Fig 1.
A simple road network.
Fig 2.
The degree distribution histograms of the Porto map traffic graph.
a: Indegree distribution (vertices). b: Outdegree distribution (vertices). c: Indegree distribution (edges). d: Outdegree distribution (edges).
Fig 3.
A Markov kernel (on edges) with its stationary distribution (on vertices) on the road network in Fig 1.
Fig 4.
The two-dimensional s.d. (on edges) with its equidistributed marginals (on vertices) on the road network in Fig 1 for the Markov kernel in Fig 3.
One can easily check that the sums of probabilities written on the edges in and out each vertex are equal, respectively.
Fig 5.
The graph created from the OSM data has 33,961 nodes, 53,126 edges, and covers a total of 857.26 km of road. The size of the area is about 43.68 km2. (Base map and data from OpenStreetMap and OpenStreetMap Foundation. Reprinted from OpenStreetMap under a CC BY license, with permission from OpenStreetMap, original copyright 2020. ©OpenStreetMap contributors).
Fig 6.
Histogram of trajectory lengths.
The rightmost bar represents trajectories longer than 12,500 meters. The average trajectory length is 3,628.93 meters.
Fig 7.
Histogram of number of sample points per trajectories.
The rightmost bar represents trajectories with more than 200 sample points. On the average, a trajectory consists of 40 sample points and takes 10 minutes.
Fig 8.
Distribution of trajectory points of the filtered dataset.
a: Distribution of all trajectory points shown in a 2D histogram (number of bins: 80 × 80). b: Difference of trajectory starting and endpoints shown in a 2D histogram (number of bins: 80 × 80). The color of each bin represents the number of trajectory starting points minus the number of trajectory endpoints that fall in that bin. c: Histogram of the difference of trajectory starting and endpoints.
Table 1.
Descriptive statistics of lengths of trajectories.
(82,345 total trajectories).
Table 2.
Simulation results, absolute bias and SE (inside parenthesis), for the Markov kernel in Fig 3 on the road network in Fig 1.
(k—number, n—length of trajectories).
Table 3.
Simulation results, absolute bias and SE (inside parenthesis), for a part of Porto’s map with 1000 vertices.
(k—number, n—length of trajectories).
Fig 9.
A visual explanation of transitions of intersection 1110673569.
TP means transition probability, red dots indicate nodes. (Base map and data from OpenStreetMap and OpenStreetMap Foundation. Reprinted from OpenStreetMap under a CC BY license, with permission from OpenStreetMap, original copyright 2020. ©OpenStreetMap contributors. Annotated by the authors).
Table 4.
Transitions of intersection 1110673569.
(TP—transition probability).
Fig 10.
The change of the distribution of cars during the simulation (5,000, 10,000, 20,000 and 50,000 cars).
The thickness of the street is proportionate with the number of cars on the street. a: Initial step (5,000 cars). b: After 30 mins (5,000 cars). c: After 60 mins (5,000 cars). d: Initial step (10,000 cars). e: After 30 mins (10,000 cars). f: After 60 mins (10,000 cars). g: Initial step (20,000 cars). h: After 30 mins (20,000 cars). i: After 60 mins (20,000 cars). j: Initial step (50,000 cars). k: After 30 mins (50,000 cars). l: After 60 mins (50,000 cars).
Fig 11.
The stationary distribution of cars in Porto based on the TTP dataset.
Fig 12.
Chi-square test results.