The authors have declared that no competing interests exist.

Conceived and designed the experiments: NS EBL. Performed the experiments: NS. Analyzed the data: NS EBL. Contributed reagents/materials/analysis tools: NS EBL. Wrote the paper: NS EBL.

Human mobility patterns (HMP) have become of interest to a variety of disciplines. The increasing availability of empirical data enables researchers to analyze patterns of people’s movements. Recent work suggested that HMP follow a Levy-flight distribution and present regularity. Here, we present an innovative agent-based model that simulates HMP for various purposes. It is based on the combination of regular movements with spatial considerations, represented by an expanded gravitation model. The agents in this model have different attributes that affect their choice of destination and the duration they stay in each location. Thus, their movement mimics real-life situations. This is a stochastic, bottom-up model, yet it yields HMP that qualitatively fit HMP empirical data in terms of individuals, as well as the entire population. Our results also correspond to real-life phenomena in terms of urban spatial dynamics, that is, the emergence of popular locations in the city due to bottom-up behavior of people. Our model is novel in being based on the assumption that HMP are space-dependent as well as follow high regularity. To our knowledge, we are the first to succeed in simulating HMP not only at the inter-city scale but also at the intra-urban one.

Recently, human mobility patterns (HMP) have become of interest to a variety of disciplines. This is due to the importance of understanding HMP as the basis for developing epidemiology models, mobile wireless network planning, urban and transportation planning, and more [

The classic models of HMP suggested that it can be simulated by Brownian motion or random walk [

More recently, [

Another work [

More recently, [

The presented model is a spatially embedded agent based model (ABM). An ABM is a method to compute simulations of complex systems, where each agent represents an autonomous entity that acts based on predetermined rules [

Our model is based on the combination of regular movements that can be found in people’s daily/weekly/monthly routine, combined with spatial considerations that are represented by an expanded gravitation model (see

The remainder of the paper is organized as follows: in section 2 we explain the spatial setting we use to simulate urban environment. In section 3 we present the agent-based model for simulating human mobility patterns, and in section 4 we present the results of the above model and compare them to real-world empirical data. We close with a discussion and some concluding remarks.

Our proposed model is a spatially-embedded one. Thus, it was important for us to specifically define the spatial environment we run our agents on. For that, we have decided to use an environment that resembles a real modern city on the one hand, yet simplify its complexity on the other. We developed a methodology which is used to construct the spatial basis of our model, and used the city of Tel Aviv as a basis for the statistical properties. This methodology, however, can naturally be applied to other cities as well.

Our environment is based on a cellular grid, where each cell represents 25*25 square meters. The total size of the grid is 100*100 squares, representing an environment of 2,500*2,500 square meters. This area resembles the city center of Tel Aviv. Next, we defined six land uses: residential, employment, open public spaces, public buildings, entertainment and retail, and a mixed land use of residential, employment, and retail. To determine the mixture of land uses in the city as well as the typical sizes of clusters they occupy, we studied the case of Tel Aviv. Based on municipal plans and a comparison of these plans to reality (which was done as some of the plans had gone through spot-zoning amendments over time), we defined the percentage of each land use and the range of the typical sizes of their clusters. Then, we used these percentages to set a list of possible clusters, defined by their land uses and sizes, and arranged them randomly in space based on the range of possible clusters each land use comprises. This means that at each iteration a land-use was picked at random and allocated with a random cell as well as a size (chosen from the list described above). At the following iterations the cluster of this land use was enlarged by adding to it adjacent cells, until it reached its designated size. Then, another land use was picked at random from the list and the entire process is repeated, until no more clusters (and vacant locations) were left.

The distribution of clusters sizes was either normal or exponential, based on the analysis of the real data. _{i}. The specific attractiveness values of all the cells followed a normal distribution.

