Human Mobility: Models and Applications

1.1. Motivation and History

• Human mobility spans individual and collective movement across space and time, with daily travel shaped by regularities and migration increasingly influenced by socio-economic conditions.Mobility affects transportation spending, greenhouse-gas emissions, communities, and the environment, motivating quantitative explanations of trip decisions, destinations, predictability, and randomness.Source: §1.1 · pp. 3–4
• Distance and socio-economic opportunity became foundational explanatory factors through Ravenstein’s migration laws, Stouffer’s intervening-opportunities model, and Zipf’s gravity law.These traditions differ in whether distance acts directly or through intervening opportunities, but both shaped subsequent research on population movement.Source: §1.1 · pp. 4, 5, 7
• Time geography formalized individual trajectories in space and time, while mobile phones, GPS, computing, and data-mining enabled fine-grained mobility analysis from individuals to populations.The review predominantly focuses on these later developments, which supplied data across scales from hours to decades and renewed scientific interest in human mobility.Source: §1.1 · pp. 7–8

1.2. Scope and Limitations

• The review unifies findings across interdisciplinary communities and provides newcomers with accessible tools, metrics, concepts, and models.Its motivation is the rapid growth of research and the parallel development of overlapping terminology and results across academic communities.Source: §1.2 · p. 9
• Spatial constraints such as topography, roads, and transportation infrastructure shape mobility, but spatial networks and the science of cities are treated only when needed for mobility concepts.The survey explicitly excludes detailed treatment of city forms, urban transport networks, and urban scaling laws.Source: §1.2 · p. 10

1.3. Organization

• The review progresses from data sources and mobility metrics to generative and phenomenological models, applications across scales, and future challenges.It covers individual, population, and intermodal models; applications from intra-urban movement to continental flows and epidemics; and an appendix of basic modeling tools.Source: §1.3 · p. 10

2.1. Census Data

• Census data provides aggregated workplace, residence, commuting, and migration flows for calibrating and validating models, including 3,141 US counties and 34,116,820 commuters used to evaluate the radiation model.US census work-flow files distinguish residence and workplace formats and include transport mode and travel time; supporting spatial and sociodemographic data enables validation of flow statistics.Source: §2.1 · pp. 10–11, §2.1.1 · p. 11

2.1.2. Tax Revenue Data

• Tax-return records estimate annual residential or workplace migration by matching successive filings and comparing addresses, while census-based ACS surveys provide complementary yearly migration estimates.US migration data from 1992–1993 to 2006–2007 was available from matched IRS returns.Source: §2.1.2 · p. 12

2.1.3. Local Travel Surveys

• Local travel surveys capture trip purpose, transport mode, timing, and other detailed metadata, but their smaller samples, limited geographic coverage, and self-reporting errors constrain statistical validation and dynamic mobility analysis.The Chicago survey covered 10,552 households, while a Los Angeles survey yielded 46,000 trips across 2,017 zones; surveys can be combined with GPS tracks.Source: §2.1.3 · p. 13

2. Data Sources

• Across sources, censuses offer scale but coarse patterns, surveys offer detail but limited scale, and neither alone provides a dynamic picture of mobility.These trade-offs motivate combining complementary sources, such as small-scale surveys with GPS tracks, to link accurate positions with annotated trip purposes.Source: §2.1.3 · p. 13

2.2. Dollar Bills

• Currency tracking infers human trajectories from bank-note reports at large scale, but each trajectory may combine multiple carriers and few observations, making individual mobility inference inaccurate.Brockmann et al. analyzed trajectories of 464,670 dollar bills; approximately 11% were reported multiple times.Source: §2.2 · pp. 13–14

2.3. Mobile Phone Records

• Mobile phone CDRs support individual mobility analysis from neighborhood to country scales, but irregular sampling and tower-level localization can confound results, while privacy restrictions make reproducibility problematic.Orange’s D4D Ivory Coast data included individual trajectories for 50,000 users over two weeks and 500,000 users over an entire year [50].Source: §2.3 · pp. 15–16

