=E_{k}^{L}(\theta_{k})+E_{k}^{W}(\theta_{k})=-\frac{1}{\theta_{k }}\Big{[}\log\Big{(}\mathbb{E}_{\gamma_{k}^{L}}\Big{\{}e^{-\theta_{k}B_{k}^{L }\log_{2}\left(1+P_{k}^{L}\gamma_{k}^{L}\right)}\Big{\}}\Big{)}+\log\Big{(} \mathbb{E}_{\gamma_{k}^{W}}\Big{\{}e^{-\theta_{k}B_{k}^{W}\log_{2}\left(1+P_{ k}^{W}\gamma_{k}^{W}\right)}\Big{\}}\Big{)}\Big{]}. \tag{19}\]  
Therefore, for the multiservice NWA uplink traffic scheduling problem, the following optimization problems can be established as Equation (20):  
\[\underset{P^{-},B^{+}}{\operatorname{argmax}}\Bigg{\{}\sum_{k=1}^{k=K}-\frac {1}{\theta_{k}}\Big{[}\log\Big{(}\mathbb{E}_{\gamma_{k}^{L}}\Big{\{}e^{- \theta_{k}B_{k}^{L}\log_{2}\left(1+P_{k}^{L}\gamma_{k}^{L}\right)}\Big{\}} \Big{)}+\log\Big{(}\mathbb{E}_{\gamma_{k}^{W}}\Big{\{}e^{-\theta_{k}B_{k}^{W} \log_{2}\left(1+P_{k}^{W}\gamma_{k}^{W}\right)}\Big{\}}\Big{)}\Big{]}\Bigg{\}}, \tag{20}\]  
\[\text{s.t.}\ P_{k}^{L}+P_{k}^{W}\leq p^{\operatorname{max}}, \tag{21}\]  
\[M_{u,c}\geq\max_{c\in A_{u}}(M_{u,c})-M^{rmw}, \tag{14}\]0  
\[M_{u,c}\geq\max_{c\in A_{u}}(M_{u,c})-M^{rmw}, \tag{14}\]1  
\[M_{u,c}\geq\max_{c\in A_{u}}(M_{u,c})-M^{rmw}, \tag{14}\]2  
The optimization objective function is a summation of multiple log functions, and, given that the constraints are linear, the problem is a convex optimization one. To reduce complexity, it is assumed that the minimum granularity of UE power allocation is represented by the link. Additionally, the constraint in Equation (21) indicates that the sum of the transmit power allocated by the user to the NR and WLAN links does not exceed the total maximum transmit power.