CityLines

In our study, we use the Google GeoCoding to retrieve the bounding box of Shenzhen. The bounding box is defined between $22.45^{\circ}$ to $22.70^{\circ}$ in latitude and $113.75^{\circ}$ to $114.30^{\circ}$ in longitude. The covered area is about $1,300km^{2}$.

Our trip demands data are extracted from large GPS trajectory dataset (from taxis) and AFC billing dataset (from buses and subway trains) collected from Shenzhen, China during March 2014.

In Figure 1 and Figure 2, we visualized the distribution of source and destination locations of our trip demands. It clearly shows that most of source and destination locations are located at downtown and its sounding residential areas. This pattern fits our common sense of urban transportation which is dominated by daily commuting.

Figure 3 presents our optimal hybrid hub-and-spoke (OHHS) framework for CityLines system. It takes trip demand data and road map data as inputs. The whole framework consists of three stages in Figure 5: (1) map gridding, (2) trip demand aggregation, and (3) optimal hybrid hub-and-spoke (OHHS) planning.

The road map is divided into equal grids with a side-length of 0.01 degree in latitude and longitude. Then, a filtering process is conducted to eliminate those grids off the road network, so that the remaining $n$ grids are strongly connected by the road map, namely, each grid can reach any other grid through the road map. We refer to those remaining grids as spokes in the urban area. Then, we estimate average travel time between each spoke pair. Thus, an $n$ by $n$ travel time matrix $C$ is obtained, which contain the least travel time of each pair of spokes in the urban area.

In this stage, all sources and destinations of trip demands are aggregated to the spokes extracted in stage 1. Hence, a trip demand <$src, dst, t$> is aggregated as <$s, s' , t$>, where $s$ and $s'$ are the spokes where source $src$ and destination $dst$ are located at. Then, a spoke level trip demand matrix $V$ is obtained with each entry $V_{ij}$ representing the number of trip demands originating from spoke $i$ and terminating at spoke $j$.

Given a budget of $M$ point-to-point transit paths, and $L$ hub stations to deploy, we propose a two-step optimization framework to tackle the optimal hybrid hub-and-spoke (OHHS) planning problem, including an optimal hub selection (OHS) step and an optimal trip assignment (OTA) step. The OHS problem is formulated as a maximum coverage problem, that selects $M + L$ high quality hub candidates from $n$ spokes. The OTA problem is formulated as a p-HLP problem, which optimally assigns the trips to point-to-point transits or one hub to detour, with the goal of minimizing the average travel time per trip