2.4. GPS Data

• GPS data offers the most accurate and temporally frequent trajectories, supporting individual and traffic studies, but typically covers fewer users and can suffer signal loss, battery, indoor, and coverage limitations.Vehicle GPS records provide high temporal precision for velocity, distance, path length, and activity distributions, while mobile-phone datasets can cover millions of users.Source: §2.4 · pp. 17–18

2.5. Online Data

• Online social and location-based networks provide geotagged locations, timestamps, social context, and mobility measures from routine trips to worldwide travel, but require cleanup and may not represent the general population.Only approximately 3% of users were found to enable geotagging, and UK Twitter data showed demographic differences from census data.Source: §2.5 · pp. 18–20

3.1.1. Jump Lengths

• Jump lengths are defined as Euclidean distances between recorded positions, and their population distribution P(∆r) commonly exhibits power-law or truncated-power-law behavior.Banknote trajectories yield β = 0.59 ± 0.02, while mobile-phone data yield β = 0.75 ± 0.15; GPS data show mode-specific log-normal distributions whose combination produces truncated power laws.Source: §3.1.1 · pp. 20–21

3.1.2. Mean Square Displacement (MSD)

• MSD distinguishes mobility regimes: GPS participants were super-diffusive up to approximately 30 minutes and sub-diffusive thereafter as jump lengths changed from power-law to Gaussian.For continuous-time random walks, MSD scales as ⟨∆r(t)2⟩∼t^ν with ν = 2α/β.Source: §3.1.2 · pp. 22, 24

3.1.3. Radius of Gyration

• The radius of gyration captures an individual’s typical distance from their trajectory’s center, but returners and explorers require k-radius measures to distinguish recurrent and dispersed mobility.Returners’ characteristic distance is approximated by k-radius for k ≥2, whereas explorers’ k-radius is much smaller than their overall rg.Source: §3.1.3 · pp. 24, 27, 28

3.1.4. Most Frequented Locations and Motifs

• Location visitation follows a Zipf law, with the probability of finding a user at rank L approximately P(L) ∼1/L.Ranks distinguish highly important locations such as home or work from less frequently visited places.Source: §3.1.4 · pp. 28–29
• ∼90% of recorded trips are captured by 17 daily mobility-network motifs, revealing recurring regularities useful for modeling and simulating human movement.Each motif is a daily trip pattern occurring in more than 0.5% of the datasets.Source: §3.1.4 · p. 29

3.1.5. Origin-Destination Matrices

• Origin-destination matrices count or estimate travelers between spatial zones, with resolution determined by the partitioning and data source, and support aggregate mobility modeling.They are central to population-level models such as gravity and intervening-opportunities models; digital footprints provide alternatives to costly, infrequently updated surveys and counts.Source: §3.1.5 · pp. 29–30
• Mobile-phone records can misrepresent arrival times and stay durations, so survey-derived probability distributions can correct timing before constructing user trips and aggregate OD matrices.Users may be excluded when they fail representativeness conditions, such as averaging at least one daily visit to their home location.Source: §3.1.5 · p. 31
• Lenormand et al. found strong cross-source OD correlation in Madrid and Barcelona, with ρ > 0.9 on 2km grids and ρ > 0.99 after aggregation to administrative municipalities.The comparison used census, mobile-phone CDR, and Twitter data for journey-to-work matrices.Source: §3.1.5 · p. 31
• OD correlation estimates vary with spatial aggregation and methodology, with simpler mobile-phone OD estimation producing lower correlations than approaches using stricter filtering and antenna fusion.The literature includes multiple algorithms and subsequent methodological refinements.Source: §3.1.5 · p. 31

