Burstiness

In statistics, burstiness is the intermittent increases and decreases in activity or frequency of an event.^[1][2] One measure of burstiness is the Fano factor—a ratio between the variance and mean of counts.

Burstiness is observable in natural phenomena, such as natural disasters, or other phenomena, such as network/data/email network traffic^[3][4] or vehicular traffic.^[5] Burstiness is, in part, due to changes in the probability distribution of inter-event times.^[6] Distributions of bursty processes or events are characterised by heavy, or fat, tails.^[1]

Burstiness of inter-contact time between nodes in a time-varying network can decidedly slow spreading processes over the network. This is of great interest for studying the spread of information and disease. ^[7]

Burstiness score

One relatively simple measure of burstiness is burstiness score. The burstiness score of a subset ${\displaystyle t}$ of time period ${\displaystyle T}$ relative to an event ${\displaystyle e}$ is a measure of how often ${\displaystyle e}$ appears in ${\displaystyle t}$ compared to its occurrences in ${\displaystyle T}$. It is defined by

${\displaystyle \mathrm {Burst} (e,t)=\left({\frac {E_{t}}{E}}-{\frac {1}{T}}\right)}$

Where ${\displaystyle E_{t}}$ is the total number of occurrences of event ${\displaystyle e}$ in subset ${\displaystyle t}$ and ${\displaystyle E}$ is the total number of occurrences of ${\displaystyle e}$ in ${\displaystyle T}$.

Burstiness score can be used to determine if ${\displaystyle t}$ is a "bursty period" relative to ${\displaystyle e}$. A positive score says that ${\displaystyle e}$ occurs more often during subset ${\displaystyle t}$ than over total time ${\displaystyle T}$, making ${\displaystyle t}$ a bursty period. A negative score implies otherwise. ^[8]

See also

• Burst transmission
• Poisson clumping
• Time-varying network

References

1. Lambiotte, R. (2013.) "Burstiness and Spreading on Temporal Networks", University of Namur.
2. Neuts, M. F. (1993.) "The Burstiness of Point Processes", Commun. Statist.—Stochastic Models, 9(3):445–66.
3. D'Auria, B. and Resnick, S. I. (2006.) "Data network models of burstiness", Adv. in Appl. Probab., 38(2):373–404.
4. Ying, Y.; Mazumdar, R.; Rosenberg, C.; Guillemin, F. (2005.) "The Burstiness Behavior of Regulated Flows in Networks", Proceedings of the 4th IFIP-TC6 International Conference on Networking Technologies, Services, and Protocols, Performance ofo Computer and Communication Networks, Mobile and Wireless Communication Systems, 3462:918–29.
5. Jagerman, D. L. and Melamed, B. (1994.) "Burstiness Descriptors of Traffic Streams: Indices of Dispersion and Peakedness", Proceedings of the 1994 Conference on Information Sciences and Systems, 1:24–8.
6. Goh, K.-I. and Barabasi, A.-L. (2006.) "Burstiness and Memory in Complex Systems", Physics Data.
7. P. Holme, J. Saramäki. Temporal Networks. Phys. Rep. 519, 118–120; 10.1016/j.physrep.2012.03.001 (2012)
8. A. Hoonlor et al. (2013). "An Evolution of Computer Science Research", Communications of the ACM, 56(10):79