# Exploring Hybrid-Multimodal Routing to Improve User Experience in Urban Trips
## 4 User Experience Model
### Individual Route Selection  
This section proposes a strategy for selecting routes among different options based on scores and they can be used to create a recommendation set. The recommendation should also consider other issues, such as the impact of recommended routes in the overall system when the adoption rate is high. The recommendation approach is responsible for mitigating this issue by, for instance, load balancing the set of reasonable routes [42]. We do not address the issue of load balancing recommendations in the present study. The described model has three main results: (i) the total opportunity cost (Equation (4)) to be used to select a route among different choices; (ii) the generalized cost (Equation (5)), which measures an overall cost/benefit of an option considering its cost, users' perception and duration; and, (iii) the generalized time (Equation (9)), which removes the cost and only evaluates the users' perceptions of time. These metrics model general users in specific populations. However, when it comes to individual choices, these values may vary. We introduce a profile operator to tackle the issue of different opinions of users when selecting routes. This operator is inspired by the concept of Mixed Strategies from Game Theory, which is a probability distribution over a set of actions taken by an agent [43]. We consider that the decision-maker has two Pure Strategies: always choose the shortest duration or always choose the cheapest trip. To produce a Mixed Strategy, we allow the decision-maker to pick a probability \(p\) in which the QoE is favored, despite the cost. The remaining odds (\(1-p\)) lie in the event of choosing a trip based on the cost. The Expected Utility [44] (Equation (16)) of the outcome of selecting routes, based on the Mixed Strategy that was adopted by the decision-maker, is obtained in this case, for two variables, as:  
\[\mathbf{E}[P]=u(A)p+u(B)(1-p), \tag{16}\]  
where \(p\) is the probability that defines the profile \(P\) and \(u(A)\) and \(u(B)\) are the utilities of the choices \(A\) and \(B\), respectively. The difference in our operator is that, in our equation, we use two utility functions for the same action, resulting in Equation (17). \[\zeta=u_{1}(r)p+u_{2}(r)(1-p), \tag{17}\]  
where \(\zeta\) denotes our proposed operator, \(u_{1}(r)\) and \(u_{2}(r)\) are the two different utility functions for the action of selecting the route \(r\), and \(p\), \((1-p)\) the respective complementary probabilities. If we select \(u_{1}=(t+T)/2\), and \(u_{2}=c\) from the utility functions previously described, then the profile operator \(\zeta\) of a route \(r\) given the profile \(p\) becomes, as shown in Equation (18). \(u_{1}\), represents the QoE-related aspects and \(u_{2}\) the monetary costs. \[\zeta(r,p)=p\left[\frac{t_{r}+T(r)}{2}\right]+(1-p)c_{r}. \tag{18}\]  
where the profile operator \(\zeta\) for a given route \(r\) and profile \(p\) is given in terms of the duration \(t_{r}\), the generalized time \(T(r)\), and the cost \(c_{r}\), and its related probabilities \(p\) and \(1-p\). In Equation (18), \(p\in[0,1]\) represents the value that a specific user gives to QoE-related variables. QoE represents the duration and overall user impressions about the duration. We oppose the cost to the quality metrics, i.e., users expecting better quality might pay more for the trip, while a user expecting to pay less may have a worse service. The best route, according to the model, obtains the smallest value for \(\zeta\). To apply Equation (18), \(t_{r}\), \(c_{r}\) and \(T(r)\) must be normalized. We use the z-score normalization function for the experiments in this work. We selected the z-score, since it assesses the distance between a route aspect measurement and the average of all measurements of that same aspect for a trip. This evaluation of distance is given in terms of standard deviations; it counts how many times an option is worse than others in terms of standard deviations.