3.2.1. Distance, travel time, and e

• Apparent speed increases with travel distance as a power law with exponent β ≈ 0.5, due to transportation hierarchies and decreasing waiting times.Trips may involve multiple connections and transportation modes, each contributing mode-specific waiting times.Source: §3.2.1 · p. 32
• Hierarchical roads produce effective acceleration because longer trips increasingly use faster roads, followed by a descending cascade near destinations [103].GPS data show speed saturation beyond two hours because transportation hierarchies contain a finite number of layers [103].Source: §3.2.1 · p. 32, Figure 15 · p. 33

3.2.2. Travel time budget

• Congestion causes commuting time to increase with population as a power law with δ ≈ 0.3, contradicting a universal one-hour travel-time budget.For 97 US urbanized areas, total congestion delay has fitted exponent 1.270 ± 0.067.Source: §3.2.2 · p. 33, Figure 16 · p. 34

3.2.3. Energy arguments

• Scaled daily travel-time distributions across walking, cycling, bus, and car travel suggest a canonical-like energy distribution based on constant average daily energy consumption.The model requires a low-energy cutoff because very small energy expenditures are rarely observed, resembling the Simonson effect.Source: §3.2.3 · pp. 34–35

3.3. Interpolation of scales: the importance of multimodality

• Multimodal connections account for roughly 23% of travel time in UK trips, making interchange costs a substantial component of mobility.Transition costs increase with the number or level of modes used.Source: §3.3 · pp. 35–36
• Travel-time structure varies by trip length and city: short trips outside London are dominated by waiting, while longer multimodal trips increasingly involve inter-layer waiting and walking [102].The dominant regimes shift between bus, metro, and rail layers as trip length increases.Source: §3.3 · p. 36, Figure 18 · p. 36
• Time-respecting paths account for arrival, departure, and connection times, whereas ideal quickest paths neglect inter-modal delays and require perfect synchronization between modes.Across UK cities, synchronization inefficiency δ versus path length l collapses onto a common curve, with ν ≈ 0.5.Source: §3.3 · pp. 36–37, Figure 19 · p. 37
• Reducing synchronization inefficiency by a factor of 2 requires a 10-fold increase in stop-event frequency Ω, effectively demanding unimodal travel [102].The inefficiency–Ω relationship has exponent μ ≈ 0.3 ± 0.1, while multimodal interchange remains a key challenge in large cities.Source: §3.3 · pp. 37–38

Individual mobility

• Individual mobility models address stochastic trip patterns while exploiting trajectory regularity and predictability to forecast whereabouts and generate realistic mobility.Minimal models draw on random walks and Brownian motion, but individual trajectories are not purely random.Source: §4 · p. 38

Population mobility

• Population mobility models reproduce Origin-Destination matrices by estimating average travelers between regions per unit time.Flows may represent daily commuting or yearly migration and commonly depend on distances, population, GDP per capita, and related regional variables.Source: §4 · p. 38

Review organization

• The review organizes models by scale, moving from individual mobility to population flows and finally to inter-modality between these levels.Distinct frameworks are needed because mobility spans spatial scales from hundreds of meters to thousands of kilometers and temporal scales from hours to years.Source: §4 · p. 38

4.1. Individual-Level (Random walks)

• A random walk sums independent displacement draws from f(∆x), while its position PDF P(x, t) determines spatial and temporal measures such as MSD and higher moments.RMSD scaling classifies motion: Brownian walks scale as t^1/2, slower walks are sub-diffusive, and faster walks are super-diffusive.Source: §4.1 · pp. 38–39

4.1.1. Brownian Motion

• Brownian motion is the Gaussian, ordinary-diffusion limit of symmetric random walks, with MSD = t and RMSD R(t) ∼t^1/2.The same limiting construction extends to d-dimensional Brownian motion.Source: §4.1.1 · pp. 39–40

4.1.2. L´evy Flight

• L´evy Flights use long-tailed jump distributions with divergent second moments, but their instantaneous large jumps make them only a rough approximation to human trajectories.Their limiting distributions are α-stable rather than Gaussian.Source: §4.1.2 · p. 40

