Circadian pattern and burstiness in mobile phone communication

📝 Abstract

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.

💡 Analysis

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.

📄 Content

Circadian pattern and burstiness in mobile phone communication Hang-Hyun Jo1, M´arton Karsai1, J´anos Kert´esz1,2 and Kimmo Kaski1 1 BECS, Aalto University School of Science, P.O. Box 12200, FI-00076 2 Institute of Physics and BME-HAS Cond. Mat. Group, BME, Budapest, Budafoki ´ut 8., H-1111 E-mail: joh1@aalto.fi Abstract. 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. PACS numbers: 89.75.-k, 05.45.Tp Submitted to: New J. Phys. arXiv:1101.0377v2 [physics.soc-ph] 17 Oct 2011 Circadian pattern and burstiness 2

1. Introduction Recently modern information-communication-technology (ICT) has opened us access to large amounts of stored digital data on human communication, which in turn has enabled us to have unprecedented insights into the patterns of human behavior and social interaction. For example we can now study the structure and dynamics of large- scale human communication networks [1, 2, 3, 4] and the laws of mobility [5, 6, 7], as well as the motifs of individual behavior [8, 9, 10, 11, 12, 13, 14]. One of the robust findings of these studies is that human activity over a variety of communication channels is inhomogeneous, such that high activity bursts of rapidly occurring events are separated by long periods of inactivity [15, 16, 17, 18, 19, 20]. This feature is usually characterized by the distribution of inter-event times τ, defined as time intervals between, e.g., consecutive e-mails sent by a single user. This distribution has been found to have a heavy tail and show a power-law decay as P(τ) ∼τ −1 [8]. In human behavior obvious causes of inhomogeneity are the circadian and other longer cycles of our lives as results of natural and societal factors. Malmgren et al. [9, 10] suggested that an approximate power-law scaling found in the inter-event time distribution of human correspondence activity is a consequence of circadian and weekly cycles affecting us all, such that the large inter-event times are attributed to nighttime and weekend inactivity. As an explanation they proposed a cascading inhomogeneous Poisson process, which is a combination of two Poisson processes with different time scales. One of them is characterized by the time-dependent event rate representing the circadian and weekly activity patterns, while the other corresponds to the cascading bursty behavior with a shorter time scale. Their model was able to reproduce an apparent power-law behavior in the inter-event time distribution of email and postal mail correspondence. In addition they calculated the Fano and Allan factors to indicate the existence of some correlations for the email data as well as for their model of inhomogeneous Poisson process, with quite good comparison [12]. However, the question remains whether in addition to the circadian and weekly cycle driven inhomogeneities there are also other correlations due to human task execution that contribute to the inhomogeneities observed in communication patterns, as suggested, e.g., by the queuing models [8, 21]. There is evidence for this by Goh and Barab´asi [22], who introduced a measure that indicates the communication patterns to have correlations. Recently, Wu et al. have studied the modified version of the queuing process proposed in [8] by introducing a Poisson process as the initiator of localized bursty activity [23]. This was aimed at explaining the observation that the inter-event time distributions in Short Message (SM) correspondence follow a bimodal combination of power-law and Poisson distributions. The power-law (Poisson) behavior was found dominant for τ < τ0 (τ > τ0). Since the event rates extracted from the empirical data have the time scales larger than τ0 (also measured empirically), a bimodal distribution was successfully obtained. However, in their work the effects of circadian and weekly activity patterns were not considered, thus needing to be investigated in detail. Circadian pattern and burstiness 3 As the circadian and weekly cycles affect human communication patterns in quite obvious ways, taking place mostly during the daytime and differently during the weekends, our aim in this paper is to remove or de-se

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