Surprising Patterns for the Call Duration Distribution of Mobile Phone Users
How long are the phone calls of mobile users? What are the chances of a call to end, given its current duration? Here we answer these questions by studying the call duration distributions (CDDs) of individual users in large mobile networks. We analyzed a large, real network of 3.1 million users and more than one billion phone call records from a private mobile phone company of a large city, spanning 0.1 TB. Our first contribution is the TLAC distribution to fit the CDD of each user; TLAC is the truncated version of so-called log-logistic distribution, a skewed, power-law-like distribution. We show that the TLAC is an excellent fit for the overwhelming majority of our users (more than 96% of them), much better than exponential or lognormal. Our second contribution is the MetaDist to model the collective behavior of the users given their CDDs. We show that the MetaDist distribution accurately and succinctly describes the calls duration behavior of users in large mobile networks. All of our methods are fast, and scale linearly with the number of customers.
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- 1.Bennett, S.: Log-logistic regression models for survival data. Journal of the Royal Statistical Society. Series C (Applied Statistics) 32(2), 165–171 (1983)Google Scholar
- 7.Guo, J., Liu, F., Zhu, Z.: Estimate the call duration distribution parameters in gsm system based on k-l divergence method. In: International Conference on Wireless Communications, Networking and Mobile Computing, WiCom 2007, pp. 2988–2991 (September 2007)Google Scholar
- 9.Hill, S., Nagle, A.: Social network signatures: A framework for re-identification in networked data and experimental results. In: CASON ’09: Proceedings of the 2009 International Conference on Computational Aspects of Social Networks, pp. 88–97. IEEE Computer Society, Washington (2009)CrossRefGoogle Scholar
- 10.Hill, S., Provost, F.J., Volinsky, C.: Learning and inference in massive social networks. In: Frasconi, P., Kersting, K., Tsuda, K. (eds.) MLG (2007)Google Scholar
- 11.Lawless, J.F.: Statistical Models and Methods for Lifetime Data (Wiley Series in Probability & Mathematical Statistics). John Wiley & Sons, Chichester (1982)Google Scholar
- 15.Nanavati, A.A., Gurumurthy, S., Das, G., Chakraborty, D., Dasgupta, K., Mukherjea, S., Joshi, A.: On the structural properties of massive telecom call graphs: findings and implications. In: CIKM ’06: Proceedings of the 15th ACM International Conference on Information and Knowledge Management, pp. 435–444. ACM, New York (2006)CrossRefGoogle Scholar
- 18.Seshadri, M., Machiraju, S., Sridharan, A., Bolot, J., Faloutsos, C., Leskove, J.: Mobile call graphs: beyond power-law and lognormal distributions. In: KDD ’08: Proceeding of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 596–604. ACM, New York (2008)CrossRefGoogle Scholar
- 19.Tejinder, S., Randhawa, S.H.: Network Management in Wired and Wireless Networks. Springer, New York (2003)Google Scholar
- 20.Willkomm, D., Machiraju, S., Bolot, J., Wolisz, A.: Primary users in cellular networks: A large-scale measurement study. In: 3rd IEEE Symposium on New Frontiers in Dynamic Spectrum Access Networks, DySPAN 2008, pp. 1–11 (2008)Google Scholar