4.1.3. CTRW

• CTRW models randomize both jump lengths and waiting times; finite moments recover Brownian motion, power-law jumps recover L´evy Flights, and power-law waits yield R(t) ∼tα/2.With heavy-tailed jumps and waits, R(t) ∼tα/β, whose diffusion type depends on α and β.Source: §4.1.3 · pp. 41–42
• Measured human mobility shows heavy-tailed jump lengths and waiting times, with α = 0.42–0.8 and β = 0.31–0.75, motivating ambivalent CTRW models.Ambivalent CTRWs are super-diffusive, sub-diffusive, or ordinarily diffusive according to β relative to 2α.Source: §4.1.3 · p. 42

4.1.4. Preferential Return

• Preferential return produces movement saturation, with measured ζ = 1.2 ± 0.1 indicating long-time dominance by an individual’s most visited location.This contrasts with standard CTRW drift away from the origin and better matches expected human behavior.Source: §4.1.4 · pp. 43–44

4.1.5. Recency

• Recency-based mobility models combine frequency and recency ranks, capturing the broader empirical distribution of recently visited locations that preferential return misses.For the two datasets, α = 0.1 and ν = 1.6, while γ = 0.6 was retained from.Source: §4.1.5 · p. 45

4.1.6. Social-based models

• Social-based models exploit mobility correlations: shared locations predict friendships, social-network history improves mobility forecasts by about one or two orders of magnitude, and co-location improves tie prediction.These correlations motivate transport microsimulations and agent-based models linking movement, social ties, and shared objectives.Source: §4.1.6 · pp. 46–47
• A network-coupled mobility model produces degree distributions ranging from approximately Poissonian at small c to increasingly non-Poissonian forms, while also reproducing correlations, giant clusters, and cliques.Agents are replaced after finite lifetimes by new agents without social links, allowing a stationary state whose network characteristics depend on c and agent lifetime.Source: §4.1.6 · p. 47
• The mobility-and-network model alternates friend visits with population-density-constrained Lévy-like jumps, then forms local or random social links, reproducing multiple online-network properties.Only the friend-visit probability and distance-independent link-creation probability remain free after calibrating other components from measurements.Source: §4.1.6 · pp. 47–48, Figure 23 · p. 48
• Adding social pressure to preferential return improves reproduction of CDR re-visitation profiles by directing exploration toward locations previously visited by similar contacts.With probability α, a contact is selected according to co-similarity in location-visiting profiles; otherwise, the baseline preferential-return behavior is retained.Source: §4.1.6 · pp. 48–49

4.2. Population-Level

• OD matrices represent travel demand as directed weighted flows between locations, making accurate estimation important for transportation, geography, urban planning, and related applications.Individual mobility can be aggregated into flows, but disaggregating flows is generally not possible; spatial interaction models therefore infer them from static local attributes.Source: §4.2 · p. 49

4.2.1. Gravity models

• Gravity models estimate flows from origin and destination attributes combined with a decreasing travel-cost function, but their simplification and parameter sensitivity can limit empirical accuracy.Constrained variants preserve measured outflows or both outflows and inflows, while entropy maximization provides a theoretical derivation and parameters are calibrated against observed flows.Source: §4.2.1 · pp. 51, 53, 54

4.2.2. Intervening opportunities models

• Intervening-opportunity models determine flows by the accessibility and cumulative number of opportunities before destinations, rather than distance alone, and generally perform comparably to gravity models.They can be formulated as gravity-model variants or hybrid distance-and-opportunity models, but have lost popularity because their advantages and practical implementation benefits are not overwhelming.Source: §4.2.2 · pp. 54–55

4.2.3. The radiation model

• The radiation model selects the closest opportunity exceeding a traveler’s fitness threshold, avoids calibration parameters, and its extended version improves performance by introducing a scale-dependent opportunity parameter.Its job-search interpretation yields a distance distribution independent of the fitness distribution in non-pathological cases and satisfactorily reproduces empirical commuting-distance features.Source: §4.2.3 · pp. 56–58

