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In this paper, we investigate possible time correlation of answered call arrivals in sets of real GSM telephone traffic data. Instead of attempting to model the empirical distribution of the call interarrival time, as done in several previous works in literature, we emphasize results obtained by the modified Allan variance (MAVAR), a widely used time-domain quantity with excellent capability of discriminating power-law noise types. The call arrival rate exhibits a diurnal trend, with peak hours in the morning and late afternoon. Besides this diurnal rate change, the number of call arrivals in a second is found perfectly uncorrelated to the number of arrivals in other seconds and Poisson distributed, with good consistency by X/sup 2/- test evaluation. Uniform and accurate whiteness of call arrivals per second is verified in all hours, regardless the time of the day. In all series analyzed, the empirical statistics of both originated and terminated call arrivals proves excellent consistency with the ideal Poisson model with diurnal variable rate lambda(t). This study may be valuable to researchers concerned about realistic traffic modelling in planning and performance evaluation of cellular networks.