Fig 1.
Illustration of finding the equilibrium solution in traffic as a fixed-point iteration.
The equilibrium solution of path flows satisfies f(X) = X, where f = r ∘ l is joint process of network loading l : X → C that generates traffic conditions C based on flows X, and routing r : C → X that assigns path flows given traffic conditions C.
Fig 2.
Trip distance and time distributions.
(a) Comparison of trip distance distributions for all trips (cyan) and for map-matched trips (dark grey). Inset compares trip duration distributions for all trips (cyan) and for map-matched trips (dark grey). (b) Comparison of the lognormal distribution fitted to trip distances in Shenzhen to the lognormal distribution of commuting trip distances in five major cities as reported in Ref. [41].
Fig 3.
Difference between GPS-revealed actual routes and the shortest paths.
(a) Overlap between actual routes followed by the users and shortest paths resulting from travel costs computed following FF (cyan), UE (dark grey), and SO (orange) assumptions. (b) Percentage of users following the shortest path computed according to FF (cyan), UE (dark grey), and SO (orange) assumptions grouped by Euclidean distance between the origin and the destination of the trips. We used a threshold of <10% on route overlaps to classify a user to follow the shortest path.
Fig 4.
Venn diagram depicting the relations between the hypothetical patterns FF ∩ O, UE ∩ O and SO ∩ O represent the intersection between the observed paths O and the three hypothetical patterns; FF, UE and SO, respectively.
The numbers indicate the percentage of correctly reproduced paths in each region.
Fig 5.
Description of the multilayered network approach.
(a) Illustration of the two-layer network; the logical OD graph and the physical road network. Each logical edge from the OD graph is mapped onto the road network as a path in the mapping layer. (b) Node degree distribution of the physical layer. (c) Total weight distribution of nodes in the logical layer Gλ. (d) Weight distribution of edges obtained from the mapping Mμ using actual taxi trajectories.
Fig 6.
Comparison in node loads between actual routes and shortest paths.
Comparison of the node loads lact that result from the actual routes as revealed by GPS tracks and map-matching process to the node loads resulting from shortest paths based on (a) the free flow travel time lff, (b) the experienced travel time lue, and (c) the marginal travel time lso. (d) Cumulative distribution of the resulting traffic loads; F(l). Spatial distribution of errors with (e) FF, (f) UE and (g) SO patterns. We include nodes with negligible estimation error (gray) and nodes with absolute percentage error <50% (green), >50% and <100% (yellow), >100% (red).
Table 1.
Regression results and error measures.
Fig 7.
Computation of the derivative travel time.