## 4 Impact of Network Latency on Teleoperation
### Modelling Network Delay  
For network latency, a major problem is with the variability (unpredictable fluctuations) of the delay rather than its magnitude, which degrades the teleoperation performance [29], suggesting that there needs to be a deterministic delay [41].  
Researchers have modelled delays using simulations and emulations or have gathered data from real communication networks. These delays are injected into simulated or emulated networks. The delays used in these experiments can be classified as constant (fixed time delay) or varying (incorporating network jitter) [42]. [PERSON] and [PERSON] [43] categorise some predictive methods based on constant and variable time delays. Further, the end-to-end delay can be symmetric or asymmetric [43]. Symmetric means the uplink and downlink delays are approximately equal. Meanwhile, asymmetric delays refer to different delay values in the uplink and downlink, which is usually the case for teleoperation, i.e., the uplink sensor data delays are greater than the downlink control command delays.  
Many studies in the literature predominantly perform teleoperation in fixed or constant time delay settings, testing their methodologies on different levels of constant delays. For example, [PERSON] et al. [36] use constant delay values of 150 ms, 200 ms, and 400 ms in WiFi LAN communication. [PERSON] et al. [44] set their delay as 0.5 \(\pm\) 0.1 s. [PERSON] et al. [45] set the control delay to 300 ms and the sensor delay to 600 ms. [PERSON] et al. [46; 47] utilise Simulink blocks to add delays of 300 ms into their simulator model. Other similar examples include Refs. [21; 22; 48; 49; 50; 51].  
However, it is crucial to evaluate teleoperation performance on delay values close to real-world networks exhibiting many fluctuations. Studies that model real-world network delays tend to have varying delays that can fit a predefined time sequence (such as a distribution or a function) or model them as a random process [42]. It has been shown that the generalised extreme value (GEV) distribution can model delays for mobile communication data [35; 42]. The GEV distribution has been used to model variable delay in various studies [35; 42; 62; 63; 64]. The probability density function (PDF) of \(GEV(\xi,\mu,\sigma)\) is defined as  
\[f_{\xi\
eq 0,\mu,\sigma}=\frac{1}{\sigma}\bigg{(}1+\xi\frac{x-\mu}{\sigma} \bigg{)}^{-\frac{1}{\xi}-1}e^{-\big{(}1+\xi\frac{x-\mu}{\sigma}\big{)}^{- \frac{1}{\xi}}} \tag{4}\]  
where \(x\) is a random variable for the delay value, \(\xi\) is the shape parameter, \(\mu\) is the location parameter, and \(\sigma\) is the scale parameter. Based on extreme value theory, if \(\xi>0\), the distribution has a heavy tail with \(\mu-\frac{\sigma}{\xi}\) as the lower bound.  
The authors in [PERSON] et al. [65] characterise the function of RTT delays as a defined delay threshold (where it is not very significant), rapidly and linearly decaying, and then, ending with a long tail. Examples of such functions include piecewise linear [66], algebraic, logistic, and log-logistic [67]. Thus, [PERSON] et al. model delays using the following algebraic function:  
Some studies have shown that latency has a more significant effect on teleoperation than actuator delay [18]. Moreover, latency has a significant impact on video streaming methods such as field of view (FOV), orientation, camera viewpoint, depth perception, video quality, and frame rate [22], which might affect the situational awareness of the operator.  
Further, latency depends on the wireless technologies being used. Different network types and mediums provide different QoS and have diverse requirements and effects on latency [90].