detours are assigned to access hubs that are already in the remaining itinerary of the rider (bold lines in Figure \[fig: Rider\]); (ii) the rider tour is perturbed due to a lack of capacity at an access hub, and thus has to perform an immediate detour to a neighboring access hub before pursuing the rest of the regular tour (dash lines in Figure \[fig: Rider\]).

Given approximation (\[VRPDaganzo\]), if the number of detours performed by riders in local cell $LC$ in period $\tau$ in scenario $\omega$ is $n_{LC}^R(\tau, \omega)$, the route length estimation with detours of riders’ operations is:

$$\label{VRPRider}
VRP^R_{LC}(\tau, \omega) = 2r_{LC}m_{\tau}^R(\omega) + (n_{LC}+n_{LC}^R(\tau, \omega))k^R(\delta_{LC})^{-\frac{1}{2}}$$

where $n_{LC}$ is the total number of access hubs in local cell $LC$, $r_{LC}$ is the average distance between $LC$’s local hub(s) and its access hubs, and $m_{\tau}^R(\omega)$ is the number of riders’ operating.\
The cumulative time (in time-rider) necessary to perform tours approximated in (\[VRPRider\]) is: $$\label{rider time cumulative}
T^R_{LC}(\tau, \omega) = m_{\tau}^R(\omega)(t^R_s + \frac{2r_{LC}}{s^R_0}) + (n_{LC} + n_{LC}^R(\tau, \omega))(\frac{ k^R(\delta_{LC})^{-\frac{1}{2}}}{s^R} + t^R_a) + (\sum_{l \in LC}(\rho_l^D(\tau,\omega) + \rho_{l}^P(\tau,\omega)))t^R_u$$ where the first term is the time spent to setup tours ($t_s^R$ per tour) and perform the line-haul at a speed of $s_0^R$, 