Predicting highway freight transportation networks using radiation models

Highway freight transportation (HFT) plays an important role in the economic activities. Predicting HFT networks is not only scientifically significant in the understanding of the mechanism governing the formation and dynamics of these networks, but also of practical significance in highway planning and design for policymakers and truck allocation and route planning for logistic companies. In this work we apply parameter-free radiation models to predict the HFT network in mainland China and assess their predictive performance using metrics based on links and fluxes, which can be done in reference to the real directed and weighted HFT network between 338 Chinese cities constructed from about 15.06 million truck transportation records in five months. It is found that the radiation models exhibit relatively high accuracy in predicting links but low accuracy in predicting fluxes on links. Similar to gravity models, radiation models also suffer difficulty in predicting long-distance links and the fluxes on them. Nevertheless, the radiation models perform well in reproducing several scaling laws of the HFT network. The adoption of population or gross domestic product in the model has a minor impact on the results, and replacing the geographic distance by the path length taken by most truck drivers does not improve the results.

Figure 1

Examples of flux map with different transportation fluxes. The arrows of the segments are omitted. In plot (a) we show the origin-destination pairs with $F_{ij}>2000$. In plot (b) we show the origin-destination pairs with $F_{ij}=100$ or $F_{ij}=101$.

Figure 2

Important traits of the two distance measures. (a) Asymmetry of the driving distance matrix between different cities. (b) The relationship between driving distance and geographic distance.

Figure 3

Empirical distribution of $S_{ij}$ between two cities. (a) The population $S_{ij}^{P,\mathrm{geo}}$ (billion people) is determined by geographic distance $d_{ij}^{\mathrm{geo}}$. (b) The population $S_{ij}^{P,\mathrm{cost}}$ (billion people) is determined by driving distance $d_{ij}^{\mathrm{cost}}$.

Figure 4

Comparison of $S_{ij}^{M,\mathrm{geo}}$ and $S_{ij}^{M,\mathrm{cost}}$ to investigate the influence of driving distance and geographic distance. (a) The radiation models are based on population with $M=P$ (billion people). (b) The radiation models are based on GDP with $M=G$ (trillion yuan).

Figure 5

Asymmetric relationship between $S_{ij}^P$ and $S_{ji}^P$. (a) The population $S_{ij}^{P,\mathrm{geo}}$ is determined by driving distance $d_{ij}^{\mathrm{geo}}$. (b) The population $S_{ij}^{P,\mathrm{cost}}$ is determined by driving distance $d_{ij}^{\mathrm{cost}}$.

Figure 6

Comparing the predicted flux, ${\tilde{F}}_{ij}^{P,d}$, with the measured flux, $F_{ij}$, for each pair of cities. We compare the real data with two formulations of the radiation model, $d_{ij}=d_{ij}^{\mathrm{geo}}$ (a) and $d_{ij}=d_{ij}^{\mathrm{cost}}$ (b). Data points are scatter plot for each pair of cities.

Figure 7

Correlation between influx and outflux of a city. (a) Real data. (b) Obtained from the raw radiation model with $M=P$ and $d=d^{\mathrm{geo}}$. (c) Obtained with the cost-based radiation model with $M=P$ and $d=d^{\mathrm{cost}}$. (d) Obtained from the raw radiation model with $M=G$ and $d=d^{\mathrm{geo}}$. (e) Obtained with the cost-based radiation model with $M=G$ and $d=d^{\mathrm{cost}}$.

Figure 8

Comparison of the power-law dependence of influx with respect to population and GDP in the raw and cost-based radiation models. (a, b) Real data from the measured transportation network. (c, d) Predicted influxes from the raw radiation model with $M=P$. (e, f) Predicted influxes from the cost-based radiation model with $M=P$.

Figure 9

Comparing the predictions of out-links started from Chengdu for the four radiation models with the real data. The first column shows the out-links with more than one truck from Chengdu ($F_{ij}>0,{\tilde{F}}_{ij}>0$). The second column shows the out-links with more than ten trucks from Chengdu ($F_{ij}>100,{\tilde{F}}_{ij}>100$). The third column shows the out-links with more than one hundred trucks from Chengdu ($F_{ij}>1000,{\tilde{F}}_{ij}>1000$). The panels in different rows display in turn the real data (a, b, c), the predicted out-links from the raw radiation model with $M=P$ (d, e, f), and out-links from the cost-based radiation model with $M=P$ (g, h, i).

Figure 10

Comparing the predictions of in-links started from Chengdu for the four radiation models with the real data. The first column shows the in-links with more than one truck from Chengdu ($F_{ij}>0,{\tilde{F}}_{ij}>0$). The second column shows the in-links with more than ten trucks from Chengdu ($F_{ij}>100,{\tilde{F}}_{ij}>100$). The third column shows the in-links with more than one hundred trucks from Chengdu ($F_{ij}>1000,{\tilde{F}}_{ij}>1000$). The panels in different rows display in turn the real data (a, b, c), the predicted out-links from the raw radiation model with $M=P$ (d, e, f), and out-links from the cost-based radiation model with $M=P$ (g, h, i).