## 3 System Model
### Probabilistic Models of RTAs  
The QoE in VLC heterogeneous networks is predominantly influenced by the activity of RTAs. Consequently, the decision-making process for performing a VHO in such networks necessitates careful consideration of both the link state and the RTA activity status of the mobile terminal (MT). Human tolerance for application delays is typically categorized into objective time and perceived time, with the latter being generally longer than the former. Specifically, interruptions exceeding 1 s in video-based applications surpass the maximum psychological tolerance threshold, causing users to lose interest in the ongoing task after 2 s. Furthermore, for all application types, a wait time of 10 s leads to a departure of half of the users [19]. Regarding data interaction applications, the duration of data arrival significantly impacts user satisfaction, with longer arrival times resulting in diminished QoE [20]. In this context, the active probability of RTAs is defined as following a Bernoulli distribution [3].  
\[A(\theta)=\left\{\begin{array}{ll}1-\rho&if\ \theta=0\\ \rho&if\ \theta=1\end{array}\right., \tag{5}\]  
In the proposed framework, the probability of having an active RTA is denoted by \(\rho\), while \(\theta\) serves as an indicator to determine the presence or absence of an active RTA. Specifically, when \(\theta\) is set to 0, it signifies that no RTA is active, whereas a value of 1 indicates the presence of an active RTA [3].  
Upon identifying the presence of active RTAs, uniform allocation is performed across the video, audio VoIP, and web for the three distinct types of RTA, as follows:  
\[Ac(servicetype)=\left\{\begin{array}{ll}0.5&if\ servicetype=\{`Video^{ \prime}\}\\ \sigma&if\ servicetype=\{`VolP^{\prime}\}\\ 0.5-\sigma&if\ servicetype=\{`Web^{\prime}\}\end{array}\right., \tag{6}\]  
The MT is assumed to possess the capability of determining the specific type of RTA based on its QoS requirements at a given moment [21]. Subsequently, we uniformly distribute the probabilities of different types of RTA activation. Specifically, the probability of VoIP-based RTA appearance is represented by \(\sigma\), and while considering the sensitivity  
Figure 4: Schematic of MT random movement.  
of the video-based RTA service to bearer capacity and delay jitter, we set its appearance probability to 0.5. Consequently, the probability of web-based RTA service appearance is calculated as (\(0.5-\sigma\)). The probability distribution model is depicted in Figure 5.  
The specific calculation of the QoE MOS for each RTA type is shown below [22]:  
\[MOS_{Video}(P_{SINR})=4.5-\frac{3.5}{\left[1+\exp(b_{1}\times(P_{SINR}-b_{2})) \right]}, \tag{7}\]  
\[MOS_{VoIP}(R_{f})=1+0.335R_{f}+7\times 10^{-6}\times\]  
\[R_{f}(R_{f}-60)(100-R_{f})\]  
\[MOS_{Web}(R,P_{l})=2.1\times\log_{10}[0.3\times R\times(1-P_{l})], \tag{9}\]  
where \(P_{SINR}\) is the signal-to-noise power ratio, and \(R_{f}\) is a factor defined by the ITU that responds to the quality loss of the audio signal and is related to the resulting delay, which we mainly consider in the VHO scheme. \(R\) is the data rate, and \(P_{l}\) is the packet loss rate. \(b_{1}\) and \(b_{2}\) are parameters that determine the shape of the function [23], and in this paper, \(b_{1}\) is set to 0.5 and \(b_{2}\) to 30.  
Equations (7)-(9) show the computational mechanism of QoE MOS values for video RTA, VoIP RTA, and network RTA, respectively. The QoE MOS value of the video RTA are a function of the experienced SINR, \(P_{SINR}\). The QoE MOS value of the VoIP RTA is mainly affected by delay, while the QoE MOS value of the web RTA is mainly related to the data rate and packet loss rate. Therefore, PSNR, latency, data rate, and packet loss rate become the key factors used to evaluate the performance of VHO solutions and improve the overall QoE. When faced with a situation where these three parameters are subject to change, making the appropriate VHO can improve the QoE to some extent.