Homesick Lévy walk: A mobility model having Ichi-go Ichi-e and scale-free properties of human encounters (1408.0427v1)

Abstract: In recent years, mobility models have been reconsidered based on findings by analyzing some big datasets collected by GPS sensors, cellphone call records, and Geotagging. To understand the fundamental statistical properties of the frequency of serendipitous human encounters, we conducted experiments to collect long-term data on human contact using short-range wireless communication devices which many people frequently carry in daily life. By analyzing the data we showed that the majority of human encounters occur once-in-an-experimental-period: they are Ichi-go Ichi-e. We also found that the remaining more frequent encounters obey a power-law distribution: they are scale-free. To theoretically find the origin of these properties, we introduced as a minimal human mobility model, Homesick L\'evy walk, where the walker stochastically selects moving long distances as well as L\'evy walk or returning back home. Using numerical simulations and a simple mean-field theory, we offer a theoretical explanation for the properties to validate the mobility model. The proposed model is helpful for evaluating long-term performance of routing protocols in delay tolerant networks and mobile opportunistic networks better since some utility-based protocols select nodes with frequent encounters for message transfer.

• The paper introduces the Homesick Lévy walk (HLW) model to explain statistical properties of human encounters, addressing limitations of traditional mobility models.
• The HLW model successfully reproduces two key properties of human encounters: the Ichi-go Ichi-e principle (most encounters are singular) and a scale-free distribution of frequent encounters.
• By combining long-distance Levy walk steps with a tendency to return to a 'home' point, the HLW model provides a realistic representation of mobility, relevant for optimizing routing protocols in mobile networks like DTNs.

Analysis of "Homesick Levy Walk: A Mobility Model Having Ichi-go Ichi-e and Scale-Free Properties of Human Encounters"

The paper presents a novel stochastic model for human mobility, termed the "Homesick Levy Walk" (HLW), which attempts to capture the fundamental statistical properties of human encounters. By exploring Ichi-go Ichi-e and scale-free principles, it strives to provide deeper insights into human mobility patterns, with potential applications in evaluating routing protocols in Delay Tolerant Networks (DTN) and Mobile Opportunistic Networks (MON).

Summary of Findings

The researchers identified two primary statistical properties of human encounters:

1. Ichi-go Ichi-e Principle: Derived from the Japanese phrase, this principle highlights that the majority (80-90%) of human encounters are singular events within an experimental period.
2. Scale-Free Principle: The remaining occurrences of interactions fit a power-law distribution, signifying a scale-free property where the variance diverges. This denotes that certain encounters may happen more frequently, unlike others, which reflect the unequal nature of social interactions.

Homesick Levy Walk Model

HLW seeks to explain these properties through a blend of two mechanisms:

• Long-Distance Travel: Aligning with the Levy Walk characteristic, it overcomes the limitations of traditional Random Walk models by integrating power-law distributed walk lengths.
• Homesickness: Unlike typical Levy Walkers, HLW incorporates a tendency for walkers to return to a "home" point with a specified probability, reflecting real-world behaviors of social hubs.

Experimental Methodology and Numerical Simulations

The paper employed Bluetooth and Wi-Fi technologies to gather data on human contacts, subsequently revealing the prevalent statistical trends. Using simulations, it validated the HLW model's capacity to replicate these trends and support the theoretical underpinnings.

Theoretical Implications

• Mean-Field Analysis: Through a mean-field theoretical framework, the paper explains how these properties emerge via the synergistic effects of the HLW model's defining factors.
• Balance of Mechanisms: The convergence of long-distance travels and returning behavior reflects a realistic portrayal of human mobility, suggesting that individual's networks are largely influenced by competing desires to explore and return to known locations.

Practical Implications and Future Work

• Routing Protocols in DTNs: By aligning mobility models closer to real human behaviors, the research has implications for improving performance evaluations of contact-based routing protocols, such as PRoPHET and MAXPROP.
• Broader Contexts: Beyond human encounters, the principles illustrated may extend to animal behavior studies, emphasizing mobility patterns informed by nests or homing instincts.
• Population Density Effects: Future investigations could explore the impact of population density variations across urban and rural contexts on mobility and contact frequencies.

Conclusion

This paper advances the understanding of human mobility by emphasizing the statistical properties governing encounter frequencies and proposing an HLW model to capture these dynamics. By fusing empirical data with simulation-driven insights, the work carries potential ramifications for DTNs and offers a springboard for further interdisciplinary exploration into mobility patterns.