Studies of human mobility in the past decade revealed a number of general scaling laws. However, to reproduce the scaling behaviors quantitatively at both the individual and population levels simultaneously remains to be an outstanding problem. Moreover, recent evidence suggests that spatial scales have a significant effect on human mobility, raising the need for formulating a universal model suited for human mobility at different levels and spatial scales. Here we develop a general model by combining memory effect and population-induced competition to enable accurate prediction of human mobility based on population distribution only. A variety of individual and collective mobility patterns such as scaling behaviors and trajectory motifs are accurately predicted for different countries and cities of diverse spatial scales. Our model establishes a universal underlying mechanism capable of explaining a variety of human mobility behaviors, and has significant applications for understanding many dynamical processes associated with human mobility.

Significance: With the same static road network, it is essentially unknown for urban traffic if traffic flows have the same spatial organization properties for different hours. Based on real-time high-resolution GPS data on the city scale, our results indicate two distinct modes characterized by different percolation critical exponents. The mode during rush hours on working days behaves like a 2D lattice with mainly short-range links, while the mode for other instants behaves like a small world (i.e., a lattice with long-range links). The difference between these two modes is explained here by the free flow on urban highways during nonrush hours, which is like adding long-range links in a 2D lattice. In contrast, during rush hours, such links almost disappear.

Significance: Different traffic states experienced by commuters may be due to localized random jams or overall network states, which is decided by system response to perturbations. While for natural systems, the existence of multiple states is common, the evidence for multiple states in transportation has so far been unclear, which hinders our ability to predict and prevent the spread of traffic jams. Based on percolation theory and high-resolution GPS datasets, we find strong evidence for the existence of multiple metastable network states corresponding to distinct system performance regimes. Our results may provide deep insight for a city traffic manager seeking to design early warning signals to prevent the system from shifting to a state of severe congestion.

In metro systems, a tactical train schedule with the rolling stock circulation plan aims to determine the movements of all physical trains. To utilize the regenerative energy as much as possible, this paper proposes an integrated model to simultaneously generate the optimal train schedule and rolling stock circulation plan, in which the brake-traction overlapping time at stations is maximized. In particular, our model rigorously considers the train turn-around constraints, train circulation constraints, and dynamic passenger demands to tackle the train loading capacity constraints. To eliminate the effect of non-linear constraints, we reformulate the original model into its equivalent linear model that can be efficiently solved by linear programming solvers. Finally, the numerical experiments based on Beijing Yizhuang Metro Line are implemented to demonstrate the effectiveness of our proposed model.