In this study, call arrival process is characterized considering both flow directions of voice traffic in the cellular networks; the uplink and the downlink In this respect, correlation in time domain and suitability to the Poisson model assumed in classical teletraffic theory is investigated for voice calls in both directions. In analyses, a set of experimental data obtained from 2G/3G networks is used. An Android operating system-based data collection system is designed and implemented for collecting voice call statistics without affecting users' daily telephone traffic. With this data collection system, network traffic is logged per user (separately fir each individual) and calls of a single user's cellphone are separated into sub-groups as incoming (downlink) and outgoing (uplink). Thus, call arrival process can now be characterized separately for each group both as individually and collectively. Using the modified Allan variance (MAVAR), wavelet. and autocorrelation function of Hurst parameter estimation methods, it is determined that calls in mentioned groups have statistical properties of white noise and so a call in a second is independent from a call in any other second. In addition, suitability of each call group to Poisson distribution is also shown.