On power-law decay exponents and Barabasi models for subscriber usage behaviour in mobile networks

We consider whether Barabási multiclass priority service queueing models are appropriate for modelling voice and short message service interusage and voice usage residual time distributions for a set of high usage subscribers of an Asian telecommunication service provider. We find that a model with a non priority service discipline rather than any priority discipline provides an alternative explanation for the fitted power-law for the interusage time distributions. We also find that a Barabási model provides an alternative explanation to the fitted power-law for the voice usage residual time distribution. However, the exponent of the fitted power-law has not been observed before. Therefore, we propose and analyse a new Barabási list-of-tasks priority model with time varying and discrete task priorities. For a special case we show that the waiting time distribution has a power-law with a previously unknown power-law decay exponent, which is different from the observed exponent for the voice usage residual time distribution.