Circadian pattern and burstiness in mobile phone communication

The temporal communication patterns of human individuals are known to be inhomogeneous or bursty, which is reflected as the heavy tail behavior in the inter-event time distribution. As the cause of such bursty behavior two main mechanisms have been suggested: a) Inhomogeneities due to the circadian and weekly activity patterns and b) inhomogeneities rooted in human task execution behavior. Here we investigate the roles of these mechanisms by developing and then applying systematic de-seasoning methods to remove the circadian and weekly patterns from the time-series of mobile phone communication events of individuals. We find that the heavy tails in the inter-event time distributions remain robustly with respect to this procedure, which clearly indicates that the human task execution based mechanism is a possible cause for the remaining burstiness in temporal mobile phone communication patterns.

💡 Research Summary

The paper investigates why human communication events, specifically mobile phone calls and short messages, display bursty temporal patterns characterized by heavy‑tailed inter‑event time distributions. Two competing explanations are considered: (a) external periodicities such as daily (circadian) and weekly cycles that modulate activity rates, and (b) intrinsic task‑execution dynamics, often modeled by priority‑queue or cascading processes, that generate rapid bursts of activity followed by long idle periods.

To disentangle these mechanisms the authors develop a systematic “de‑seasoning” procedure that removes the influence of known periodicities from the raw time stamps. For a set of users Λ they first compute the event count nΛ(t) at each second. Using a chosen period T (e.g., 1 day or 7 days) they construct a time‑varying event rate ρΛ,T(t) = (T / sΛ) Σk nΛ(t + kT), where sΛ is the total number of events for the set. The cumulative rate defines a transformed time axis t* = ∫0t ρΛ,T(t′) dt′. In this rescaled time the event rate is constant (ρ* = 1), meaning that high‑activity intervals are stretched and low‑activity intervals are compressed, effectively flattening the circadian and weekly rhythms.

With the rescaled timestamps the authors recompute inter‑event intervals τ* = ∫tj t_{j+1} ρΛ,T(t′) dt′ and compare the resulting distribution P(τ*) to the original P(τ). Burstiness is quantified by the parameter B = (σ – μ)/(σ + μ), where μ and σ are the mean and standard deviation of the inter‑event times. B ranges from –1 (perfect regularity) to 1 (maximal burstiness). The original burstiness B0 is contrasted with the de‑seasoned burstiness BT for various T values.

The empirical analysis uses a large mobile‑call dataset from a European operator covering 119 days (January 2–May 1, 2007). After filtering for bidirectional links the data contain 5.2 million users, 10.6 million edges, and 322 million call events. Short‑message data are also examined in the appendix.

Key findings:

1. Individual users – Even after removing daily (T = 1 day) and weekly (T = 7 days) cycles, most users retain a positive burstiness. Low‑activity users (≈200 calls) see B drop from ~0.20 to ~0.10 when a monthly (T = 28 days) cycle is removed, while high‑activity users (≈3 200 calls) maintain B ≈ 0.22 after the same de‑seasoning.

2. Groups with identical strength – Aggregating users with the same total call count s and applying the same de‑seasoning yields only modest reductions in B (e.g., from ~0.25 to ~0.18 for s = 200).

3. Broad strength groups – When users are binned into wide strength intervals (e.g., 0–100, 100–500, etc.), the de‑seasoned burstiness remains essentially unchanged across all bins, indicating that the effect is not an artifact of heterogeneity in activity levels.

4. Extreme de‑seasoning – If the period T is set equal to the full observation window (T ≈ T_f), all rescaled inter‑event times collapse to a constant T_f / s, yielding B = –1 (perfect regularity). However, realistic de‑seasoning periods (days to weeks) never achieve this collapse; the heavy‑tailed P(τ*) persists with an apparent power‑law exponent close to 1.

These results demonstrate that the heavy tails and burstiness observed in mobile communication are not solely a consequence of circadian or weekly rhythms. The robustness of the bursty signature after de‑seasoning strongly supports the hypothesis that intrinsic human task‑execution processes—such as priority‑driven queuing or cascading Poisson processes—play a dominant role. Consequently, models of human communication should incorporate mechanisms beyond simple inhomogeneous Poisson processes, explicitly accounting for the correlated decision‑making dynamics that generate bursts of activity.

In summary, the paper provides a rigorous methodological framework for removing known periodicities from event streams and shows, through extensive empirical evidence, that human‑driven task execution is a plausible and likely primary source of burstiness in mobile phone communication. This insight has implications for the design of more accurate predictive models of information spread, network load forecasting, and the broader understanding of temporal human behavior.