A Poissonian explanation for heavy-tails in e-mail communication (0901.0585v1)

Abstract: Patterns of deliberate human activity and behavior are of utmost importance in areas as diverse as disease spread, resource allocation, and emergency response. Because of its widespread availability and use, e-mail correspondence provides an attractive proxy for studying human activity. Recently, it was reported that the probability density for the inter-event time $\tau$ between consecutively sent e-mails decays asymptotically as $\tau^{-\alpha}$, with $\alpha \approx 1$. The slower than exponential decay of the inter-event time distribution suggests that deliberate human activity is inherently non-Poissonian. Here, we demonstrate that the approximate power-law scaling of the inter-event time distribution is a consequence of circadian and weekly cycles of human activity. We propose a cascading non-homogeneous Poisson process which explicitly integrates these periodic patterns in activity with an individual's tendency to continue participating in an activity. Using standard statistical techniques, we show that our model is consistent with the empirical data. Our findings may also provide insight into the origins of heavy-tailed distributions in other complex systems.

• The paper introduces a model that attributes heavy-tailed inter-event times in email communication to inherent daily and weekly cycles.
• The methodology employs a cascading non-homogeneous Poisson process with Monte Carlo testing to closely match extensive empirical data.
• The findings imply that integrating periodic behaviors simplifies modeling of human activities and improves predictive accuracy in communication patterns.

A Poissonian Explanation for Heavy Tails in Email Communication

The paper of human activity patterns through electronic records has provided deep insights into behavioral dynamics. The paper "A Poissonian explanation for heavy tails in e-mail communication" addresses the observed power-law distribution in inter-event times of email communication, suggesting it emerges from the intrinsic periodicity of human behavior—circadian and weekly cycles—rather than non-Poissonian deliberate actions. This paper revisits the assumptions on the origins of heavy-tailed distributions in human activities by proposing a model based on a non-homogeneous Poisson process.

Core Contributions and Methodology

The central hypothesis of this paper posits that the power-law scaling observed in email communication's inter-event time distribution is significantly influenced by external periodic factors—daily and weekly cycles—rather than purely individual decision-making processes. The researchers propose a cascading non-homogeneous Poisson process model to encapsulate these periodic patterns, integrating the tendency of individuals to continue activities once initiated.

1. Data and Analysis: The analysis relies on an extensive dataset comprising email records from a European university. The dataset includes temporal stamps, allowing precise modeling of inter-event times. The model compares empirical data against standard statistical techniques to validate its consistency, using the non-homogeneous Poisson process, which modulates activity rates periodically.
2. Model Description: Unlike a homogeneous Poisson process, where events occur at a constant rate, the non-homogeneous Poisson process presented accounts for a variable rate dependent on the time of day and week. This aligns with observable human routines, which influence email activity patterns, leading to the noted power-law asymptotic behavior.
3. Statistical Approach: The application of Monte Carlo hypothesis testing and simulated annealing procedures aids in parameter estimation and model validation. This methodological rigor ensures the model's predictions align closely with real-world data patterns, revealing systematic deviations from truncated power-law models in the context of periodic patterns.

Findings and Implications

The research findings suggest that the periodicities of human behavior are sufficient to explain the heavy-tailed distributions seen in email communication, challenging interpretations that emphasize complex cognitive models of decision-making. This insight simplifies behavioral modeling by attributing statistical patterns to regular, external cycles.

1. Model Effectiveness: The proposed model showcases substantial agreement with empirical data, with only one out of 394 users showing significant deviation at the 5% significance level, compared to 344 users for the truncated power-law model. The convergence of empirical distributions towards the model predictions reinforces the hypothesis that circadian and weekly cycles significantly dictate email traffic patterns.
2. Broader Applications: Beyond email, this model's principles could apply to several human activities displaying similar heavy-tailed behavior, such as telephone calls and other regular communications, suggesting a broader applicability across different domains.
3. Theoretical Implications: The approach presents a simplified understanding of complex systems, advocating for models that incorporate essential periodic features over those requiring intensive rationalization of each action. This paradigm shift suggests reconsideration of underlying assumptions in models attributing activity patterns to intricate decision processes.
4. Future Research Directions: This paper opens avenues for expanded research into hierarchical activity models and further refinement of point process models to include multiple activities or to account for transitional dynamics in individual behavior patterns. Enhanced empirical evidence or real-time data collection strategies could further validate and enhance the robustness of such models.

In conclusion, this paper contributes a nuanced understanding of email communication patterns by leveraging external cyclic behaviors, thus providing a compelling alternative to traditional mechanistic explanations. Its insights pave the way for future explorations into the fundamental causes of behavioral regularities across varied human activities, advocating periodic-driven models in understanding complex systems.