# Exploring Hybrid-Multimodal Routing to Improve User Experience in Urban Trips
## 4 User Experience Model
### Experiment Instances  
To evaluate the satisfaction of users in route segments in the present study, we consider that both functions \(w\) and \(P\) vary with the transportation mode. Additionally, the impression about the level of service in a segment depends on the time spent; and, the acceptability of a given segment is a function that depends on the length of the segment, i.e.,  
\[S(s)=w_{m_{s}}(t_{s})P_{m_{s}}(l_{s}). \tag{12}\]  
where \(m_{s}\) is the mode used on the segment \(s\); \(w_{m_{s}}\) and \(P_{m_{s}}\) are respectively the impression of the user and the depreciation function in relation to the transport mode used in that segment. We consider a limited set of modes and use data from a survey [35] to obtain Equation (13), an instance of \(w\). We combine bicycle and walking modes, since both require physical effort to perform, i.e., active transportation. We do not have the actual multiplier for the bicycle mode, but a study conducted in Beijing suggests bike satisfaction to be high when compared to vehicles [36].  
\[w_{m_{s}}(t_{s})=\begin{cases}1.54t_{s},\text{ if }m_{s}\text{ is in-vehicle congestion}\\ 0.78t_{s},\text{ if }m_{s}\text{ is in-vehicle headway}\\ 1.70t_{s},\text{ if }m_{s}\text{ is waiting}\\ 1.65t_{s},\text{ if }m_{s}\text{ is walking or bicycle}\end{cases}. \tag{13}\]  
where the impressions of the user \(w_{m_{s}}\) in relation to the transport mode \(m_{s}\) is obtained in function of the duration of the trip segment \(t_{s}\).  
\(P_{m_{s}}(l_{s})\) presented in Equation (11) is a depreciation factor that decreases the user satisfaction in a segment according to its length, which depends on the transportation mode \(m_{s}\). In the urban context, vehicles and public transportation usually perform the longest journeys (modes as helicopters are omitted). Thus, the impact of \(P_{m_{s}}(l_{s})\) in such routes is minimal. However, the impact on the walk and bicycle modes is highly relevant and they are usually mentioned as walkability [37] and bikeability [38], respectively. They may consider more factors other than the distance (e.g., accessibility, air pollution).  
One way of guessing the likelihood of someone adopting a segment of active transportation is to observe a dataset of trips with their lengths. We can estimate the probability of choosing a segment by calculating an inverse cumulative distribution function of trip lengths in the dataset. This approach is already used in the literature to estimate walking and bicycling acceptabilities (The Netherlands [39] and US [40,41]). Moreover, these abilities vary according to the trip purpose. For everyday commute trips using public transportation, they also depend on the accessed mode--one might walk twice the distance for using rapid modes as metro or tram [41].  
In this work, we estimate bikeability using data from the Citi Bike NYC ([[https://www.citibikenyc.com/](https://www.citibikenyc.com/)]([https://www.citibikenyc.com/](https://www.citibikenyc.com/)), accessed on 14 May 2021) in New York. However, we did not have access to a dataset to estimate walkability. Thus, we use previous results that were obtained for US cities [40]. We defined both functions by interpolating the results for walkability and bikeability. \(P_{w}\) (Equation (14)) is used to evaluate the acceptability when walking, and \(P_{b}\) (Equation (15)) when using a bicycle. We also account for users' will to walk further for accessing rapid transportation modes [41]. The value of \(l_{s}\) for the equations is given in kilometers. Additionally, the values of \(P\) are capped between 1 and 0.01 to prevent invalid outcomes. Section 5.5 discusses walkability and bikeability, and shows the shape of the inverse cumulative distributions.  
\[P_{w}(x)=-6.829x^{4}+9.788x^{3}-2.847x^{2}-1.858x+1, \tag{14}\] \[P_{b}(x)=-2.11\times 10^{-4}x^{5}+3.93\times 10^{-3}x^{4}\] \[-2.63\times 10^{-2}x^{3}+7.50\times 10^{-2}x^{2}\] (15) \[-8.05\times 10^{-2}x+1.01.\]