Statistical properties of user activity fluctuations in virtual worlds

Abstract

User activity fluctuations reflect the performance of online society. We investigate the statistical properties of 1-min user activity time series of simultaneously online users inhabited in 95 independent virtual worlds. The number of online users exhibits clear intraday and weekly patterns due to human's circadian rhythms and week cycles. Statistical analysis shows that the distribution of absolute activity fluctuations has a power-law tail for 44 virtual worlds with an average tail exponent close to 2.15. The partition function approach unveils that the absolute activity fluctuations possess multifractal features for all the 95 virtual worlds. For the sample of 44 virtual worlds with power-law tailed distributions of the absolute activity fluctuations, the width of singularity ∆α is negatively correlated with the maximum activity (p-value=0.070) and the time to the maximum activity (p-value=0.010). The negative correlations are not observed for neither the other 51 virtual worlds nor the whole sample of the 95 virtual worlds. In addition, numerical experiments indicate that both temporal structure and large fluctuations have influence on the multifractal spectrum. We also find that the temporal structure has stronger impact on the singularity width than large fluctuations. [Chaos, Solitons & Fractals 105, 271-278 (2017)]

Dynamics of calling activity to toll-free numbers in China

“…Further, the same intraday patterns of standard deviation on working and rest days shows that the variability of days is not related to work or rest, and that it is only related to circadian cycles. Weekly and circadian cycles have been reported by many studies on human behaviors such as web browsing behavior [35], activity in the virtual world [36], and calling activity [29,43]. The intraday patterns in call frequency observed in the present study were similar with those reported in these studies; however, the intraday patterns of average call duration were quite different.…”

“…Studies on dynamics of behaviors such as calling [7,[25][26][27][28][29] and sending short messages [30,31] have revealed that the inter-event time (interval between two activities) exhibits a nonpoisson distribution, which is consistent with the findings of studies on other human behaviors such as email communication [32][33][34] and online activities [35][36][37][38]. There are three popular mechanisms used to explain the non-poisson distribution of inter-event time; decisionbased queuing process [32], adaptive interests [39], and poisson processes modulated by circadian and weekly cycles [33,34].…”

“…Before and after these two time points, standard deviations are greatly different, indicating different variability. Several studies have reported similar intraday patterns for web browsing behavior [35], activity in the virtual world [36], and calling activity [29,43]. Intraday patterns for the average call duration are almost the opposite to these reported patterns.…”

“…Interestingly, n d on the Spring Festival (gray area in Fig 1(a)), the most important traditional festival in China, was significantly lower than that on other days. In Fig 1(c) [16,21,33,34,36,37,43].…”

“…Moreover, considering the findings of previous studies [29,33,34], we also examine the time-related characteristics of calling activity to reveal the dynamics more clearly. Commonly, daily patterns and intraday patterns are examined to discover time-related characteristics of human behavior, such as calling activity between individuals [43], web browsing activity [35], user activity in virtual worlds [36], Wikipedia editorial activity [37], activity on Twitter and Instagram [38], and spatio-temporal properties of cities in Spain [44]. Motivated by these studies, we apply the k-means method and statistical analysis to examine daily patterns and intraday patterns.…”