4.2.4. Comparison between models

• Model comparison requires validating predicted flows against empirical data on an equal footing, because accuracy depends on spatio-temporal scale, available information, missing data, and whether outflow or inflow constraints are imposed.The reviewed models range from unconstrained formulations to production-constrained models preserving outflows and doubly constrained models preserving both outflows and inflows.Source: §4.2.4 · p. 58
• Trip distributions P_ij are independent of trip production O_i, destination choices have no memory effects, and flows are separable into opportunity- and distance-related variables.Source: §4.2.4 · p. 58
• These assumptions enable statistical laws governing travel distributions P_ij and models with varying levels of constraints.Source: §4.2.4 · p. 58

PAR LON USA

• Fair model comparison requires adapting each model to the information available in the dataset.Source: PAR LON USA · p. 59
• The models were evaluated using CPC for predicted-versus-observed flows and CPL for overlap between simulated and observed network links.CPC equals one for perfect agreement and zero for no overlap, while CPL measures topological link agreement on the same scale.Source: PAR LON USA · pp. 59–60
• Gravity models moderately outperform intervening-opportunity and radiation variants on the reported commuting datasets, although performance may vary across datasets.The comparison covered England and Wales, France, Italy, Mexico, Spain, the USA, London, and Paris, with multiple constraint levels.Source: PAR LON USA · pp. 59–60, Figure 28 · p. 59

4.3. Intermodality

• Multilayer or multiplex networks represent transport modes as layers, locations as nodes, and intermodal transfers as cross-layer connections.This framework captures multimodal transport such as roads, subways, and airlines, with links encoding flows or travel frequency.Source: §4.3 · p. 60
• Traditional single-mode transport networks use L-space or P-space representations, with links defined by consecutive stops or shared lines.Link weights can additionally incorporate passenger counts and other route features.Source: §4.3 · pp. 60–61
• Multilayer representations combine transport modes or network spaces and alter accessibility, diffusion, navigation, congestion, and responses to disruptions.They can produce dynamic regimes absent from monolayers and abrupt reactions to small topological changes.Source: §4.3 · p. 61
• PT-space multilayers assign link weights to trip durations, enabling optimal-time routes across modes and analysis of efficient connections, modal preferences, and congestion.Representing layers as transport modes emphasizes topology and coverage, whereas representing layers as individual lines reveals transfer inefficiencies.Source: §4.3 · pp. 61–62

5.1.1. Pedestrian movement

• Pedestrian models reproduce free flow, congestion, shock waves, intermittent exits, stripes and clogging, while social-force refinements capture turbulent high-density regimes.The Hughes model yields free-flow and congestion regimes with moving fronts and avalanches; centrifugal-force modifications add laminar and turbulent behavior missing from earlier social-force models.Source: §5.1.1 · pp. 63–66
• Pedestrian cellular automata trade local detail for scalable simulation, reaching crowds of size 10^5 with runtime scaling linearly with population size.These models study clogging, bottlenecks and stripes while incorporating friction, heterogeneous agents, destination-time path selection and long-range awareness.Source: §5.1.1 · p. 66

5.1.2. Air Transportation

• Air-transport networks show heavy-tailed degree, traffic and betweenness distributions, modular traffic structure, and nonlinear route passengers related to origin and destination traffic with θ ≈1/2.Static network analyses identify highly connected and high-betweenness airports, while smaller-scale modular divisions are not seasonally stable in the US network.Source: §5.1.2 · pp. 67–68
• Air-transport delay models reproduce delayed flights, major departure-delay airports, network congestion and bad-weather effects, identifying passenger and crew connections as the strongest delay mechanism.The models combine aircraft-level agents, operational disruptions and network-specific queueing, and were validated against empirical performance data with acceptable accuracy and precision.Source: §5.1.2 · pp. 69, 71

