approximation (\[VRPDaganzo\]) represents the line-haul (back and forth) performed by vehicle to travel from the depot to the area where customers are located, and the second term represents the tour performed by traveling between each successive stops. Based on these seminal works, the next subsection proposes an adaptation of these equations to the operational context of riders and couriers, and develops an explicit time-based estimation of their operations.\

### Riders operations {#riders-operations .unnumbered}

Riders work in local cells, which are clusters of access hubs served by the same upper level local hub(s) as illustrated in Figure \[fig: Rider\]. Riders visit a set of $n_{LC}$ access hubs within their local cell of area $A_{LC}$ (and density $\delta_{LC} = \frac{n_{LC}}{A_{LC}}$) to pickup and deliver parcels as part of a defined route (e.g. planned beforehand based on averaging network’s load). At the time of deployment, underlying riders’ routes are not known with certainty, but need to be estimated in order to anticipate operations performance. When a rider makes his tour in period $\tau$ under scenario $\omega$ two cases are possible: (i) the tour is operated as planned because sufficient capacity is deployed at all visited access hubs in the route or because the 