Surprising patterns for the call duration distribution of mobile phone users

Authors:
Pedro O. S. Vaz De Melo;Leman Akoglu;Christos Faloutsos;Antonio A. F. Loureiro
Affiliations:
Universidade Federal de Minas Gerais and iLab, Heinz College;Carnegie Mellon University and School of Computer Science and iLab, Heinz College;Carnegie Mellon University and School of Computer Science and iLab, Heinz College;Universidade Federal de Minas Gerais
Venue:
ECML PKDD'10 Proceedings of the 2010 European conference on Machine learning and knowledge discovery in databases: Part III
Year:
2010

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Abstract

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 0.1TB. 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.