5.1.3. Sea Networks

• Sea networks connect global ports through weighted shipping routes, concentrate traffic among a few heavy-tailed hubs, support multiplex analyses by ship type, and model flows with gravity models.Singapore, Antwerp, Bushan and Rotterdam rank highly in traffic and load; the connectivity–traffic relation has exponent 1.46 ± 0.1, while these networks also inform species-invasion studies.Source: §5.1.3 · p. 72

5.2.1. Intra urban mobility

• Urban mobility studies exploit dense digital-trace data to examine congestion, super-linear CO2 emissions, inequality, multimodal navigation and hidden temporal networks of familiar strangers.City data include mobile-phone records, social-network activity and smart-transport-card traces, though these sources have documented social and spatial biases.Source: §5.2.1 · pp. 72–73
• Intra-urban mobility studies link travel distances to residence, built environment, segregation, city morphology, and destination opportunities, while city-scale jump lengths are often better fitted by exponential than power-law distributions.Comparative studies found longer overall commuting distances among Los Angeles residents than New York residents, but substantial neighborhood-level heterogeneity and mobility segregation in Boston and Los Angeles.Source: §5.2.1 · pp. 74–75

5.2.2. Epidemic Spreading

• GLEaM predicted global H1N1 arrival and prevalence peaks after early calibration, with predictions later validated against surveillance reports and estimates of Mexico’s initial cases.The model combines long-range air transport calibrated from the world airport network with short-range commuting or gravity-based mobility.Source: §5.2.2 · p. 79
• Epidemic models use either detailed agent-based populations or analytically tractable metapopulations, balancing realism and data requirements in disease-propagation simulations.Agent-based models support fine-grained intervention analyses, whereas metapopulations divide populations into subpopulations with within-group mixing and mobility-network connections.Source: §5.2.2 · pp. 78–79
• Travel restrictions generally delay rather than prevent global disease propagation unless air networks are nearly or completely shut down, while newer models incorporate behavior and population heterogeneity.The section also identifies real-time ICT mobility data and hybrid agent-based–metapopulation frameworks as future directions.Source: §5.2.2 · p. 80

5.3.1. Web (Online) Mobility

• Online navigation exhibits physical-mobility-like regularities, including subdiffusion, heavy-tailed returns, lognormal jump lengths and waiting times, stretched-exponential visitation, and similar explorer–returner profiles.The analogy remains limited because virtual activity is newer and context-dependent, although online foraging behavior supports shared psychological mechanisms with offline mobility.Source: §5.3.1 · pp. 81–82

• The survey covers human-mobility data, metrics, individual and population models, and applications to real-world problems.It presents the field’s development and selected applications demonstrating its practical insights.Source: §6 · p. 83
• Human-mobility research raises fundamental questions about memory, learned behavior, and the explorer–returner division in mobility patterns.These questions connect mobility research to exploration–exploitation problems in social learning, economics, computer science, marketing, and advertising.Source: §6 · p. 83
• The intersection between human mobility and social networks remains a nascent research area requiring deeper investigation.Understanding movement alongside the structures and ties connecting people and organizations is identified as an important frontier.Source: §6 · p. 84
• Autonomous vehicles will raise questions about changing mobility habits, vehicle control, route planning, fuel and time use, congestion, and pollution.Answers may depend on understanding individual and collective human mobility and behavior.Source: §6 · p. 84
• Interdisciplinary collaboration is essential for applying mobility research to societal challenges including crime, urban planning, energy consumption, and social integration.Relevant expertise includes computer science, physics, social science, environmental studies, engineering, and government.Source: §6 · p. 84

A. Modeling Frameworks and Algorithms

• The section outlines practical building blocks for constructing mobility models and implementing simulations of human traveling behaviors.As models become more refined, researchers may need efficient graph libraries, GIS capabilities, and statistical routines; widely available language libraries let them focus on substantive contributions.Source: A. Modeling Frameworks and Algorithms · p. 114

