# Multiservice-Based Traffic Scheduling for 5G Access Traffic Steering, Switching and Splitting
## 2 System Model
### Effective Network Capacity  
Most services use data packet-switching technology, which requires a guaranteed QoS to ensure the order of control-information resources during data transmission across the network. An effective and practical QoS support mechanism requires an accurate and simple channel model [40]. For this reason, it is necessary to model the wireless channel based on QoS indicators, such as data rate, delay, and delay violation probability. The queuing system model in Figure 2 shows that the source traffic and the network service are matched using a first-in first-out buffer (queue). Thus, the queue prevents the loss of packets that could occur when the source rate exceeds the service rate, at the expense of an increased delay. Using the effective capacity and statistical delay service quality parameters proposed in [41], the end-to-end delay of each user is modeled. The model aims to characterize wireless channels in terms of functions that can be easily mapped to link-level QoS metrics, such as delay-bound violation probability. This transmission model is also the theoretical basis of our heterogeneous network multiservice transmission. During data-packet queuing, multiple services, such as those pertaining to voice, data, and video, are ordered, and different network resources are allocated to each.  
Consequently, we assume that end-to-end communications are modeled based on a queuing system, wherein the DQoS index, \(\theta\), is given by Equation (7) [42]:where  
\[-\lim_{x\rightarrow\infty}\frac{\log(\Pr\{Q(\infty)>x\})}{x}=\theta, \tag{7}\]  
Figure 2: Queuing system model.  
\(x\) represents the queue-length threshold. According to the large-deviation theory, the probability that the queue-length process \(Q(t)\) exceeds the threshold \(x\) decreases exponentially as \(x\) increases. Additionally, the DQoS index, \(\theta\), is used to measure the exponential decay rate of the current link-violation service; the larger the \(\theta\) value, the greater the possibility that the link satisfies strict delay service requirements. Conversely, the smaller the \(\theta\) value, the greater the possibility that the channel is guaranteed only by a loose delay service [43]. Furthermore, Equation (7) shows that the probability that the queue-length violates the threshold, \(x\), can be expressed as follows [44]:  
\[\Pr\{Q(\infty)>x\}=e^{-\theta x}. \tag{8}\]  
The instantaneous data rate on link \(i\), \(R_{i}\), which can be determined using [PERSON]'s formula, is expressed as follows:  
\[R_{i}=B\log_{2}(1+P_{i}\gamma_{i}). \tag{9}\]  
where \(B\) represents the bandwidth of link \(i\), \(P_{i}\) represents the transmission power allocated by the user to link \(i\), and \(\gamma_{i}\) represents the instantaneous SNR obtained by the uplink \(i\). Assuming that \(\theta_{i}\) represents the DQoS index for link \(i\), the effective network capacity \(E(\theta_{i})\) of link \(i\) can be represented according to Equation (10), where \(\mathbb{E}_{\gamma_{i}}(\cdot)\) represents the expectation of \(\gamma_{i}\).  
\[E(\theta_{i})=-\frac{1}{\theta_{i}}\log\Bigl{(}E_{\gamma_{i}}\Bigl{\{}e^{- \theta_{i}R_{i}}\Bigr{\}}\Bigr{)}=-\frac{1}{\theta_{i}}\log\Bigl{(}E_{\gamma_ {i}}\Bigl{\{}e^{-\theta_{i}B\log_{2}\left(1+P_{i}\gamma_{i}\right)}\Bigr{\}} \Bigr{)}. \tag{10}\]