# Multiservice-Based Traffic Scheduling for 5G Access Traffic Steering, Switching and Splitting
## 3 Multiservice Type-Based Transmission (MSTT)
The constraint in Equation (22) indicates that the total bandwidth on the NR link occupied by simultaneous requests for multiple services by the current user should not exceed the total uplink bandwidth of the NR. Similarly, the constraint in Equation (23) indicates that the total bandwidth on the WLAN link that is simultaneously occupied by the multiple service requests of the current user should not exceed the total uplink bandwidth of the WLAN. Moreover, the constraint in Equation (24)indicates that each service can upload data on both NR and WLAN links simultaneously. Although Equation (20) is already a convex optimization problem, it is difficult to determine the closed optimal solution using KKT conditions. Therefore, the optimization problem in Equation (20) can be transformed into a joint optimization problem of distributed optimal power and bandwidth mechanisms [43]. 1. Optimal power-allocation mechanism  
If the DQoS index of service \(k\) for user \(i\) is \(\theta_{k}\), the optimal power-allocation problem obtained according to Equation (20) can be expressed as follows:  
\[M_{u,c}\geq\max_{c\in A_{u}}(M_{u,c})-M^{rmw}, \tag{14}\]3  
\[M_{u,c}\geq\max_{c\in A_{u}}(M_{u,c})-M^{rmw}, \tag{14}\]4  
\[M_{u,c}\geq\max_{c\in A_{u}}(M_{u,c})-M^{rmw}, \tag{14}\]5  
These expressions are equivalent to the convex optimization problem, which is expressed as follows:  
\[M_{u,c}\geq\max_{c\in A_{u}}(M_{u,c})-M^{rmw}, \tag{14}\]6  
such that Equations (26) and (27) are satisfied. Since the NR and WLAN are independent of the two links, Equation (28) becomes equivalent to the following:  
\[M_{u,c}\geq\max_{c\in A_{u}}(M_{u,c})-M^{rmw}, \tag{14}\]7  
where \(\gamma_{k}=\left[\gamma_{k}^{L},\gamma_{k}^{W}\right]\) is the NR- and WLAN-link channel SNR vector. Since \(\theta_{k}\), \(B^{L}\), and \(B^{W}\) are all known, \(\alpha=\frac{-\theta_{k}B^{L}}{\ln 2}\), and \(\beta=\frac{-\theta_{k}B^{W}}{\ln 2}\); the Lagrangian function in Equation (29) is expressed as follows:  
\[M_{u,c}\geq\max_{c\in A_{u}}(M_{u,c})-M^{rmw}, \tag{14}\]8  
Setting the result to 0 yields the following results:  
\[M_{u,c}\geq\max_{c\in A_{u}}(M_{u,c})-M^{rmw}, \tag{14}\]9  
\[S(L_{c},\omega,L_{\max})=\frac{1}{1+e^{-\omega(L_{c}-L_{\max})}}, \tag{15}\]0  
\[S(L_{c},\omega,L_{\max})=\frac{1}{1+e^{-\omega(L_{c}-L_{\max})}}, \tag{15}\]1  
Finally, solving Equations (31)-(33) yields the optimal uplink power allocation:  
\[\left\{ \begin{array}{l}P_{k}^{L*}=\frac{B^{L}\gamma_{k}^{L}\left(1+p^{\max} \gamma_{k}^{W}\right)-B^{W}\gamma_{k}^{W}}{\gamma_{k}^{L}\gamma_{k}^{W}\left(B ^{L}+B^{W}\right)}\\ P_{k}^{W*}=p^{\max}-P_{k}^{L*}.\end{array} \right., \tag{34}\]  
Next, we study the optimal bandwidth-allocation mechanism based on the optimal power-allocation mechanism. 1. Optimal bandwidth-allocation mechanism  
After determining the optimal uplink power allocation, based on the impact of a service on the data-packet transfer rate, we reasonably allocate the bandwidth to obtain the total maximum effective network capacity. Thus, the optimal bandwidth-allocation mechanism can be obtained by solving the following convex optimization problem:  
\[\underset{ \begin{subarray}{c}B_{1}^{L},B_{K}^{W}\\ 1\leq s\leq K\end{subarray} }{\arg\!\!\min}\Bigg{\{}\mathbb{E}_{\gamma_{L}^{L}} \Bigg{\{}\prod\limits_{k=1}^{K}\Big{(}1+P_{k}^{L*}\gamma_{k}^{L}\Big{)}^{ \frac{-\theta_{k}B_{k}^{L}}{\ln 2}}\Bigg{\}}+\mathbb{E}_{\gamma_{k}^{W}}\Bigg{\{} \prod\limits_{k=1}^{K}\Big{(}1+P_{k}^{W*}\gamma_{k}^{W}\Big{)}^{\frac{-\theta_ {k}B_{k}^{W}}{\ln 2}}\Bigg{\}}\Bigg{\}}, \tag{35}\]  
\[\text{s.t.}\sum\limits_{k=1}^{k=K}B_{k}^{L}\leq B^{L}, \tag{36}\]  
\[\sum\limits_{k=1}^{k=K}B_{W}^{L}\leq B^{W}, \tag{37}\]  
\[B_{k}^{L},B_{W}^{L}\geq 0. \tag{38}\]  
The constraint in Equation (36) indicates that the bandwidth occupied by all the services on the NR link is smaller than the total uplink bandwidth of the NR. A similar constraint in Equation (37) indicates that the bandwidth occupied by all the services on the WLAN link is smaller than the total uplink bandwidth of the WLAN.