Exact Solution of the Gyration Radius of an Individual's Trajectory for a Simplified Human Regular Mobility Model

Abstract

Gyration radius of individual's trajectory plays a key role in quantifying human mobility patterns. Of particular interests, empirical analyses suggest that the growth of gyration radius is slow versus time except the very early stage and may eventually arrive to a steady value. However, up to now, the underlying mechanism leading to such a possibly steady value has not been well understood. In this Letter, we propose a simplified human mobility model to simulate individual's daily travel with three sequential activities: commuting to workplace, going to do leisure activities and returning home. With the assumption that individual has constant travel speed and inferior limit of time at home and work, we prove that the daily moving area of an individual is an ellipse, and finally get an exact solution of the gyration radius. The analytical solution well captures the empirical observation reported in [M. C. González et al., Nature, 453 (2008) 779]. We also find that, in spite of the heterogeneous displacement distribution in the population level, individuals in our model have characteristic displacements, indicating a completely different mechanism to the one proposed by Song et al. [Nat. Phys. 6 (2010) 818].

Adaptive Modeling of Urban Dynamics during Armada Event using CDRs

“…The resulted are classified into 6 samples of (5,10,15,20,25, and 30) km, where the individuals are travel within these common . The developed algorithm to compute radius of gyration distribution has ) comp lexity, and it is implemented with Matlab2015 platform.…”

“…the individual displacements in spatio-temporal unit. Therefore, the consecutive mobile phone activit ies are good proxies to estimate human mob ility in mu lti-level of abstraction as macroscopic level, mesoscopic level, or microscopic level [19,20]. …”

Human Trajectories Characteristics

“…The individual trajectory has time-invariant properties; however trajectories estimations need to be computed according to common individual mobility characteristics [1,12,13,14,15,6,16,18]. The individual's activities sparseness causes incomplete spatial information, therefore the mobile individual has some general physical characteristics, that are useful to compensate the lack of data (when no activity recorded), that could be used to build mathematical model of human mobility patterns, in order to verify the behavior and life patterns using the most common mobility characteristics, which are as follows [30,19,20,21,22,23,6,16,24,18]:…”

Cascading Walks Model for Human Mobility Patterns

“…For the ultraslow diffusion, the model reported in Ref. [ 29 ] indicates that it seems to be the result of the high-frequency trips between homes and working locations. And some recent studies focus on the effect of social interactions and propose models based on the co-evolution between agents’ mobility and social networks, creating scaling properties on both social networks and mobility patterns [ 30 ].…”