## 3 Model to Quantify Human Uncertainty in Human-Centric Cyber-Physical-Social Systems
Based on the reference architecture shown in Figure 2, Equation (1) (taken from [16]) is derived, proposing an analytical model to calculate \((\rho_{i})\), which represents the probability that a driver chooses an alternative route instead of the one suggested by the VFH application. The value of \((\rho_{i})\) is determined periodically for each driver, enabling an evaluation of  
Figure 1: MMtQHU model (from [16]). Figure 2: Reference architecture applied to the 5G VFH use case evaluated (from [16]). whether a route change is necessary in each situation. These probabilities are determined based on contributions from disjoint sets of events, each reflecting a different nature. \[\rho_{i}=pPP+pDS+pRF. \tag{1}\]  
The probability of a route change, \(\rho_{i}\), is determined by three primary components: psychophysiology (\(pPP\)), demographic segment (\(pDS\)), and role fit (\(pRF\)). The psychophysiology component, \(pPP\), captures the likelihood of a route change based on the driver's dominant personality trait and the impact of heart rate on behavior. It is assumed that the probability of altering a predefined route is uniformly distributed across a range of values specific to each personality trait, denoted by \(pp\). Additionally, the driver's awareness of their heart rate contributes additively to this probability, represented by \(pg\). Therefore, the total psychophysiological contribution is given by \(pPP=(pp+pg)\). The demographic segment component, \(pDS\), evaluates the probability of a route change by considering the driver's age and gender. The influence of age on this probability is inferred from the distribution of car accidents across different age groups, represented by \(pd_{1}\). Similarly, the impact of gender is derived from the probability of accidents involving males and females, denoted by \(pd_{2}\). These contributions are assumed to be independent, resulting in \(pDS=(pd_{1}\cdot pd_{2})\). The role fit component, \(pRF\), quantifies the probability of a route change based on the driver's role, e.g., whether they are an owner or an employee, and their response to social media information and institutional and organizational factors. The influence of social media is represented by \(ps_{1}\), while the response to institutional (\(i_{1},i_{2}\)) and organizational (\(o_{1},o_{2}\)) factors is captured by the joint probability \(p(i_{1},i_{2},o_{1},o_{2})\). Assuming independence among these factors, \(p(i_{1},i_{2},o_{1},o_{2})\) is defined as \(p(i_{1},i_{2},o_{1},o_{2})=[(pi_{1}\cdot pi_{2})\cdot(po_{1}\cdot po_{2})]\). Consequently, the total contribution from role fit is expressed as \(pRF=ps_{1}+p(i_{1},i_{2},o_{1},o_{2})\), or more explicitly, \(pRF=ps_{1}+[(pi_{1}\cdot pi_{2})\cdot(po_{1}\cdot po_{2})]\). The role fit component, \(pRF\), quantifies the probability of a route change based on the driver's role, i.e., whether they are an owner or an employee, and their response to social media, institutional, and organizational factors. Social media influence is captured by \(ps_{1}\), representing the use of Waze as a navigation tool. Institutional factors include \(i_{1}\) for speed limits and \(i_{2}\) for overtaking restrictions, while organizational factors are \(o_{1}\) (star ratings) and \(o_{2}\) (dynamic pricing). The joint probability of these institutional and organizational factors, assuming independence, is given by \(p(i_{1},i_{2},o_{1},o_{2})=(pi_{1}\cdot pi_{2})\cdot(po_{1}\cdot po_{2})\). The total contribution to role fit is then expressed as \(pRF=ps_{1}+p(i_{1},i_{2},o_{1},o_{2})\), or more explicitly, \(pRF=ps_{1}+[(pi_{1}\cdot pi_{2})\cdot(po_{1}\cdot po_{2})]\). Equation (2), taken from [16], expands the condensed terms in Equation (1):  
\[\rho_{i} =(pp+pg)\] \[\quad+(pd_{1}\cdot pd_{2})\] \[\quad+ps_{1}+[(pi_{1}\cdot pi_{2})\cdot(po_{1}\cdot po_{2})]. \tag{2}\]  
For a detailed example of the MMtQHU model's application, along with the complete algorithm governing its operation within the context of a VFH application, readers are referred to [16].