Land Use | Cells | Percentage (%) | Size of Max Cluster |
---|---|---|---|

3,400 | 34 | 1000 | |

1,000 | 10 | 500 | |

1,200 | 12 | 200 | |

2,400 | 24 | 300 | |

800 | 8 | 40 | |

1,200 | 12 | 100 |

As people move differently at different times of the day and week, we divided the time in our model as follows: a week consists of 5 working days and a 2-day weekend, where a day is defined as 24 hours, divided into 6 periods: morning (6am-12pm), morning rush-hour (7:30am-9:30am), noon (12pm-5pm), evening rush-hour (5pm-7pm), evening (7pm-10pm), and night (10pm-6am). Each iteration in the model represents 15 minutes in reality. As we elaborate on in the next section, each time slot has a significant role in determining the agents’ nature of behavior.

There are 4 types of agents in our model that represent different types of people who share common characteristics, among them similar daily and weekly routines. These groups are based on the agents’ age and/or marital status: teenagers, bachelors, married people, and seniors. Each agent is characterized by the following attributes:

Home address: each agent is assigned a home address which is randomly selected from all available locations of the

Employment status: students, married people, and seniors are either working or not (each groups is represented by a different percentage of working community).

Work/school address: each of the teenagers and the students is given a school/university address which is randomly selected from all available locations of public buildings, and working agents are given a work location out of all available locations of the

Working/studying agents have a weekly routine of going to school/university/work at the morning of each weekday, but they leave these locations at different times (e.g. a teenager pupil leaves school earlier than a working agent leaves his work). During the afternoons and evenings each group follows a different behavior patterns – a family man usually returns home or stops at one location before heading there (for example – the grocery store) while a student might go from the university to work or to study with a friend or even to a pub after his day at the university ends. The senior group, on the other hand, is divided into working and retired people. The working seniors work less hours than the other working groups and the retired ones do not have a definite routine. This, of course, corresponds to real-life situations, where people follow routine behavior such as going to work/school, but occasionally they have other activities that interfere with their routine (e.g. running urgent errands). Additionally, as in real life, agents at retirement age either work less hours that younger ones, or do not work at all. In the next section we explain the algorithm that governs the agents’ movements, based on their characteristics and their spatio-temporal location.

People mobility patterns can be roughly divided into regular and irregular movements. The regular movements depend on their routines while the irregular ones can be either to places they visit once (e.g. jury duty) or to places they return to on an irregular basis (for example, a restaurant one likes or the theater). To simulate these two behaviors the movement of the agents in the model depends on their type, their current location, and on the time of day and the day in the week.

Our algorithm is divided into two stages; in the first stage it is decided if the agent is going to move or stay put. If the agent is to move, his destination is set in the second stage. Appendices A and B in

Stage 1:

For agents who have a daily routine, i.e. pupils, students, or working agents, the probability of moving on mornings of weekdays, is very high if their location is not their working place/school/university. Otherwise, each group of agents is characterized by a set of probabilities to move, depending on their location and time of day.

Stage 2:

After determining whether the agent is going to move (based on the probabilities mentioned above), the algorithm sets their destination. This is done based on the type of movement (routine/irregular) and the agents’ characteristics. If the agent has a regular routine and he is going to follow it, the location is predetermined and the agents goes there (i.e. school, university, working place). However, if they do not move towards their regular destination they can either stay home or move to a unique destination, this is determined based on different probabilities that represent the agents’ likelihood to move toward a specific land use, at each of the 6 time periods of a weekday. (see a detailed description of these probabilities in Appendix C in

Where _{i} is the distance from the agents’ current location to cell _{i} is the size of the cluster to which cell _{i} represents the specific attractiveness of cell _{i,rand} is a random parameter, and _{agent} represents the individual preferences of the examined agent (each agent has 40 locations in the city that he favors. These locations are randomly assigned to each agent. For the rest of the cells this value is set at unity).

To demonstrate how the IAC is calculated we can use the following example: if an agent is staying at a specific cell _{16} = 0.95^{(27.22)} * 1.02^{29} * 0.93 * 1.03 * 1 = 0.42).