Model composition

• Computational mobility models combine smaller processes whose validity determines the soundness of the resulting macrolevel dynamics, including waiting-time and jump-length distributions, social interactions, and environmental features.A continuous-time random walk (CTRW) is composed of waiting-time and jump-length distribution models.Source: §A.1 · p. 114
• Mobility models rely on Monte Carlo methods that generate repeated random samples to approximate human displacements, including models based on physical mechanisms and first principles.Source: §A.1 · p. 115

Simulation approaches

• Simulations include numerical, particle-based, and agent-based models, plus discrete-event and system-dynamics simulations used to compare generated data with real-world mobility traces.Numerical simulations can lose adherence to reality when substantial abstraction is required.Source: §A.1 · p. 115

Agent-based models

• Agent-based models represent entities through simple rules and micro-level interactions, making them suitable for adaptive processes, local interactions, second-order dynamics, emergent phenomena, memory, social networks, and spatial capabilities.Their core advantage is connecting individual behavior to complex macroscopic regularities.Source: §A.1 · p. 115

A.2. Algorithms

• The section presents pseudocode for mobility-model algorithms and random-number generation from specified probability distributions.The individual-mobility models use the agent-based framework introduced in Sec. A.1.Source: §A.2 · p. 116

Random Walk

• Random walks reproduce some long-term statistical movement properties through successive random displacements and direction changes, with unbiased lattice steps chosen uniformly.A simple 2D implementation repeatedly selects up, down, left, or right with equal probability for N steps.Source: §A.2.1 · pp. 116–117

Lévy Flight and CTRW

• Lévy flights replace fixed lattice steps with heavy-tailed jump lengths, producing mostly short movements and occasional long jumps, while CTRW additionally models variable waiting times between jumps.Lévy-walk implementations choose a uniformly random direction and power-law jump length in the Euclidean plane; CTRW need not use power laws, but power-law variants model human mobility.Source: §A.2.1 · pp. 116, 120

Exploration-Preferential Return

• Exploration-Preferential Return adds exploration and return mechanisms missing from Lévy-flight and CTRW models, using power laws with exponential cutoffs for jump lengths and waiting times [81].The model tracks visited locations and their frequencies, while continuous coordinates are mapped to discrete locations such as grid squares or Voronoi patches.Source: §A.2.1 · pp. 120, 123

Recency

• The recency model extends preferential return by selecting returns through either visitation frequency or recency, allowing recently visited but infrequently visited locations.Compared with frequency-based return, recency produces more evenly distributed visitation frequencies and spatial clusters farther from the starting location.Source: §A.2.1 · pp. 121, 124, Figure A.48 · p. 124

Social Models

• Social mobility models incorporate contacts, proximity, and social strength, governing returns or new locations through social links and mobility similarity [140, 141].One model chooses a social contact with probability pv and otherwise follows a Lévy-like flight; another uses cosine similarity between agents’ location-visiting profiles to select socially influenced destinations.Source: §A.2.1 · p. 125

• OD matrices contain counts T_ij of individuals traveling from zone i to zone j, formalizing population flows between locations.The matrix is typically square, with T_ii = 0, and its entries define the origin-destination network.Source: §A.2.2 · p. 125
• Unlike segment counts, OD matrices define time-dependent directed weighted networks but are difficult and costly to measure because flows depend on land use, industry, residences, and accessibility.Segment measurements count travelers using a transportation link, whereas OD matrices specify their origins and destinations.Source: §A.2.2 · p. 125
• At each time t, the simulation normalizes OD(t) so each P_ij gives the probability that an agent moves from i to j, then applies MOVE-AGENT(i,j) during each time step.The algorithm sums all T_ij values to obtain a total and divides each entry by that total before evaluating agent movements.Source: §A.2.2 · pp. 125–126
• This agent-simulation framework applies to gravity, intervening-opportunities, and radiation models, whose main difference is how they compute the OD entries T_ij.When movements are mapped spatially, agent flux between locations estimates traffic intensity along their connection.Source: §A.2.2 · p. 126