# Multiservice-Based Traffic Scheduling for 5G Access Traffic Steering, Switching and Splitting
## 2 System Model
### Service Utility Model  
The utility function is derived from economics and is used to express the quantitative relationship between the utility obtained by consumers during consumption and the combination of commodities consumed, i.e., it measures the degree of satisfaction that consumers obtain from the consumption of a given combination of commodities. In recent years, utility functions have been increasingly adopted in research on wireless network resource allocation to effectively characterize the users' preferences and network performances [34; 35]. The utility function is also used in delay-critical businesses. For example, [PERSON]. [36] considered a multi-path routing problem of maximizing the aggregate user utility over a multi-hop network. Furthermore, [PERSON]. [37] studied delay-optimal packet scheduling strategies for a M2M uplink, with heterogeneous data arriving at a M2M Application Server via multiple M2M Aggregators. In these studies, the utility function measures the impact of any time delay on user satisfaction. In our research, the utility function is used for performance evaluation of the end-to-end communication delay. Generally, UEs initiate multiple services simultaneously, and the completion of each service is subject to different QoS requirements. Since the utility function can quantify QoS and measure user satisfaction in recent years it has increasingly been employed to realize resource allocation, power control, and flow control [38; 39]. We define three utility functions, namely the constant bit rate (CBR), download service (DS), and variable bit rate (VBR). \(U_{i}\) and \(V_{i}\) represent the utility function and transmission rate, respectively, corresponding to service \(i\), and \(Td_{i}\) represents the threshold that service \(i\) must reach to be successfully completed.  
CBR  
Usually, CBR services do not require a high rate and only need to meet a threshold to ensure normal data transmission. However, if this threshold is not reached, the user experience is drastically impaired. For voice services, users are more sensitive to delay than to transmission rate. Therefore, normal voice communication only needs to meet an 8 Kbps threshold; however, if this threshold is not reached, the communication is interrupted, and this further impacts the user experience. The utility function for CBR services is represented by the following step function:  
\[U_{cbr}=\left\{\begin{array}{l l l}0\ \,&\ \ \ \ \ \ if\ \ \ V_{cbr}<Td_{cbr}\\ 1\ \,&\ \ \ \ \ if\ \ \ V_{cbr}\geq Td_{cbr}\ \.\end{array}\right. \tag{4}\]  
DS  
DSs, including file transfer and multimedia streaming, have relatively high throughput requirements. As the data rate increases, user satisfaction increases and user sensitivity reduces. Therefore, the relationship between data rate and user satisfaction is not linear. Thus, the utility function of data services is expressed as follows:  
\[U_{ds}=1-e^{-\frac{V_{dt}}{Td_{ds}}}. \tag{5}\]  
VBR  
Although the usefulness of VBR services improves with increase in data rate, much like with DSs, VBR services have more stringent requirements for packet loss rate. For example, the utility of video services changes smoothly when the data rate is very low or very high. This is because at very low data rates packet loss rate is high and increases the link failure rate, while at very high data rates packet loss rate is low and can ensure video quality. We use a sigmoid function to express the utility function of VBR services as follows:  
\[U_{cbr}=\frac{1}{1+e^{-\omega(V_{cbr}-Td_{cbr})}}. \tag{6}\]