All cells with the same land use are ranked, based on their IAC values and one cell is picked from the first 10 highest scores. By following this method, we assure that the destination is chosen for a unique agent in a unique time. Thus, an irregular movement is combined with the individual preferences of the agents.

We ran the model 20 times with 10,000 agents over a period of a month. While the agents were generated randomly in each run, the city configuration remained the same. We examine the results of the agents’ movement in several aspects: (1) distance distribution of the agents, (2) regularity of the movements and (3) attractiveness of specific locations. Based on the above, in this section we present results which represent typical examples for the qualitative behavior of the model.

The results of the model suggest that the distribution of traveled distances (of all agents) obey a heavy-tailed distribution (see

X and Y axes represent space while the Z axis represents time. The agent’s movements are represented by the lines. Note that there is on obvious regularity in the agent’s movement.

In this section we present the results of the model concerning the regularity or irregularity of the agents’ movements. In other words, we examine how often each agent returns to specific locations. Empirical data found in [

Note that despite the qualitative similarity of the different agents’ behavior, there are quantitative differences among them.

Here, we focus on the attractiveness of specific locations to all agents in the model. Urban areas are not homogenous in terms of popularity. For all kind of land uses, some areas are more attractive than others. In our model, the attractiveness of a cell is not predetermined as the IAC of each cell is different for each agent as it is depended on the agent’s characteristics, location, the time of day, and a random parameter. Nevertheless, the results of the model show that some locations are far more attractive than others.

We wanted to examine the distribution of visits per cell for the above 3 groups. However, as group A consist of only 18 cells, we present the rank size distribution instead. Both distributions can actually be replaced with each other (see [

The distributions of visits per cell for groups B and C can be seen in

In this work we presented a spatio-temporal agent-based model for human mobility patterns. This is a bottom-up, stochastic model that is based on the behavior of 10,000 agents, where their movement imitates real-life behavior, and depends on several attributes, among them are the attraction to a specific location and the distance from it (i.e. spatial gravitation). The results of our model correspond to empirical data on human mobility patterns in the intra-urban scale. This is achieved by combining some basic characteristics of human agents such as their employment status, marital status, personal preferences, etc., and in particular, the consideration of regular and irregular trajectories, along with the gravitation model. Note, that the regularity of the agent’s movement is not a pre-determined (top-down) one, but results from the probabilities that affect the agent’s decision to move, and where to move to. Our results fit the movement of the agents themselves in terms of individuals and of the entire population, as well as to spatial dynamics of the urban environment, i.e. the emergence of popular locations in the city due to bottom up human behaviors that are not governed by any top-down forces. This suggests that by combining the gravitation model with additional considerations, it can be applied to the city’s scale as well as to larger scales (as shown by [

The presented model is innovative and significant as it is based on the assumption that HMP are space-dependent and follow high regularity. Although these assumptions are known in the field of urban geography since the 1960s, they have not been implemented in urban simulation models of this type. To the best of our knowledge this is the first time simulating human mobility patterns at the intra-urban scale was carried out successfully. Thus, it holds a potential to be used as the basis of many urban simulations which rely on human mobility. This model allows isolating specific parameters of the complex reality, thus revealing the effects of their mutual effect and interdependencies. By modeling situations that are being observed in real cities, we can expand our understandings on HMP, and therefore improve urban planning, transportation planning, epidemiology models, mobile wireless network planning and more.

Appendix A in S1 File. The algorithm that determines whether the agent is going to move or stay put. Appendix B in S1 File. The algorithm that sets the agent’s destination (once it has been determined that the agent is indeed moving). Appendix C in S1 File. The probabilities that represent the agents’ likelihood to move toward a specific land use, at each of the 6 time periods of a weekday. Appendix D in S1 File. A description of land use combinations for each group, in different runs of the model

(ZIP)

The authors thank Dr. Yair Shokef for his insightful comments on this work.