Fig 1.
Illustration of an individual’s trajectory.
The example is taken from the Chicago origin-destination survey on a land-use map. It shows one person’s one-day trajectory.
Fig 2.
The fraction of destination land-use type per trip purpose.
The trip purpose categories are as follows: 1. home activities, 2. visiting friends or relatives, 3. eating out, 4. attending class, 5. household errands or personal business, 6. service private vehicle, 7. shopping, 8. dropped off or picked up passenger, 9. civil and religious activities, 10. health care, 11. work related, 12. business related, 13. change of type of transportation, 14. recreation and entertainment. The land-use types are as follows: 1. residential, 2. urban mix, 3. educational, 4. government institutes, 5. office and business park, 6. shopping, 7. medical and health care facilities, 8. entertainment, 9. manufacturing and warehouse, 10. open space for leisure, 11. forest, 12. construction, 13. agricultural, 14. river, 15. transportation related, 16. social infrastructure. The land-use types are aggregated from 50 categories in the original data (how is explained in the Methods section).
Fig 3.
The land-use transition probability matrix in two levels of aggregation.
(A) shows the original categorization, (B) shows our coarser categorization (note that it is a different aggregation than in Fig 2 which is explained further in Methods). The land-use types in this aggregation are: I. residential, II. primarily retail and service, III. primarily office and professional, IV. urban mix, V. other commercial and service, VI. institutional, VII. industrial, VIII. transportation, IX. other transportation, communication and utilities, X. agricultural land, XI. open space, XII. vacant, wetlands or under construction, XIII. water.
Fig 4.
Comparison of population density distribution of empirical data and our model.
Panel (A) shows the Chicago land-use map. (B) displays the effective population density distribution from the Chicago OD survey data. Panels (C) and (D) shows the effective population density from our simulations with distance exponents σ = 1.5 and 2.5 respectively (the optimal value is in between—σ = 1.90±0.04). The resolution of the map (i.e. the dimensions of a grid cell) is 700m × 700m.
Fig 5.
Relation between empirical and predicted population density distribution and trip flux.
Panel (A) shows the average observed population density as a function of the population density predicted by the model. The data is binned into 50 segments such that each bin has an equal number of data points (although due to the log-scale the points with population density zero are not seen). Panel (B) show a similar plot (binned in the same way) for the trip flux computed according to Eq (3). Note that both the quantities in (A) and (B) are non-dimensionalized by measuring the population in fraction of the total (i.e. dividing it by 25,845) and measuring distances in units of the grid cell side d0 = 700 m. Error bars represent standard error. The step-like structure in (B) comes from location pairs with one, two, or three observed trips (the absence of error bars for these points is an artifact of the finite sample size).
Fig 6.
This figure shows the trip length distribution from the Chicago OD survey and a best fit to in by our activity model.
Fig 7.
Comparison of trip length distribution with different distance exponents.
In panel (A) we plot the trip length distributions with different distance exponents along with the empirical trip length distribution from the survey data. In panel (B), we show the values of the χ2 statistics as a function of the distance exponent value.
Fig 8.
Gravity model simulation with other population density models.
(A) shows results when we use the empirical population density distribution. (B) displays the effective population density calculated from the land-use maps. Panel (C) shows an instance of our random null model where the area per land use is conserved but everything else randomized. (D) illustrates a uniform population distribution. (E) is the trip length distribution of all four population distributions. For all curves, we use σ = 1.90.